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A Caltech Library Repository Feedhttp://www.rssboard.org/rss-specificationpython-feedgenenTue, 16 Apr 2024 15:46:23 +0000A Statistical Theory of Polycrystalline Plasticity
https://resolver.caltech.edu/CaltechAUTHORS:20180105-154320925
Authors: {'items': [{'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'M.'}, 'orcid': '0000-0001-5877-4824'}, {'id': 'Popov-E-P', 'name': {'family': 'Popov', 'given': 'E. P.'}}]}
Year: 1982
DOI: 10.1098/rspa.1982.0025
The plasticity and viscoplasticity of polycrystalline materials are studied analytically in terms of lattice dislocations, with the principal effects attributed to non-extended obstacles. Non-equilibrium statistical mechanics is used to describe the evolution of the dislocation structures during loading and unloading processes. A plausible variation in the probability density function for mobile dislocations for such processes is suggested. The proposed material model is in good qualitative agreement with several observed phenomena that previously could not be quantified on the basis of the dislocation theory. Numerical examples illustrate the effect of the rate of loading, the variations in the recovery effect as it relates to the extent of load reversal, and a means for treating materials that exhibit a yield plateau. In the limit, the proposed model yields results for inviscid plasticity.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/2hm13-63686Plain concrete as a composite material
https://resolver.caltech.edu/CaltechAUTHORS:20180105-153942293
Authors: {'items': [{'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'Miguel'}, 'orcid': '0000-0001-5877-4824'}, {'id': 'Popov-E-P', 'name': {'family': 'Popov', 'given': 'Egor P.'}}]}
Year: 1982
DOI: 10.1016/0167-6636(82)90042-4
The purpose of this paper is to study the consequences of the composite nature of concrete. A plausible energy balance equation is postulated and the Green-Rivlin invariance principle is applied to it to derive the linear and angular momentum balance laws. General constitutive equations are discussed with the aid of thermodynamic potentials and Coleman's method. The distribution of the applied stresses between mortar and aggregate is also studied in detail, showing for instance that substantial tensile lateral stresses may appear in mortar under uniaxial compressive loading. These results are used to derive a criterion for the onset of inelasticity in concrete.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/60e2v-3q563A Physical Model for the Inelasticity of Concrete
https://resolver.caltech.edu/CaltechAUTHORS:20180105-154518480
Authors: {'items': [{'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'M.'}, 'orcid': '0000-0001-5877-4824'}, {'id': 'Popov-E-P', 'name': {'family': 'Popov', 'given': 'E. P.'}}]}
Year: 1982
DOI: 10.1098/rspa.1982.0123
A physical model for the inelasticity of concrete is proposed in this paper. The main effects are attributed to microcracking and softening elastoplastic coupling. The composite nature of concrete is seen to influence decisively the process of microcracking, resulting, for instance, in stable crack growth under uniaxial compression, but unstable crack growth under uniaxial tension. A model is proposed that relates the degradation of the elastic compliances of the material to the extent of microcracking, as described by a set of internal variables that represent the sizes of the microcracks oriented along some selected directions. A thermodynamic approach to the inelasticity of concrete is then presented that proves advantageous in characterizing the coupling between the plasticity of the material and its elastic degradation, i. e. elastoplastic coupling. It is shown that a softening elastoplastic coupling may result in lack of normality and in unstable behaviour, in violation of Drucker's postulates of classical plasticity. A suitable thermodynamic plastic stability criterion is proposed that generalizes Drucker's second postulate in the presence of elastoplastic coupling allowing for unstable plastic behaviour. A specific model of elastoplastic coupling is then proposed that allows for the explicit generalization of the classical yield criteria when elastoplastic coupling is present. It is shown, with the aid of this model, how a general anisotropic distribution of microcracks renders the plastic yield criterion anisotropic. It is also shown that the plastic strain rates depart from isochoricity in the presence of microcracking, even if the uncracked material exhibits isochoric plasticity. The proposed thermodynamic criterion for the extension of microcracks is seen to generalize the Griffith criterion in the presence of elastoplastic coupling. It is shown that tensile plastic strains in the direction normal to a microcrack tend to decrease the critical stress for the extension of the microcrack, and that compressive plastic strains tend to increase it. Finally, the proposed model is seen to lead to rate-independent stress─strain incremental relations with symmetric tangent stiffness compliances.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/5fbp9-8h274Operator split methods in the numerical solution of the finite deformation elastoplastic dynamic problem
https://resolver.caltech.edu/CaltechAUTHORS:20180105-152230031
Authors: {'items': [{'id': 'Pinsky-P-M', 'name': {'family': 'Pinsky', 'given': 'Peter M.'}}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'Miguel'}, 'orcid': '0000-0001-5877-4824'}, {'id': 'Taylor-R-L', 'name': {'family': 'Taylor', 'given': 'Robert L.'}}]}
Year: 1983
DOI: 10.1016/0045-7949(83)90126-8
The spatial formulation of the elastoplastic dynamic problem for finite deformations is considered. A thermodynamic argument leads to an additive decomposition of the spatial rate of deformation tensor and allows an operator split of the evolutionary equations of the problem into "elastic" and "plastic" parts. This operator split is taken as the basis for the definition of a global product algorithm. In the context of finite element discretization the product algorithm entails, for every time step, the solution of a nonlinear elastodynamic problem followed by the application of plastic algorithms that operate on the stresses and internal variables at the integration points and bring in the plastic constitutive equations. Suitable plastic algorithms are discussed for the cases of perfect and hardening plasticity and viscoplasticity. The proposed formalism does not depend on any notion of smoothness of the yield surface and is applicable to arbitrary convex elastic regions, with or without corners. The stability properties of the global product algorithm are shown to be identical to those of the algorithm used for the integration of the nonlinear elastodynamic problem. Numerical examples illustrate the accuracy of the method.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/k2ks3-0z190Unconditionally stable element-by-element algorithms for dynamic problems
https://resolver.caltech.edu/CaltechAUTHORS:20180105-153425697
Authors: {'items': [{'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'Miguel'}, 'orcid': '0000-0001-5877-4824'}, {'id': 'Pinsky-P-M', 'name': {'family': 'Pinsky', 'given': 'Peter M.'}}, {'id': 'Taylor-R-L', 'name': {'family': 'Taylor', 'given': 'Robert L.'}}]}
Year: 1983
A collection of results is presented regarding the consistency, stability and accuracy of operator split methods and product formula algorithms for general nonlinear equations of evolution. These results are then applied to the structural dynamics problem. The basic idea is to exploit an element-by-element additive decomposition of a particular form of the discrete dynamic equations resulting from a finite element discretization. It is shown that such a particular form of the discrete dynamic equations is obtained when velocity and stress are taken as unknowns. By applying the general product formula technique to the element-by-element decomposition, unconditionally stable algorithms are obtained that involve only element coefficient matrices. The storage requirements and operation counts are comparable to those of explicit methods. The method places no restriction on the topology of the finite element mesh.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/8m8tf-q4482Operator split methods for the numerical solution of the elastoplastic dynamic problem
https://resolver.caltech.edu/CaltechAUTHORS:20180105-153718420
Authors: {'items': [{'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'Miguel'}, 'orcid': '0000-0001-5877-4824'}, {'id': 'Pinsky-P-M', 'name': {'family': 'Pinsky', 'given': 'Peter M.'}}, {'id': 'Taylor-R-L', 'name': {'family': 'Taylor', 'given': 'Robert L.'}}]}
Year: 1983
DOI: 10.1016/0045-7825(83)90018-X
The elastoplastic dynamic problem is first formulated in a form that facilitates the application of product formula techniques. The additive decomposition of the dynamic equations into elastic and plastic parts is taken as a basis for the definition of product algorithms that exploit such decomposition. In the context of a finite element discretization, these product algorithms entail, for every time step, the solution of an elastic problem followed by the application of plastic algorithms that operate on the stresses and internal variables at the integration points and bring in the plastic constitutive relations. Suitable plastic algorithms are discussed for the cases of perfect and hardening plasticity and viscoplasticity. The proposed formalism does not depend on any notion of smoothness of the yield surface and is applicable to arbitrary convex elastic regions, with or without corners. The stability properties of the product algorithm are identical to those of the elastic algorithm used whereas the computational expense is practically equal to that of an elastic problem.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/gdbzs-j9z10Distortional Hardening Rules for Metal Plasticity
https://resolver.caltech.edu/CaltechAUTHORS:20180105-153010711
Authors: {'items': [{'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'Miguel'}, 'orcid': '0000-0001-5877-4824'}, {'id': 'Popov-E-P', 'name': {'family': 'Popov', 'given': 'Egor P.'}}]}
Year: 1983
DOI: 10.1061/(ASCE)0733-9399(1983)109:4(1042)
A brief overview of the available experimental data regarding distortional hardening of metals is first presented. This material is subsequently used to motivate the need for accurate distortional hardening rules in computation. A general expression for the yield surface of a plastic material is proposed that includes the isotropic‐kinematic von Mises model as a particular case and that can be systematically used to incorporate distortional hardening features into the material modeling in a simple manner. This expression is complemented with suitable rate equations for the parameters involved. The proposed model is particularly convenient for computer implementation.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/gc4hd-cqn08Numerical integration of rate constitutive equations in finite deformation analysis
https://resolver.caltech.edu/CaltechAUTHORS:20180105-152657675
Authors: {'items': [{'id': 'Pinsky-P-M', 'name': {'family': 'Pinsky', 'given': 'Peter M.'}}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'Miguel'}, 'orcid': '0000-0001-5877-4824'}, {'id': 'Pister-K-S', 'name': {'family': 'Pister', 'given': 'Karl S.'}}]}
Year: 1983
DOI: 10.1016/0045-7825(83)90087-7
In analysis of finite deformation problems the use of constitutive equations in rate form is often required. In a spatial setting, these equations may express a relationship between some objective rate of spatial stress tensor and the rate of deformation. Constitutive equations of this type characterize a variety of material models including hyperelasticity, hypoelasticity and elastoplasticity. Employing geometrical concepts, a family of unconditionally stable and incrementally objective algorithms is proposed for the integration of such rate constitutive equations. These algorithms, which are appropriate for finite deformation analysis, are applicable to any choice of stress rate and, in most cases, employ quantities that arise naturally in the context of finite element analysis. Examples illustrate the objectivity and accuracy of the algorithms,https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/vz7aa-nfx86A variational formulation for convection-diffusion problems
https://resolver.caltech.edu/CaltechAUTHORS:20180105-152010629
Authors: {'items': [{'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'M.'}, 'orcid': '0000-0001-5877-4824'}]}
Year: 1985
DOI: 10.1016/0020-7225(85)90004-7
A variational principle is proposed that under certain restrictions is shown to be equivalent to the advection-diffusion boundary value problem. Based on this variational principle, an upwind finite element method is derived that precludes spurious oscillations while possessing optimal convergence properties even in the multidimensional case. The formulation also points to a canonical choice of weighting functions for the Petrov-Galerkin method proposed by the Dundee and Swansea groups.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/8bd9h-gv064A constitutive theory for the inelastic behavior of concrete
https://resolver.caltech.edu/CaltechAUTHORS:20180105-151816056
Authors: {'items': [{'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'Michael'}, 'orcid': '0000-0001-5877-4824'}]}
Year: 1985
DOI: 10.1016/0167-6636(85)90007-9
A general theory for the inelasticity of concrete is proposed, the main constituents being a new, rate independent model of distributed damage for mortar and the application of mixture theories to account for the composite nature of concrete. The proposed theory of damage is capable of accommodating fully anisotropic elastic degradation, both in tension and in compression, in a manner which is ideally suited for computation. Mixture theories, on the other hand, are found to provide a simple yet effective tool for characterizing the values of the phase stresses that act on mortar and aggregate and which drive damage and plastic flow. This uneven distribution of stresses between mortar and aggregate is seen to lie at the foundation of effects such as the characteristic splitting failure modes in uniaxial compression and the unloading hysteretic loops that arise during cyclic loading. Further to furnishing useful insights into the physical mechanisms underlying the inelastic behavior of concrete, the proposed model provides a simple means of quantifying such behavior in a way which can be readily implemented in any standard finite element code. Possible generalizations of the theory are suggested. In particular, it is noted how rate and rheological effects can be incorporated into the proposed framework by extending it into the viscoplastic range and through the use of Eyring's theory of thermal activation.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/vmvqr-as107A unified approach to finite deformation elastoplastic analysis based on the use of hyperelastic constitutive equations
https://resolver.caltech.edu/CaltechAUTHORS:20180105-151340644
Authors: {'items': [{'id': 'Simo-J-C', 'name': {'family': 'Simo', 'given': 'J. C.'}}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'M.'}, 'orcid': '0000-0001-5877-4824'}]}
Year: 1985
DOI: 10.1016/0045-7825(85)90061-1
By assuming from the outset hyperelastic constitutive behavior, an alternative approach to finite deformation plasticity and viscoplasticity is proposed whereby the need for integration of spatial rate constitutive equations is entirely bypassed. To enhance the applicability of the method, reference is made to a general formulation of plasticity and viscoplasticity which embodies both the multiplicative and additive theories. A new return mapping algorithm capable of accommodating general yield conditions, arbitrary flow and hardening rules and non-constant tangent elasticities is proposed. Finally, a numerical example is presented which illustrates the excellent performance of the method for very large time steps.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/cmq87-6j842Accuracy and stability of integration algorithms for elastoplastic constitutive relations
https://resolver.caltech.edu/CaltechAUTHORS:20180105-151552444
Authors: {'items': [{'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'M.'}, 'orcid': '0000-0001-5877-4824'}, {'id': 'Popov-E-P', 'name': {'family': 'Popov', 'given': 'E. P.'}}]}
Year: 1985
DOI: 10.1002/nme.1620210902
An analysis of accuracy and stability of algorithms for the integration of elastoplastic constitutive relations is carried out in this paper. Reference is made to a very general internal variable formulation of plasticity and to two families of algorithms that generalize the well-known trapezoidal and midpoint rules to fit the present context. Other integration schemes such as the radial return, mean normal and closest point procedures are particular cases of this general formulation. The meaning of first and second-order accuracy in the presence of the plastic consistency condition is examined in detail, and the criteria derived are used to identify two second-order accurate members of the proposed algorithms. A general methodology is also derived whereby the numerical stability properties of integration schemes can be systematically assessed. With the aid of this methodology, the generalized midpoint rule is seen to have far better stability properties than the generalized trapezoidal rule. Finally, numerical examples are presented that illustrate the performance of the algorithms.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/a7rwf-hnq02A note on energy conservation and stability of nonlinear time-stepping algorithms
https://resolver.caltech.edu/CaltechAUTHORS:20180105-151113322
Authors: {'items': [{'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'Michael'}, 'orcid': '0000-0001-5877-4824'}]}
Year: 1986
DOI: 10.1016/0045-7949(86)90346-9
An example of a nonlinear time-stepping algorithm which preserves energy exactly but is unstable is presented and used to illustrate the fact that energy conservation is not sufficient for numerical stability in the nonlinear range.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/acxa7-02f54An analysis of a new class of integration algorithms for elastoplastic constitutive relations
https://resolver.caltech.edu/CaltechAUTHORS:20180105-150600580
Authors: {'items': [{'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'M.'}, 'orcid': '0000-0001-5877-4824'}, {'id': 'Simo-J-C', 'name': {'family': 'Simo', 'given': 'J. C.'}}]}
Year: 1986
DOI: 10.1002/nme.1620230303
An accuracy analysis of a new class of integration algorithms for finite deformation elastoplastic constitutive relations recently proposed by the authors, is carried out in this paper. For simplicity, attention is confined to infinitesimal deformations. The integration rules under consideration fall within the category of return mapping algorithms and follow in a straightforward manner from the theory of operator splitting applied to elastoplastic constitutive relations. General rate-independent and rate-dependent behaviour, with plastic hardening or softening, associated or non-associated flow rules and nonlinear elastic response can be efficiently treated within the present framework. Isoerror maps are presented which demonstrate the good accuracy properties of the algorithm even for strain increments much larger than the characteristic strains at yielding.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/b21sw-2y455Unconditionally stable concurrent procedures for transient finite element analysis
https://resolver.caltech.edu/CaltechAUTHORS:20180105-150834527
Authors: {'items': [{'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'Michael'}, 'orcid': '0000-0001-5877-4824'}, {'id': 'Nour-Omid-B', 'name': {'family': 'Nour-Omid', 'given': 'Bahram'}}]}
Year: 1986
DOI: 10.1016/0045-7825(86)90094-0
A new class of algorithms for transient finite element analysis which is amenable to an efficient implementation in parallel computers is proposed. The suitability of the method for parallel computation stems from the fact that, given an arbitrary partition of the finite element mesh, each subdomain in the partition can be processed over a time step independently and simultaneously with the rest. Both element-by-element and coarse partitions of the mesh are discussed. For the former, the proposed algorithms are shown to have the structure of an explicit scheme. In particular, no global equation solving effort is involved in the update procedure. However, in contrast to explicit schemes the proposed algorithms are shown to be unconditionally stable over a certain range of the algorithmic parameters. In structural dynamics problems, good accuracy is obtained with a constant time step integration. For heat conduction problems accuracy limitations suggest the use of a step-changing technique. When this is done, numerical tests indicate the good behavior of the method. The case in which the mesh is partitioned into a small number of subdomains, typically as many as processors in the computer, is also explored in detail. Good accuracy is obtained over a wide range of time steps. Finally, extensions to second- and higher-order accuracy methods are discussed.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/zwkdw-br505Global viscoelastic behavior of heterogeneous thermoelastic materials
https://resolver.caltech.edu/CaltechAUTHORS:20180104-151938716
Authors: {'items': [{'id': 'Molinari-A', 'name': {'family': 'Molinari', 'given': 'A.'}}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'M.'}, 'orcid': '0000-0001-5877-4824'}]}
Year: 1987
DOI: 10.1016/0020-7683(87)90106-5
The global viscoelastic response of heterogeneous linear thermoelastic material with remote boundaries is characterized. Memory effects result from the dissipation of energy due to microscopic temperature gradients. A Fourier transform technique is used to formulate the problem as an integral equation in the image space. Using a perturbation expansion, analytical results are obtained for two- and three-dimensional examples.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/576jb-11685A method of homogenization of elastic media
https://resolver.caltech.edu/CaltechAUTHORS:20180104-151030750
Authors: {'items': [{'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'M.'}, 'orcid': '0000-0001-5877-4824'}]}
Year: 1987
DOI: 10.1016/0020-7225(87)90125-X
A perturbation technique is proposed which provides a simple means of estimating the effective behavior and fluctuation fields of a heterogeneous elastic medium. The perturbation analysis is based on an integral equation which characterizes the Fourier transform of the fluctuation stress potential. The average stress tensor drives the microstructural response and is assumed given. In contrast to other perturbation methods, the first-order approximation provides a nontrivial correction to the Voigt average moduli and information concerning the strain fluctuations. The first-order term in the expansion follows from straightforward computations and incorporates the statistical information provided by two-point spatial correlations of the elastic properties. Closed form expressions are obtained for the effective moduli of a two-phase continuum with randomly distributed inclusions and the results compared against the predictions of other methods.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/sfvcr-rh107A finite element method for localized failure analysis
https://resolver.caltech.edu/CaltechAUTHORS:20180104-150608642
Authors: {'items': [{'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'Michael'}, 'orcid': '0000-0001-5877-4824'}, {'id': 'Leroy-Y', 'name': {'family': 'Leroy', 'given': 'Yves'}}, {'id': 'Needleman-A', 'name': {'family': 'Needleman', 'given': 'Alan'}}]}
Year: 1987
DOI: 10.1016/0045-7825(87)90004-1
A method is proposed which aims at enhancing the performance of general classes of elements in problems involving strain localization. The method exploits information concerning the process of localization which is readily available at the element level. A bifurcation analysis is used to determine the geometry of the localized deformation modes. When the onset of localization is detected, suitably defined shape functions are added to the element interpolation which closely reproduce the localized modes. The extra degrees of freedom representing the amplitudes of these modes are eliminated by static condensation. The proposed methodology can be applied to 2-D and 3-D problems involving arbitrary rate-independent material behavior. Numerical examples demonstrate the ability of the method to resolve the geometry of localized failure modes to the highest resolution allowed by the mesh.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/8acae-08w41A Continuum Theory of Crack Shielding in Ceramics
https://resolver.caltech.edu/CaltechAUTHORS:20180104-150806608
Authors: {'items': [{'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'M.'}, 'orcid': '0000-0001-5877-4824'}]}
Year: 1987
DOI: 10.1115/1.3172994
A phenomenological constitutive model is proposed which aims at describing the overall effect of microfracture in ceramics. Based on this model, the asymptotic stress, strain, and displacement fields at the tip of a stationary macroscopic crack are determined in closed form. The near-tip stress-intensity factor is computed and observed to be significantly smaller than the applied stress-intensity factor even for moderate amounts of damage.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/0t9ht-p2m98An analytical study of the localized failure modes of concrete
https://resolver.caltech.edu/CaltechAUTHORS:20180104-151213758
Authors: {'items': [{'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'M.'}, 'orcid': '0000-0001-5877-4824'}]}
Year: 1987
DOI: 10.1016/0167-6636(87)90006-8
A theoretical framework for the analysis of localized failure in concrete is presented. The theory is predicated upon the assumption that discrete failure planes arise as a result of a process of localization of damage. The onset of localized modes is characterized as a bifurcation phenomenon whereby local neighborhoods of the material depart from near-uniform straining in favor of highly localized deformation patterns. Simple bifurcation techniques are discussed which suffice to detect when localization initiates and to determine the geometry of the localized deformation modes. Localization techniques are seen to provide a simple yet effective means of extending the range of applicability of traditional distributed damage models to situations of localized failure. Numerical calculations for biaxial stress paths exhibit a good overall agreement with experimental observations.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/y3er3-jk327Microstructural thermal stresses in ceramic materials
https://resolver.caltech.edu/CaltechAUTHORS:20180104-145941926
Authors: {'items': [{'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'M.'}, 'orcid': '0000-0001-5877-4824'}, {'id': 'Molinari-A', 'name': {'family': 'Molinari', 'given': 'A.'}}]}
Year: 1988
DOI: 10.1016/0022-5096(88)90024-5
The problem addressed concerns the analytical characterization of the state of residual stress in a polycrystalline ceramic material following cooling from the fabrication temperature. It is shown that, under mild assumptions on the behavior and microstructure of the material, the covariance matrix of the micro-structural residual stresses can be obtained in closed form from the equations of elasticity. The analysis does not take thermally induced microcracking into consideration and the solid is idealized as remaining essentially intact during the cooling process. However, the results so obtained are subsequently used to derive first-order estimates of microcrack densities.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/vpsbe-vwz27Microcrack coalescence and macroscopic crack growth initiation in brittle solids
https://resolver.caltech.edu/CaltechAUTHORS:20180104-150149978
Authors: {'items': [{'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'M.'}, 'orcid': '0000-0001-5877-4824'}]}
Year: 1988
DOI: 10.1016/0020-7683(88)90031-5
The problem studied in this paper concerns the analytical estimation of the effect of microcracking on crack growth initiation in brittle solids. Particular attention is given to the counteracting effects of toughness degradation and shielding by macrocracking. with a view to determining the range of dominance of each mechanism. Crack growth initiation by coalescence with microcracks is studied with the aid of a cohesive zone model. The extent of shielding of the crack tip by the intervening microcracks is estimated under isotropic damage conditions. A comparison of these effects reveals that, were the crack capable of growing within its plane, the toughness enhancement derived from shielding would be almost exactly counterbalanced by the reduction of toughness in the microcracked material. However, if microcrack deflection is taken into account levels of toughening consistent with experimental data are computed.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/yv37q-a5068Accuracy of a class of concurrent algorithms for transient finite element analysis
https://resolver.caltech.edu/CaltechAUTHORS:20180104-145355217
Authors: {'items': [{'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'Michael'}, 'orcid': '0000-0001-5877-4824'}, {'id': 'Nour-Omid-B', 'name': {'family': 'Nour-Omid', 'given': 'Bahram'}}, {'id': 'Sotelino-E-D', 'name': {'family': 'Sotelino', 'given': 'Elisa D.'}}]}
Year: 1988
DOI: 10.1002/nme.1620260207
The accuracy of a new class of concurrent, procedures for transient finite element analysis is examined. A phase error analysis is carried out which shows that wave retardation leading to unacceptable loss of accuracy may occur if a Courant condition based on the dimensions of the subdomains is violated. Numerical tests suggest that this Courant condition is conservative for typical structural applications and may lead to a marked increase in accuracy as the number of subdomains is increased. Theoretical speed-up ratios are derived which suggest that the algorithms under consideration can be expected to exhibit a performance superior to that of globally implicit methods when implemented on parallel machines.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/rntdh-99239C^0 finite element discretization of Kirchhoff's equations of thin plate bending
https://resolver.caltech.edu/CaltechAUTHORS:20180110-093224078
Authors: {'items': [{'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'M.'}, 'orcid': '0000-0001-5877-4824'}, {'id': 'Morris-G-R', 'name': {'family': 'Morris', 'given': 'G. R.'}}]}
Year: 1988
DOI: 10.1002/nme.1620260707
An alternative formulation of Kirchhoff's equations is given which is amenable to a standard C^0 finite element discretization. In this formulation, the potential energy of the plate is formulated entirely in terms of rotations, whereas the deflections are the outcome of a subsidiary problem. The nature of the resulting equations is such that C^0 interpolation can be used on both rotations and deflections. In particular, general classes of triangular and quadrilateral isoparametric elements can be used in conjunction with the method. Unlike other finite element methods which are based on three-dimensional or Mindlin formulations, the present approach deals directly with Kirchhoff's equations of thin plate bending. Excellent accuracy is observed in standard numerical tests using both distorted and undistorted mesh patterns.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/mgcm9-pcs13Localization analysis under dynamic loading
https://resolver.caltech.edu/CaltechAUTHORS:20180110-100539242
Authors: {'items': [{'id': 'Leroy-Y-M', 'name': {'family': 'Leroy', 'given': 'Y.'}}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'M.'}, 'orcid': '0000-0001-5877-4824'}]}
Year: 1989
A finite element method proposed by Ortiz et al. (1987) is used to study shear band formation in rate dependent and rate independent pressure sensitive solids under dynamic loading. Under these conditions, shear bands are observed to propagate in an irregular fashion in time and space. In particular, the development of multiple shear bands appears to be a prevalent mechanism of deformation at sufficiently high impact velocities.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/wvc5y-a5d43Finite element analysis of strain localization in frictional materials
https://resolver.caltech.edu/CaltechAUTHORS:20180104-144801759
Authors: {'items': [{'id': 'Leroy-Y-M', 'name': {'family': 'Leroy', 'given': 'Y.'}}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'M.'}, 'orcid': '0000-0001-5877-4824'}]}
Year: 1989
DOI: 10.1002/nag.1610130106
Numerical examples are given which illustrate the poor performance of conventional finite elements in problems involving strain localization in frictional materials. In one of the cases investigated, that of granular media subjected to plane strain biaxial loading, isoparametric elements are seen to inhibit localization altogether. With these examples by way of motivation, the performance of a recently proposed finite element method in the context of strain localization in frictional materials is assessed, with particular emphasis on three-dimensional problems. In passing, some issues pertaining to the post-bifurcation response of biaxial specimens are examined. In particular, the numerical simulations suggest that the observed softening is a geometrical effect not attributable to constitutive behaviour.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/ss3bz-3tc28Symmetry-preserving return mapping algorithms and incrementally extremal paths: A unification of concepts
https://resolver.caltech.edu/CaltechAUTHORS:20180104-144352841
Authors: {'items': [{'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'Michael'}, 'orcid': '0000-0001-5877-4824'}, {'id': 'Martin-J-B', 'name': {'family': 'Martin', 'given': 'John B.'}}]}
Year: 1989
DOI: 10.1002/nme.1620280810
In this work we seek to characterize the conditions under which an elastic–plastic stress update algorithm preserves the symmetries inherent to the material response. From a numerical standpoint, the aim is to determine under what conditions a stress update algorithm produces symmetric consistent tangents when applied to materials obeying normality. For the ideally plastic solid we show that only the fully implicit or closest point return mapping algorithm is symmetry preserving. For hardening plasticity, symmetry cannot be preserved in general unless suitable restrictions are imposed on the constitutive equations. We show that these restrictions amount to the existence of a pseudo-internal energy function acting as a joint potential for both the direction of plastic flow and the hardening moduli. In view of the fact that holonomic methods based on incrementally extremal paths also result in update rules possessing a potential structure and, hence, in symmetric tangents, we address the question of whether any connections exist between the two approaches. We show that holonomic methods and the fully implicit algorithm may indeed be brought into correspondence.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/nsmj5-c2r54A finite element method for analyzing localization in rate dependent solids at finite strains
https://resolver.caltech.edu/CaltechAUTHORS:20180104-144547414
Authors: {'items': [{'id': 'Nacar-A', 'name': {'family': 'Nacar', 'given': 'A.'}}, {'id': 'Needleman-A', 'name': {'family': 'Needleman', 'given': 'A.'}}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'M.'}, 'orcid': '0000-0001-5877-4824'}]}
Year: 1989
DOI: 10.1016/0045-7825(89)90067-4
The finite element method for localization analysis of Ortiz et al. [Comp. Methods Appl. Mech. Engrg. 61] is generalized to account for finite deformations and for material rate dependence. Special shape functions are added to the finite element basis to reproduce band-like localized deformation modes. The amplitudes of these additional modes are eliminated locally by static condensation. The performance of the enhanced element is illustrated in a problem involving shear localization in a plane strain tensile bar. Solutions based on the enhanced element are compared with corresponding results obtained from the underlying compatible isoparametric quadrilateral element and from crossed-triangular and uniformly reduced integration elements. In the finite deformation context, the enhanced element solution is not very sensitive to the precise specification of initial orientation of the additional band-like modes. The enhanced element formulation described here can be used for a broad range of rate independent and rate dependent material behaviors in two dimensional and three dimensional problems.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/seker-fbb86Efficiency of group implicit concurrent algorithms for transient finite element analysis
https://resolver.caltech.edu/CaltechAUTHORS:20180104-144109186
Authors: {'items': [{'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'M.'}, 'orcid': '0000-0001-5877-4824'}, {'id': 'Sotelino-E-D', 'name': {'family': 'Sotelino', 'given': 'E. D.'}}, {'id': 'Nour-Omid-B', 'name': {'family': 'Nour-Omid', 'given': 'B.'}}]}
Year: 1989
DOI: 10.1002/nme.1620281204
The performance of group implicit algorithms is assessed on actual concurrent computers. We show that, as the number of subdomains is increased, performance enhancements are derived from two sources: the increased parallelism in the computations; and a reduction in equation solving effort. Moreover, we show that these two performance enhancements are synergistic, in the sense that the corresponding speed-ups are multiplied, rather than merely added. Our numerical simulations demonstrate that, if n is the number of degrees of freedom of the structure, p the number of processors used in the computations, and s ⩾ p is the number of subdomains in the partition, the net speed-up is O(p√s) in 2D and O(ps) in 3D, asymptotically as n/s → ∞. In particular, speed-ups with respect to Newmark's method of O(p√s) in 2D and O(s) in 3D are obtained on a single-processor machine. Finally, simulations on a 32-node hypercube are presented for which the interprocessor communication efficiencies obtained are consistently in excess of 90 per cent.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/e09bp-hy723Solution of three-dimensional crack problems by a finite perturbation method
https://resolver.caltech.edu/CaltechAUTHORS:20180104-143112109
Authors: {'items': [{'id': 'Bower-A-F', 'name': {'family': 'Bower', 'given': 'A. F.'}}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'M.'}, 'orcid': '0000-0001-5877-4824'}]}
Year: 1990
DOI: 10.1016/0022-5096(90)90008-R
An incremental method is described for calculating stress intensity factors in arbitrarily shaped planar cracks subjected to a uniform remote stress. The method is based on recent work by Rice (J. appl. Mech. 52, 571, 1985; Fracture Mechanics : Perspectives and Directions (20th Symp.), ASTM-STP-1020. to appear. 1987), and gao and rice (Int. J. Fracture 33, 115, 1987a; J. appl. Mech. 54, 627, 1987b). who have developed a procedure for computing the variation in stress intensity factor caused by small changes in crack geometry. To date, this technique has only been used to calculate the effects of first-order perturbations in the shape of a crack. In this paper, the method is extended to arbitrarily large perturbations in geometry. Stress intensity factors are calculated by applying a succession of perturbations to a crack of some convenient initial geometry, such as a circular or a half-plane crack. Since this procedure reduces the analysis to evaluating repeatedly two integral equations defined only on the crack front, it has distinct advantages over other existing techniques. The accuracy of the method is demonstrated by calculating stress intensity factors for two test cases : an elliptical crack and a half-plane crack deforming into a prescribed sinusoidal shape of finite amplitude. As further examples of application of the method, solutions to the following problems are presented : a semi-infinite fatigue crack propagating through a particle; a semi-infinite crack trapped by a periodic array of tough particles ; and the unstable growth of a semiinfinite crack through material of decreasing toughness.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/5hjpv-tm020Mixed mode crack-tip fields in monolithic ceramics
https://resolver.caltech.edu/CaltechAUTHORS:20180103-140631024
Authors: {'items': [{'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'M.'}, 'orcid': '0000-0001-5877-4824'}, {'id': 'Giannakopoulos-A-E', 'name': {'family': 'Giannakopoulos', 'given': 'A. E.'}}]}
Year: 1990
DOI: 10.1016/0020-7683(90)90002-D
Asymptotic and full field finite element solutions are given for a semi-infinite planar crack in a monolithic ceramic subjected to remote mixed mode loading. The material is assumed to undergo damage in the form of elastic degradation as a result of stable microcracking. Microcracks are assumed to be preferentially oriented normal to the direction of maximum tension. An outcome of the analysis is that microcracks shield the crack tip less effectively under mode II than under mode I conditions. Other issues addressed concern the relation between the mixities of the applied loads and the near-tip fields, the path-independence of the J integral, the validity of deformation theories of damage under proportional loading, and the conditions for dominance of the singular near-tip fields.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/e0q6k-p2r19A finite element method for determining the angular variation of asymptotic crack tip fields
https://resolver.caltech.edu/CaltechAUTHORS:20180103-133602693
Authors: {'items': [{'id': 'Symington-M', 'name': {'family': 'Symington', 'given': 'M.'}}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'M.'}, 'orcid': '0000-0001-5877-4824'}, {'id': 'Shih-C-F', 'name': {'family': 'Shih', 'given': 'C. F.'}}]}
Year: 1990
DOI: 10.1007/BF00012609
A finite element method for computing the angular variation of asymptotic singular solutions is presented. For the method to be applicable, the asymptotic fields must admit a separable form in polar coordinates. The radial dependence of the fields is assumed known. We provide details of the application of the method to the problem of a stationary semi-infinite crack in a Ramberg-Osgood material subjected to in-plane remote mixed mode elastic fields. This example demonstrates the primary strengths of the method: the material model is easily implemented and accurate solutions are obtained using coarse meshes.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/brz6b-8qd64Effect of decohesion and sliding on bimaterial crack-tip fields
https://resolver.caltech.edu/CaltechAUTHORS:20180104-142347004
Authors: {'items': [{'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'Michael'}, 'orcid': '0000-0001-5877-4824'}, {'id': 'Blume-J-A', 'name': {'family': 'Blume', 'given': 'Janet A.'}}]}
Year: 1990
DOI: 10.1007/BF00018381
This work is concerned with the analytical characterization of the effect of bond decohesion and sliding on the fields surrounding the tip of an interface crack. We consider the two-dimensional problem of an interface crack along the bond between a pair of linearly elastic materials. The interface itself has a nonlinear constitutive property: it has maximum load carrying capacities in both tension normal to the bond and in shear. The interface therefore has the ability to slide and separate inelastically without loss of integrity. The effects of these physically motivated assumptions are deduced and discussed. Further impetus for this study stems from the recent resurgence of interest in interfacial fracture mechanics. This interest is partly driven by the desire to understand and alleviate the pathological difficulties associated with the crack-tip fields predicted by the linear theory of elasticity. By accounting for possible interfacial nonlinear behavior, we are able to find that near-tip fields are free of the offensive properties alluded to above.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/n5tgc-06f94Formulation of implicit finite element methods for multiplicative finite deformation plasticity
https://resolver.caltech.edu/CaltechAUTHORS:20180104-142558434
Authors: {'items': [{'id': 'Moran-B', 'name': {'family': 'Moran', 'given': 'B.'}}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'M.'}, 'orcid': '0000-0001-5877-4824'}, {'id': 'Shih-C-F', 'name': {'family': 'Shih', 'given': 'C. F.'}}]}
Year: 1990
DOI: 10.1002/nme.1620290304
Some constitutive and computational aspects of finite deformation plasticity are discussed. Attention is restricted to multiplicative theories of plasticity, in which the deformation gradients are assumed to be decomposable into elastic and plastic terms. It is shown by way of consistent linearization of momentum balance that geometric terms arise which are associated with the motion of the intermediate configuration and which in general render the tangent operator non-symmetric even for associated plastic flow. Both explicit (i.e. no equilibrium iteration) and implicit finite element formulations are considered. An assumed strain formulation is used to accommodate the near-incompressibility associated with fully developed isochoric plastic flow. As an example of explicit integration, the rate tangent modulus method is reviewed in some detail. An implicit scheme is derived for which the consistent tangents, resulting in quadratic convergence of the equilibrium iterations, can be written out in closed form for arbitrary material models. All the geometrical terms associated with the motion of the intermediate configuration and the treatment of incompressibility are given explicitly. Examples of application to void growth and coalescence and to crack tip blunting are developed which illustrate the performance of the implicit method.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/asns1-p5a11Finite element analysis of transient strain localization phenomena in frictional solids
https://resolver.caltech.edu/CaltechAUTHORS:20180104-142923188
Authors: {'items': [{'id': 'Leroy-Y-M', 'name': {'family': 'Leroy', 'given': 'Y.'}}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'M.'}, 'orcid': '0000-0001-5877-4824'}]}
Year: 1990
DOI: 10.1002/nag.1610140203
Finite elements with embedded shocks are used to investigate transient strain localization phenomena in frictional solids. In particular, we seek to elucidate the effect of rate sensitivity and inertia on the development of shear bands in solids subjected to impulsive loading. As in the static case, our results show that shear banding may induce severe softening of the specimen even as the material steadily hardens. As expected, rate sensitivity retards the onset of structural softening and tends to stabilize the post-peak response. It is verified that the static solution is indeed recovered in the inviscid limit. Under dynamic conditions, shear bands are observed to propagate discontinuously, arresting and resuming propagation repeatedly before linking up with the boundary of the specimen. The direction of the band is equally unsteady. In addition, multiple shear banding, with the development of secondary and even tertiary bands, appears to be a prevalent mechanism at sufficiently high impact velocities.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/yn2d1-20p03Crack propagation in monolithic ceramics under mixed mode loading
https://resolver.caltech.edu/CaltechAUTHORS:20180110-093214865
Authors: {'items': [{'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'M.'}, 'orcid': '0000-0001-5877-4824'}, {'id': 'Giannakopoulos-A-E', 'name': {'family': 'Giannakopoulos', 'given': 'A. E.'}}]}
Year: 1990
DOI: 10.1007/BF00036167
Finite element calculations are presented for a semi-infinite crack in a brittle solid undergoing microcracking normal to the maximum tensile direction. Microcracks are presumed stable and a saturation stage is postulated wherein the effective elastic moduli attain steady state values. Mode I, mode II and mixed mode loading conditions are investigated. In these two latter cases, the method of analysis employed allows for cracks to grow out of their initial planes. The mixed mode loading case investigated corresponds to taking equal values of the remote mode I and II stress intensity factors. Contrary to what is observed in the mode I case, no appreciable R-curve behavior is found under mode II or mixed mode conditions.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/7w1x4-7t029A soft-recovery plate impact experiment for studying microcracking in ceramics
https://resolver.caltech.edu/CaltechAUTHORS:20180103-134318947
Authors: {'items': [{'id': 'Raiser-G', 'name': {'family': 'Raiser', 'given': 'G.'}}, {'id': 'Clifton-R-J', 'name': {'family': 'Clifton', 'given': 'R. J.'}}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'M.'}, 'orcid': '0000-0001-5877-4824'}]}
Year: 1990
DOI: 10.1016/0167-6636(90)90016-9
Plate impact experiments are presented for generating microcracks in ceramics under well-characterized loading conditions which also allow recovery of the specimen to examine the induced microcracking. A star-shaped aluminum flyer plate impacts a ceramic plate backed up by a steel plate. Compressive stress pulses and reflected tensile pulses propagate through these plates and eventually leave the aluminum and ceramic plates at rest while the steel plate carries away the momentum. The central region of the specimen is loaded by plane waves which are monitored by means of laser interferometry. The recorded velocity-time profiles provide an indication of the evolution of microcracking in the ceramic. Electron microscopy of the recovered specimens shows microcracks along grain boundaries in the ceramic. Their lengths can be measured easily and accurately with a transmission electron microscope. These experiments have proven to be successful in causing controlled microcracking in α-Al_2O_3 under well known stress conditions, while still allowing microstructural examination of the specimen. The information obtained from the experiments is used to evaluate a simple model for predicting the cracks resulting from the tensile interval of the stress history, showing that these tests can be used to develop a stress dependent theory of microcracking. Such a theory would contribute to a fundamental understanding of the phenomenon of microcracking in ceramics and thereby allow further progress towards toughening these highly brittle materials.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/yxe9k-8wn65Effect of boundaries and interfaces on shear-band localization
https://resolver.caltech.edu/CaltechAUTHORS:20180102-162606388
Authors: {'items': [{'id': 'Needleman-A', 'name': {'family': 'Needleman', 'given': 'A.'}}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'M.'}, 'orcid': '0000-0001-5877-4824'}]}
Year: 1991
DOI: 10.1016/0020-7683(91)90005-Z
The emergence of general stationary-wave solutions, exemplified by Rayleigh surface waves and Stoneley interface waves, is taken as a criterion for the onset of localization in the presence of geometrical features such as free boundaries and interfaces. The stationary-wave solutions yield the possible orientations of the emerging shear bands. The influence of interfaces in crystalline solids and of free boundaries in pressure-sensitive frictional materials is investigated within this general framework. It is found that grain boundaries in polycrystals can act as both barriers to, and as sources of, shear bands. The analysis of pressure-sensitive frictional materials reveals a mismatch in orientation between the shear bands in the interior and on the boundary of the solid. The implications of this misorientation for the global behavior of specimens tested in plane strain compression are discussed.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/4t70v-7bj16A three-dimensional analysis of crack trapping and bridging by tough particles
https://resolver.caltech.edu/CaltechAUTHORS:20180102-162806476
Authors: {'items': [{'id': 'Bower-A-F', 'name': {'family': 'Bower', 'given': 'A. F.'}}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'M.'}, 'orcid': '0000-0001-5877-4824'}]}
Year: 1991
DOI: 10.1016/0022-5096(91)90026-K
The toughness of a brittle material may be substantially improved by adding small quantities of tough particles to the solid. Three mechanisms may be responsible. Firstly, the front of a crack propagating through the solid can be trapped by the particles, causing it to bow out between them. Secondly, the particles may remain intact in the wake of the crack, thereby pinning its faces and reducing the crack tip stress intensity factors. Finally, the toughness may be enhanced by frictional energy dissipation as particles are pulled out in the wake of the crack. This paper estimates the improvement in toughness that might be expected due to these mechanisms, by means of a three-dimensional model. The analysis considers a semi-infinite crack propagating through a brittle matrix material, which contains a regular distribution of tough particles. Particles in the wake of the crack are modelled by finding an appropriate distribution of point forces that pin the crack faces; and the effect of the crack bowing between obstacles is included by means of an incremental perturbation method based on work byRice [J. Appl. Mech.56, 619 (1985)]. The calculation predicts the shape of the crack as it propagates through the solid; the resulting R-curve behaviour; and the length of the bridged zone in the wake of the crack.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/5eg0n-2db54Adaptive mesh refinement in strain localization problems
https://resolver.caltech.edu/CaltechAUTHORS:20180102-162039472
Authors: {'items': [{'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'M.'}, 'orcid': '0000-0001-5877-4824'}, {'id': 'Quigley-J-J-IV', 'name': {'family': 'Quigley', 'given': 'J. J., IV'}}]}
Year: 1991
DOI: 10.1016/0045-7825(91)90184-8
An adaptive meshing method tailored to problems of strain localization is given. The adaption strategy consists of equi-distributing the variation of the velocity field over the elements of the mesh. A heuristic justification for the use of variations as indicators is advanced, and possible connections with interpolation error bounds are discussed. Meshes are constructed by Delaunay triangulation. It is shown how the Hu-Washizu principle determines a consistent transfer operator for the state variables. Examples of application are given which demonstrate the versatility of the method.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/tgfw8-a2779Discussion on 'A consistency analysis of a class of concurrent transient implicit/explicit algorithms', by C. Farhat and N. Sobh
https://resolver.caltech.edu/CaltechAUTHORS:20180102-162412775
Authors: {'items': [{'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'M.'}, 'orcid': '0000-0001-5877-4824'}]}
Year: 1991
DOI: 10.1016/0045-7825(91)90024-Z
[No abstract]https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/xskcc-k5c91An analysis of cracks in ductile single crystals—II. Mode I loading
https://resolver.caltech.edu/CaltechAUTHORS:20171213-164121235
Authors: {'items': [{'id': 'Mohan-R', 'name': {'family': 'Mohan', 'given': 'R.'}}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'M.'}, 'orcid': '0000-0001-5877-4824'}, {'id': 'Shih-C-F', 'name': {'family': 'Shih', 'given': 'C. F.'}}]}
Year: 1992
DOI: 10.1016/S0022-5096(05)80015-8
A geometrically rigorous formulation of crystalline plasticity is used to analyze the crack-tip deformation and stress fields in ductile single crystals subjected to mode I loading. The theory accounts for finite deformations and finite lattice rotations, as well as for the full three-dimensional crystallographic geometry of the crystal. An experimentally based self-hardening rule exhibiting an initial stage of rapid hardening followed by a saturation stage is also adopted. The problem of a stationary semi-infinite crack in FCC and BCC crystals is considered. As regards the dominant modes of deformation, the results are in partial agreement with earlier analytical and numerical solutions, but in excellent qualitative agreement with recent experimental observations. The results suggest that both finite-deformation and lattice rotation effects, as well as the details of the hardening law, strongly influence the structure of the solution.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/kbevd-mwg71An analysis of cracks in ductile single crystals—I. Anti-plane shear
https://resolver.caltech.edu/CaltechAUTHORS:20171213-163842621
Authors: {'items': [{'id': 'Mohan-R', 'name': {'family': 'Mohan', 'given': 'R.'}}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'M.'}, 'orcid': '0000-0001-5877-4824'}, {'id': 'Shih-C-F', 'name': {'family': 'Shih', 'given': 'C. F.'}}]}
Year: 1992
DOI: 10.1016/S0022-5096(05)80014-6
The problem of a stationary mathematically sharp semi-infinite crack in an FCC crystal is considered. We adopt a geometrically rigorous formulation of crystalline plasticity accounting for finite deformations and finite lattice rotations, as well as for the full three-dimensional crystallographic geometry of the crystal. A comparison of results with earlier small-strain solutions reveals some notable differences. These include the expected development of finite deformations and rotations near the crack tip, but also discrepancies such as a considerable spread of the plastic zones. In addition, nearly self-similar, square-root singular fields are obtained within the portion of the plastic zone where the crystal is in a state of high positive hardening. The results suggest that both finite-deformation and lattice rotation effects, as well as the details of the hardening law, strongly influence the structure of the solution.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/tjd2a-eh221A material‐independent method for extending stress update algorithms from small-strain plasticity to finite plasticity with multiplicative kinematics
https://resolver.caltech.edu/CaltechAUTHORS:20180102-160938210
Authors: {'items': [{'id': 'Cuitiño-A-M', 'name': {'family': 'Cuitiño', 'given': 'A. M.'}, 'orcid': '0000-0002-5180-9147'}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'M.'}, 'orcid': '0000-0001-5877-4824'}]}
Year: 1992
DOI: 10.1108/eb023876
We provide a method for automatically extending small‐strain state‐update algorithms and their correspondent consistent tangents into the finite deformation range within the framework of multiplicative plasticity. The procedure, when it applies, operates at the level of kinematics and, hence, can be implemented once and for all independently of the material‐specific details of the constitutive model. The versatility of the method is demonstrated by a numerical example.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/v0nkd-mq392Influence of Cracking Direction on Interfacial Fracture in Bicrystals With Symmetric Tilt Boundary
https://resolver.caltech.edu/CaltechAUTHORS:20171213-163502078
Authors: {'items': [{'id': 'Mohan-R', 'name': {'family': 'Mohan', 'given': 'R.'}}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'M.'}, 'orcid': '0000-0001-5877-4824'}, {'id': 'Shih-C-F', 'name': {'family': 'Shih', 'given': 'C. F.'}}]}
Year: 1992
DOI: 10.1115/1.2899469
Recent experiments by Wang (1990) on copper bicrystals with a [110] symmetric tilt of 38.9 degrees have shown that the mode of fracture of these bicrystals, i.e., whether fracture is of a ductile or brittle nature, depends on the direction of cracking. An analysis of this effect within the framework of continuum crystal plasticity is presented. The formulation accounts for finite deformations and finite lattice rotations, as well as for the full three-dimensional collection of slip systems in FCC crystals. Our results indicate that, whereas the level of stress ahead of the crack tip is similar for the ductile and brittle cracking directions, the sizes of the plastic regions differ significantly in the two cases.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/xn4ff-6qc10Effect of Strain Hardening and Rate Sensitivity on the Dynamic Growth of a Void in a Plastic Material
https://resolver.caltech.edu/CaltechAUTHORS:20171213-163302163
Authors: {'items': [{'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'M.'}, 'orcid': '0000-0001-5877-4824'}, {'id': 'Molinari-A', 'name': {'family': 'Molinari', 'given': 'A.'}}]}
Year: 1992
DOI: 10.1115/1.2899463
The problem studied in this paper concerns the dynamic expansion of a spherical void in an unbounded solid under the action of remote hydrostatic tension. The void is assumed to remain spherical throughout the deformation and the matrix to be incompressible. The effects of inertia, strain hardening, and rate sensitivity on the short and long-term behavior of the void, as well as on its response to ramp loading, are investigated in detail.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/kkt3k-s4k40Mode mixity effects on crack tip deformation in ductile single crystals
https://resolver.caltech.edu/CaltechAUTHORS:20171213-164302776
Authors: {'items': [{'id': 'Mohan-R', 'name': {'family': 'Mohan', 'given': 'R.'}}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'M.'}, 'orcid': '0000-0001-5877-4824'}, {'id': 'Shih-C-F', 'name': {'family': 'Shih', 'given': 'C. F.'}}]}
Year: 1992
DOI: 10.1016/0956-7151(92)90177-G
Crack tip deformation and stress fields in ductile single crystals, under mixed mode loading conditions, are examined within the framework of a geometrically rigorous formulation of crystalline plasticity. The theory accounts for finite deformations and finite lattice rotations, as well as for the full three-dimensional crystallographic geometry of the crystal. An experimentally based self-hardening rule exhibiting an initial stage of rapid hardening followed by a saturation stage is used in the analysis. For the orientation of an f.c.c. crystal considered in this study, the geometric nature of slip gives rise to competing deformation modes. Our studies reveal that mode mixity exerts a strong influence on which of these competing deformation modes prevail. It is found that the effects of mode mixity are more complex than those predicted by phenomenological flow theories of plasticity. Finite deformation and lattice rotation effects, as well as the details of the hardening law, strongly influence the structure of the solution.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/18ny1-dz784Performance of the star‐shaped flyer in the study of brittle materials: Three dimensional computer simulations and experimental observations
https://resolver.caltech.edu/CaltechAUTHORS:20171213-164520270
Authors: {'items': [{'id': 'Espinosa-H-D', 'name': {'family': 'Espinosa', 'given': 'H. D.'}}, {'id': 'Raiser-G', 'name': {'family': 'Raiser', 'given': 'G.'}}, {'id': 'Clifton-R-J', 'name': {'family': 'Clifton', 'given': 'R. J.'}}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'M.'}, 'orcid': '0000-0001-5877-4824'}]}
Year: 1992
DOI: 10.1063/1.351419
A three dimensional finite element computer simulation has been performed to assess the effects of release waves in normal impact soft‐recovery experiments when a star‐shaped flyer plate is used. Their effects on the monitored velocity‐time profiles have been identified and their implications in the interpretation of wave spreading and spall signal events highlighted. The calculation shows that the star‐shaped flyer plate indeed minimizes the magnitude of edge effects. The major perturbation to the one‐dimensional response within the central region of the target plate results from spherical waves emanating from the corners of the star‐shaped plate. Experimental evidence of the development of a damage ring located in coincidence with the eight entrant corners of the flyer plate is reported. Microscopy studies performed in the intact recovered samples revealed that this damage ring eliminates undesired boundary release waves within the central region of the specimen. Consequently, the observed damage in compression and tension within this region can be attributed primarily to the conditions arising from a state of uniaxial strain.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/0ymtb-5h073Statistical Properties of Residual Stresses and Intergranular Fracture in Ceramic Materials
https://resolver.caltech.edu/CaltechAUTHORS:20171213-160735981
Authors: {'items': [{'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'M.'}, 'orcid': '0000-0001-5877-4824'}, {'id': 'Suresh-S', 'name': {'family': 'Suresh', 'given': 'S.'}}]}
Year: 1993
DOI: 10.1115/1.2900782
The problem addressed in this paper concerns the statistical characterization of the state of residual stress generated in polycrystalline ceramics during cooling from the fabrication temperature. Detailed finite element simulations are carried out for an ensemble of large numbers of randomly oriented, planar hexagonal grains with elastic and thermal expansion anisotropy, and brittle grain interfaces. The calculations show that the distribution of normal and shear tractions induced by thermal contraction mismatch among grains is gaussian and that these tractions are statistically independent random variables. Although the gaussian nature of the distributions remains unaffected by the introduction of elastic anisotropy, the results indicate that elastic anisotropy has a significant effect on the residual stresses for finite departures from isotropy. When the hexagonal grains are randomly distorted, the magnitude and distribution of residual stresses are found to be insignificantly altered. Spontaneous microfracture due to the generation of internal stresses is also simulated in the analysis by allowing for the nucleation and growth of intergranular microcracks when the fracture energy along the grain facets exceeds a certain critical value. When such microcracking is incorporated into the computation, the levels of residual stress are markedly reduced as a consequence of stress dissipation. The dependence of intergranular microcracking on grain size and temperature variation is examined and the predicted trends on material degradation or the complete suppression of microfracture are discussed in the light of available experimental results.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/j45mm-yzr25An Analysis of Crack Trapping by Residual Stresses in Brittle Solids
https://resolver.caltech.edu/CaltechAUTHORS:20171213-161223831
Authors: {'items': [{'id': 'Bower-A-F', 'name': {'family': 'Bower', 'given': 'A. F.'}}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'M.'}, 'orcid': '0000-0001-5877-4824'}]}
Year: 1993
DOI: 10.1115/1.2900742
The residual stress distribution in a brittle polycrystalline solid may have a significant influence on its toughness. Grains in a state of residual compression are less likely to be fractured by a growing crack and may trap the crack front or be left behind as bridging particles (Evans et al., 1977). This paper estimates the toughness enhancement due to intergranular residual stresses, using a three-dimensional model. The residual stress is approximated as a doubly sinusoidal distribution acting perpendicular to the plane of an initially straight semi-infinite crack. An incremental perturbation method developed by Bower and Ortiz (1990) for solving three-dimensional crack problems is extended here to cracks loaded by nonuniform remote stresses. It is used to calculate the shape of the semi-infinite crack as it propagates through the doubly sinusoidal residual stress. It is shown that the local regions of compression may trap the crack front and give rise to some transient toughening. In addition, if the residual stress exceeds a critical magnitude, pinning particles may be left in the crack wake. However, for practical values of residual stress and grain size, the predicted toughness enhancement is insignificant. Furthermore, the analysis cannot account for the large bridging zones observed in experiments. It is concluded that the R-curve behavior and bridging particles observed in monolithic ceramics are caused by mechanisms other than residual stresses acting perpendicular to the crack plane.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/ntk0x-0xk63Computational modelling of single crystals
https://resolver.caltech.edu/CaltechAUTHORS:CUImsmse93
Authors: {'items': [{'id': 'Cuitiño-A-M', 'name': {'family': 'Cuitiño', 'given': 'A. M.'}, 'orcid': '0000-0002-5180-9147'}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'M.'}, 'orcid': '0000-0001-5877-4824'}]}
Year: 1993
DOI: 10.1088/0965-0393/1/3/001
The physical basis of computationally tractable models of crystalline plasticity is reviewed. A statistical mechanical model of dislocation motion through forest dislocations is formulated. Following Franciosi and co-workers (1980-88) the strength of the short-range obstacles introduced by the forest dislocations is allowed to depend on the mode of interaction. The kinetic equations governing dislocation motion are solved in closed form for monotonic loading, with transients in the density of forest dislocations accounted for. This solution, coupled with suitable equations of evolution for the dislocation densities, provides a complete description of the hardening of crystals under monotonic loading. Detailed comparisons with experiment demonstrate the predictive capabilities of the theory. An adaptive finite element formulation for the analysis of ductile single crystals is also developed. Calculations of the near-tip fields in Cu single crystals illustrate the versatility of the method.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/ccnpq-qr747The Influence of Grain Size on the Toughness of Monolithic Ceramics
https://resolver.caltech.edu/CaltechAUTHORS:20171213-161606680
Authors: {'items': [{'id': 'Bower-A-F', 'name': {'family': 'Bower', 'given': 'A. F.'}}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'M.'}, 'orcid': '0000-0001-5877-4824'}]}
Year: 1993
DOI: 10.1115/1.2904212
Experiments have shown that there may be an optimal grain size which maximizes the toughness of polycrystalline ceramics. In this paper, we attempt to develop a theoretical model which can predict the effect of grain size on the toughness of ceramics. We assume that three principal mechanisms affect the toughness of the material: distributed microcracking; crack trapping by tough grains; and frictional energy dissipation as grains are pulled out in the wake of the crack. The grain size influences these mechanisms in several ways. The energy dissipated due to frictional crack bridging increases with the size of the bridging grains, tending to improve toughness. However, as the grain size increases, the density of microcracks in the solid also increases, which eventually weakens the material. In addition, the level of inter-granular residual stress is also reduced by microcracking, which as a detrimental effect on the toughening due to bridging. We have developed a simple model to quantify these effects. However, the model does not predict the dramatic loss of strength which has been observed to occur beyond a critical grain size. We have therefore proposed an alternative explanation for the apparent decrease in toughness in coarse grained ceramics. Calculations indicate that in a coarse grained material, the main contribution to toughness is due to frictional crack bridging. However, to produce this toughening, the bridging zone must be over 500 grains long. In practice, the length of the bridging zone in a coarse grained solid may be comparable to the dimensions of the specimen used to measure its toughness. Under these conditions, it is not appropriate to use the concept of a geometry independent toughness to characterize the strength of the specimen. We have therefore developed a simple model of a double cantilever beam fracture specimen, which accounts for the effects of large scale bridging. Using this model, we are able to predict the apparent decrease in toughness measured in coarse grained specimens.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/gtar5-2t853A harmonic/anharmonic energy partition method for lattice statics computations
https://resolver.caltech.edu/CaltechAUTHORS:GALmsmse93
Authors: {'items': [{'id': 'Gallego-R', 'name': {'family': 'Gallego', 'given': 'Rafael'}}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'Michael'}, 'orcid': '0000-0001-5877-4824'}]}
Year: 1993
DOI: 10.1088/0965-0393/1/4/006
A method of lattice statics analysis is developed. Consideration of anharmonic effects is restricted to finite regions surrounding lattice defects. All displacements of the crystal are expressed as the effect of unknown forces applied to a perfect harmonic lattice of infinite extent. Displacements are related to the unknown applied forces by means of the Green function of the perfect harmonic lattice, so that equilibrating forces need only be applied to the anharmonic region. The unknown forces are determined so as to maximize the complementary energy of the crystal, which yields a lower bound to the potential energy. The method does not require the explicit enforcement of equilibrium or compatibility conditions across the boundary between the harmonic and anharmonic regions. The performance of the method is assessed on the basis of selected numerical examples. The rate of convergence of the method with increasing domain size is found to be cubic. This is one or two orders of magnitude faster than rigid boundary methods based on the harmonic and continuum solutions, respectively.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/e09gv-b3v21A variational boundary integral method for the analysis of 3-D cracks of arbitrary geometry modelled as continuous distributions of dislocation loops
https://resolver.caltech.edu/CaltechAUTHORS:20171213-160315284
Authors: {'items': [{'id': 'Xu-G', 'name': {'family': 'Xu', 'given': 'G.'}}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'M.'}, 'orcid': '0000-0001-5877-4824'}]}
Year: 1993
DOI: 10.1002/nme.1620362107
A finite element methodology for analysing propagating cracks of arbitrary three-dimensional geometry is developed. By representing the opening displacements of the crack as a distribution of dislocation loops and minimizing the corresponding potential energy of the solid, the kernels of the governing integral equations have mild singularities of the type 1/R. A simple quadrature scheme then suffices to compute all the element arrays accurately. Because of the variational basis of the method, the resulting system of equations is symmetric. By employing six-noded triangular elements and displacing midside nodes to quarter-point positions, the opening profile near the front is endowed with the correct asymptotic behaviour. This enables the direct computation of stress intensity factors from the opening displacements. The special but important cases of periodic and semi-infinite cracks are addressed in some detail. Finally, the geometry of propagating cracks is updated incrementally by recourse to a pseudodynamic crack-tip equation of motion. The crack is continuously remeshed to accommodate the ensuing changes in geometry. The performance of the method is assessed by means of selected numerical examples.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/0m1ts-j1262Nucleation of dislocations from crack tips under mixed modes of loading: Implications for brittle against ductile behaviour of crystals
https://resolver.caltech.edu/CaltechAUTHORS:20171213-155429973
Authors: {'items': [{'id': 'Xu-G', 'name': {'family': 'Xu', 'given': 'G.'}}, {'id': 'Argon-A-S', 'name': {'family': 'Argon', 'given': 'A. S.'}}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'M.'}, 'orcid': '0000-0001-5877-4824'}]}
Year: 1995
DOI: 10.1080/01418619508239933
The variational boundary integral method of Xu and Ortiz is taken as a basis for studying dislocation nucleation from atomically sharp cracks under combined mode I-mode II loading. The tension-shear potential of Rice et al. is extended to allow for skewness in the shear resistance curve and to account for the surface production resistance which accompanies ledge formation. The calculated unstable equilibrium configurations of the incipient dislocations and the dependence of the associated activation energies on crack tip energy release rate are found to differ from the Rice-Beltz perturbation solution and the Schöck-Püschl more approximate solution. Simulations of dislocation nucleation on inclined slip planes reveal that, while tension softening facilitates nucleation, surface production resistance impedes it. The extent to which these two effects influence critical conditions for dislocation nucleation is quantified. The calculations suggest that homogeneous dislocation nucleation on inclined planes is not favoured for materials with all but the lowest of unstable stacking-energy-to-surface-energy ratios. This emphasizes the importance of heterogeneous dislocation nucleation and nucleation on oblique slip planes on which free surface production should play a much weaker role. The implications of these findings on the nucleation-controlled brittle-ductile transition in cleavage fracture are discussed.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/8wy0p-may03Modelling and simulation of high-speed machining
https://resolver.caltech.edu/CaltechAUTHORS:20171213-155828724
Authors: {'items': [{'id': 'Marusich-T-D', 'name': {'family': 'Marusich', 'given': 'T. D.'}}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'M.'}, 'orcid': '0000-0001-5877-4824'}]}
Year: 1995
DOI: 10.1002/nme.1620382108
A Lagrangian finite element model of orthogonal high-speed machining is developed. Continuous remeshing and adaptive meshing are the principal tools which we employ for sidestepping the difficulties associated with deformation-induced element distortion, and for resolving fine-scale features in the solution. The model accounts for dynamic effects, heat conduction, mesh-on-mesh contact with friction, and full thermo-mechanical coupling. In addition, a fracture model has been implemented which allows for arbitrary crack initiation and propagation in the regime of shear localized chips. The model correctly exhibits the observed transition from continuous to segmented chips with increasing tool speed.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/5zmfj-v7633The Two-Dimensional Structure of Dynamic Boundary Layers and Shear Bands in Thermoviscoplastic Solids
https://resolver.caltech.edu/CaltechAUTHORS:20171213-152056464
Authors: {'items': [{'id': 'Gioia-Gustavo', 'name': {'family': 'Gioia', 'given': 'G.'}}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'M.'}, 'orcid': '0000-0001-5877-4824'}]}
Year: 1996
DOI: 10.1016/0022-5096(95)00071-2
A general boundary layer theory for thermoviscoplastic solids which accounts for inertia, rate sensitivity, hardening, thermal coupling, heat convection and conduction, and thermal softening is developed. In many applications of interest, the boundary layer equations can be considerably simplified by recourse to similarity methods, which facilitates the determination of steady-state and transient fully non-linear two-dimensional solutions. A simple analysis of the asymptotic behavior of the steady-state solutions leads to a classification of stable and unstable regimes. Under adiabatic conditions, the resulting material stability criterion coincides with that previously derived by Molinari and Clifton [(1987) Analytical characterization of shear localization in thermoviscoplastic solids. J. Appl, Mech. 54, 806–812] by a quasi-static, one-dimensional analysis. The transition from initially stable to unstable behavior can also be conveniently described by similarity methods. This provides a powerful semi-analytical tool for the interpretation of impact tests exhibiting dynamic shear bands, and for the characterization of the two-dimensional structure of such bands. It follows from the theory that, if the velocity of the impactor is held steady, the leading tip of the shear band propagates at a constant speed. This shear band tip speed follows readily from the theory as a function of the impact velocity and material parameters. The two-dimensional velocity, stress, temperature and plastic work fields attendant to the propagating shear band are also determined.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/7dvdm-0xr07Ductile fracture by vacancy condensation in f.c.c. single crystals
https://resolver.caltech.edu/CaltechAUTHORS:20171213-152606701
Authors: {'items': [{'id': 'Cuitiño-A-M', 'name': {'family': 'Cuitiño', 'given': 'A. M.'}, 'orcid': '0000-0002-5180-9147'}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'M.'}, 'orcid': '0000-0001-5877-4824'}]}
Year: 1996
DOI: 10.1016/1359-6454(95)00220-0
We explore the feasibility of vacancy condensation as the void-nucleating mechanism underlying ductile fracture by void growth and coalescence in single crystals at room temperature. Vacancies are presumed to be primarily generated by the dragging of intersection jogs. The equations governing the rate of growth of voids by vacancy condensation are derived. These equations are used to follow the evolution of vacancy concentrations and void sizes in the Wang and Anderson [Acta metall. 39, 779 (1991)] [1] Σ9 test. We find that, when pipe diffusions are taken into account, the time required for the nucleation of a macroscopic void in the near-tip region is of the order of one minute, which is well within the time-scale of quasistatic fracture tests.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/6t2a9-2ts92Three-dimensional crack-tip fields in four-point-bending copper single-crystal specimens
https://resolver.caltech.edu/CaltechAUTHORS:20171213-152404106
Authors: {'items': [{'id': 'Cuitiño-A-M', 'name': {'family': 'Cuitiño', 'given': 'A. M.'}, 'orcid': '0000-0002-5180-9147'}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'M.'}, 'orcid': '0000-0001-5877-4824'}]}
Year: 1996
DOI: 10.1016/0022-5096(96)00016-6
The three-dimensional near-tip fields in copper single crystals loaded in four-point bending are characterized numerically. For comparison purposes, the corresponding plane-strain fields are also computed numerically and their asymptotic behavior determined semi-analytically. On the basis of these analyses, we investigate: (i) the dependence of the fields on the hardening law; (ii) the degree of correlation between surface and interior fields in finite specimens; and (iii) the degree of correlation between plane-strain and three-dimensional fields. In particular, we endeavor to ascertain the extent to which surface observations of near-tip fields in single crystals, such as those obtained by Moire interferometry, are representative of interior fields, and the extent to which these are representative of plane-strain fields. Our calculations reveal marked differences in the pattern of slip activity in the interior and on the surface of the specimen. These discrepancies, in turn, result in significant variations in the state of stress and strain. These observations suggest that, for the test geometries under consideration, surface observations provide only an indirect measure of conditions in the interior, and point to a need for the development of experimental techniques enabling the direct observation of interior fields.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/6vt1b-5w677Quasicontinuum analysis of defects in solids
https://resolver.caltech.edu/CaltechAUTHORS:20171213-150724557
Authors: {'items': [{'id': 'Tadmor-E-B', 'name': {'family': 'Tadmor', 'given': 'E. B.'}}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'M.'}, 'orcid': '0000-0001-5877-4824'}, {'id': 'Phillips-R', 'name': {'family': 'Phillips', 'given': 'R.'}, 'orcid': '0000-0003-3082-2809'}]}
Year: 1996
DOI: 10.1080/01418619608243000
We develop a method which permits the analysis of problems requiring the simultaneous resolution of continuum and atomistic length scales-and associated deformation processes-in a unified manner. A finite element methodology furnishes a continuum statement of the problem of interest and provides the requisite multiple-scale analysis capability by adaptively refining the mesh near lattice defects and other highly energetic regions. The method differs from conventional finite element analyses in that interatomic interactions are incorporated into the model through a crystal calculation based on the local state of deformation. This procedure endows the model with crucial properties, such as slip invariance, which enable the emergence of dislocations and other lattice defects. We assess the accuracy of the theory in the atomistic limit by way of three examples: a stacking fault on the (111) plane, and edge dislocations residing on (111) and (100) planes of an aluminium single crystal. The method correctly predicts the splitting of the (111) edge dislocation into Shockley partials. The computed separation of these partials is consistent with results obtained by direct atomistic simulations. The method predicts no splitting of the Al Lomer dislocation, in keeping with observation and the results of direct atomistic simulation. In both cases, the core structures are found to be in good agreement with direct lattice statics calculations, which attests to the accuracy of the method at the atomistic scale.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/bjp9j-xq184Juan Carlos Simo, 1952–1994
https://resolver.caltech.edu/CaltechAUTHORS:20171213-151512573
Authors: {'items': [{'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'Miguel'}, 'orcid': '0000-0001-5877-4824'}]}
Year: 1996
DOI: 10.1016/S0020-7683(96)90054-2
[No abstract]https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/evzbj-w9d04Computational modelling of impact damage in brittle materials
https://resolver.caltech.edu/CaltechAUTHORS:20171213-154113812
Authors: {'items': [{'id': 'Camacho-G-T', 'name': {'family': 'Camacho', 'given': 'G. T.'}}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'M.'}, 'orcid': '0000-0001-5877-4824'}]}
Year: 1996
DOI: 10.1016/0020-7683(95)00255-3
A Lagrangian finite element method of fracture and fragmentation in brittle materials is developed. A cohesive-law fracture model is used to propagate multiple cracks along arbitrary paths. In axisymmetric calculations, radial cracking is accounted for through a continuum damage model. An explicit contact/friction algorithm is used to treat the multi-body dynamics which inevitably ensues after fragmentation. Rate-dependent plasticity, heat conduction and thermal coupling are also accounted for in calculations. The properties and predictive ability of the model are exhibited in two case studies: spall tests and dynamic crack propagation in a double cantilever beam specimen. As an example of application of the theory, we simulate the experiments of Field (1988) involving the impact of alumina plates by steel pellets at different velocities. The calculated conical, lateral and radial fracture histories are found to be in good agreement with experiment.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/sc8na-ps868Computational micromechanics
https://resolver.caltech.edu/CaltechAUTHORS:20171213-151030227
Authors: {'items': [{'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'M.'}, 'orcid': '0000-0001-5877-4824'}]}
Year: 1996
DOI: 10.1007/BF00376129
Selected issues in computational micromechanics are reviewed, with particular emphasis on multiple-scale problems and micromechanical models of material behavior. Examples considered include: the bridging of atomistic and continuum scales, with application to nanoindentation and the brittle-to-ductile transition; the development of dislocation-based constitutive relations for pure metallic crystals and intermetallic compounds, with applications to fracture of single crystals and bicrystals; the simulation of non-planar three-dimensional crack growth at the microscale, with application to mixed mode I–III effective behavior and crack trapping and bridging in fiber-reinforced composites; and the direct micromechanical simulation of fragmentation of brittle solids and subsequent flow of the comminuted phase.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/hztvx-5qv92Mixed Atomistic and Continuum Models of Deformation in Solids
https://resolver.caltech.edu/CaltechAUTHORS:20160607-114810939
Authors: {'items': [{'id': 'Tadmor-E-B', 'name': {'family': 'Tadmor', 'given': 'E. B.'}}, {'id': 'Phillips-R', 'name': {'family': 'Phillips', 'given': 'Rob'}, 'orcid': '0000-0003-3082-2809'}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'M.'}, 'orcid': '0000-0001-5877-4824'}]}
Year: 1996
DOI: 10.1021/la9508912
The modeling of processes involving multiple length scales is an area of pressing concern, especially in problems such as nanoidentation and crack tip dislocation activity. In these cases, there is more than one characteristic dimension with the nanometer scale arising due to the presence of extended defects such as dislocations and a second length scale at least 2 orders of magnitude larger set by the scale of the indenter or the crack tip itself. To properly model such processes, both scales must be treated explicitly, which is normally beyond the scope of conventional atomistic and continuum analyses alike. This paper describes a quasicontinuum method which seizes upon the strengths of both atomistic and continuum techniques and allows for the simultaneous treatment of multiple scales. The method is based upon a continuum formulation of the problem of interest as a boundary value problem treated within the confines of the finite element method. We part company with traditional approaches by utilizing direct atomistic calculations as the source of the constitutive input used in the finite element analysis. The method is illustrated through application to the case of the structure and energetics of single dislocations. This case is a stringent test as it represents an extreme limit for the model since dislocation core structures are primarily dictated by lattice effects. It is then shown how the method may be applied to problems of tribological concern such as nanoindentation, where it is found that dislocations are initiated beneath the indenter.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/20avj-ts985Two-Dimensional Structure of Dynamic Boundary Layers and Shear Bands in Thermoviscoplastic Solids
https://resolver.caltech.edu/CaltechAUTHORS:20201023-182805542
Authors: {'items': [{'id': 'Gioia-Gustavo', 'name': {'family': 'Gioia', 'given': 'G.'}}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'M.'}, 'orcid': '0000-0001-5877-4824'}]}
Year: 1997
DOI: 10.1007/978-94-011-5642-4_15
Solids deforming at high rates often develop narrow layers of intense shearing. The realistic modeling of these problems requires consideration of large plastic deformations, rate sensitivity, hardening, heat convection and conduction, thermal softening and inertia effects. Fully nonlinear multidimensional solutions to problems of this nature are rare (see Wright and Walter, 1994, for a notable exception). However, the thinness of the shear layers of interest here makes possible certain approximations in the governing equations which facilitate the analytical characterization of the flow. The systematic use of these approximations results in a much simplified set of boundary layer equations which, in some cases, lend themselves to analytical treatment.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/zm9sh-jj354Delamination of Compressed Thin Films
https://resolver.caltech.edu/CaltechAUTHORS:20171213-102407537
Authors: {'items': [{'id': 'Gioia-Gustavo', 'name': {'family': 'Gioia', 'given': 'Gustavo'}}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'Michael'}, 'orcid': '0000-0001-5877-4824'}]}
Year: 1997
DOI: 10.1016/S0065-2156(08)70386-7
In this article, we specifically concern ourselves with the buckling-driven delamination mechanism, whereby a portion of the film buckles away from the substrate, thereby forming a blister (also termed buckle or wrinkle). Blisters may grow by interfacial fracture, a process which, under the appropriate conditions, may result in the catastrophic failure of the component. Blisters are often observed to adopt convoluted-even bizarre shapes and to fold into intricate patterns. A principal objective of this article is to review some recent developments based on the use of direct methods of the calculus of variations which have proven useful for understanding the mechanics of folding of thin films (Ortiz and Gioia, 1994). These developments are reviewed in Section III, which is extracted from the original publication. The remaining sections are devoted to the application of these principles to the problem of predicting the shape of thin-film blisters.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/4gb8w-gdf75Critical configurations for dislocation nucleation from crack tips
https://resolver.caltech.edu/CaltechAUTHORS:20171213-101246565
Authors: {'items': [{'id': 'Xu-G', 'name': {'family': 'Xu', 'given': 'G.'}}, {'id': 'Argon-A-S', 'name': {'family': 'Argon', 'given': 'A. S.'}}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'M.'}, 'orcid': '0000-0001-5877-4824'}]}
Year: 1997
DOI: 10.1080/01418619708205146
In the present paper, we analyse several activation configurations of embryonic dislocations nucleated from the tip of a cleavage crack. The activation configurations include nucleation on inclined planes, on oblique planes and on cleavage ledges and are treated within the classical framework of Peierls. A variational boundary integral method with an interplanar tension-shear potential developed earlier is used to solve for the saddle-point configurations of embryonic dislocation loops and their associated energies. Based on the assumption that the brittle-to-ductile transition in cleavage fracture is a nucleation-controlled process (as is expected to be the case in bcc transition metals such as α-Fe) the results of the calculations are used to estimate the brittle-to-ductile transition temperatures. It is concluded that only dislocation nucleation on cleavage ledges furnishes realistic values of the transition temperature. The homogeneous nucleation of dislocations on either inclined or oblique planes requires transition temperatures well above the melting point. This implies that nucleation of dislocations from a crack tip in intrinsically brittle crystals is only possible at local crack front heterogeneities such as cleavage ledges, and that the homogeneous nucleation of dislocations from a straight crack front is not possible. This conclusion is supported by the experimental observation that dislocation nucleation from a crack tip is a rare event which occurs preferentially at heterogeneities.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/vrwr4-v8g68Adaptive Lagrangian modelling of ballistic penetration of metallic targets
https://resolver.caltech.edu/CaltechAUTHORS:20171213-102621794
Authors: {'items': [{'id': 'Camacho-G-T', 'name': {'family': 'Camacho', 'given': 'G. T.'}}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'M.'}, 'orcid': '0000-0001-5877-4824'}]}
Year: 1997
DOI: 10.1016/S0045-7825(96)01134-6
A Lagrangian finite element model of ductile penetration is developed. Adaptive meshing is accorded a key role in following the large deformations which develop during penetration. An explicit contact/friction algorithm is used to treat the multi-body dynamics. Rate-dependent plasticity, heat conduction and thermal coupling are also accounted for in the calculations. The properties and predictive ability of the model are exhibited in several applications: copper rod impact, perforation of aluminum plates by conical-nosed projectiles and penetration of high-strength steel targets by WHA long rods. The simulations show close agreement with experimental observations and prior numerical results.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/m5tw1-e7327A micromechanical model of cyclic deformation and fatigue-crack nucleation in f.c.c. single crystals
https://resolver.caltech.edu/CaltechAUTHORS:20171213-101558135
Authors: {'items': [{'id': 'Repetto-E-A', 'name': {'family': 'Repetto', 'given': 'E. A.'}}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'M.'}, 'orcid': '0000-0001-5877-4824'}]}
Year: 1997
DOI: 10.1016/S1359-6454(96)00368-0
We have developed a micromechanical finite-element model of fatigue-crack initiation in nominally defect-free pure f.c.c. metals. The scale of observation envisioned is that of a single persistent slip band (PSB) intersecting the free surface of a single crystal. The nucleation event is identified with the formation of a sharp surface crack, whose subsequent growth obeys the laws of fracture mechanics. Basic building blocks of the theory are: a model of cyclic plasticity tailored to PSBs which accounts for the Bauschinger effect, PSB elongation due to pair annihilation, and vacancy generation; and a model of vacancy diffusion which accounts for pipe diffusion and the surface motion resulting from the outward flux of vacancies. Our numerical simulations show that this flux causes the surface to recede, which contributes to the formation of grooves at the PSB/matrix interface. Eventually, those grooves sharpen to form a mathematically sharp crack. The model thus provides a quantitative prediction of the number of cycles required for the nucleation of a fatigue crack.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/xaw3r-xeh38Computational modeling of damage evolution in unidirectional fiber reinforced ceramic matrix composites
https://resolver.caltech.edu/CaltechAUTHORS:20150226-105909974
Authors: {'items': [{'id': 'Walter-M-E', 'name': {'family': 'Walter', 'given': 'M. E.'}}, {'id': 'Ravichandran-G', 'name': {'family': 'Ravichandran', 'given': 'G.'}, 'orcid': '0000-0002-2912-0001'}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'M.'}, 'orcid': '0000-0001-5877-4824'}]}
Year: 1997
DOI: 10.1007/s004660050239
A finite element model for investigating damage evolution in brittle matrix composites was developed. This modeling is based on an axisymmetric unit cell composed of a fiber and its surrounding matrix. The unit cell was discretized into linearly elastic elements for the fiber and the matrix and cohesive elements which allow cracking in the matrix, fiber-matrix interface, and fiber. The cohesive elements failed according to critical stress and critical energy release rate criteria (in shear and/or in tension). The tension and shear aspects of failure were uncoupled. In order to obtain converged solutions for the axisymmetric composite unit cell problem, inertia and viscous damping were added to the formulation, and the resulting dynamic problem was solved implicitly using the Newmark Method. Parametric studies of the interface toughness and strength and the matrix toughness were performed. Details of the propagation of matrix cracks and the initiation of debonds were also observed.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/4vvb6-4vs59Effect of interfacial compliance on bifurcation of a layer bonded to a substrate
https://resolver.caltech.edu/CaltechAUTHORS:20171213-102809023
Authors: {'items': [{'id': 'Bigoni-D', 'name': {'family': 'Bigoni', 'given': 'D.'}}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'M.'}, 'orcid': '0000-0001-5877-4824'}, {'id': 'Needleman-A', 'name': {'family': 'Needleman', 'given': 'A.'}}]}
Year: 1997
DOI: 10.1016/S0020-7683(97)00025-5
The effect of interfacial compliance on the bifurcation of a layer bonded to a substrate is analyzed. The bifurcation problem is formulated for hyperelastic, layered solids in plane strain. Attention is then confined to the problem of a layer of finite thickness on a half-space. The layer and substrate are subject to plane strain compression, with the compression axis parallel to the bond line. The materials in the layer and in the half-space are taken to be incrementally linear, incompressible solids, with most results presented for Mooney-Rivlin and J2-deformation theory constitutive relations. The limiting case of an undeforming half-space is also considered. The interface between the layer and the substrate is characterized by an incrementally linear traction rate vs velocity jump relation, so that a characteristic length is introduced. A variety of bifurcation modes are possible depending on the layer thickness, on the constitutive parameters of the layer and the substrate, and on the interface compliance. These include shear band modes for the layer and the substrate, and diffuse instability modes involving deformation in the layer and the substrate. For a sufficiently compliant interface, the mode with the lowest critical stress is a long (relative to the layer thickness) wavelength plate-like bending mode for the layer.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/gr8nn-xjj43Nanomechanics of Defects in Solids
https://resolver.caltech.edu/CaltechAUTHORS:20171213-092247784
Authors: {'items': [{'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'Michael'}, 'orcid': '0000-0001-5877-4824'}, {'id': 'Phillips-R', 'name': {'family': 'Phillips', 'given': 'Rob'}, 'orcid': '0000-0003-3082-2809'}]}
Year: 1998
DOI: 10.1016/S0065-2156(08)70184-4
This chapter examines different aspects of nanomechanics of defects in solids. The methods by which the classical boundary-value problems of continuum mechanics can be imbued with atomistic content are reviewed. Microscopic modeling is founded on the fundamental assertion that beneath the details of observed macroscopic phenomenology, there is a set of microscopic processes which, when understood, rationalize the observed macroscopic behavior to the extent of enabling quantitative predictions. The microscopic simulation of materials is based on the evolution of degrees of freedom that are governed by the Schrodinger equation. It is found that either phenomenologically, or through explicit calculational strategies, the electronic degrees of freedom is implicitly subsumed in the effective pair potential. Once the pair potential has been identified, it is a straightforward matter to evaluate radial derivatives and the corresponding force fields. The energy associated with each distortion may be computed explicitly by recourse to direct atomistics. The contribution due to slip may be extracted by subtracting off the bulk elastic energy. As a result, the exact misfit energy is determined from atomistics. The cohesive-zone theories applied to fracture are also elaborated.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/5ck70-j6f85The 1998 Center for Simulation of Dynamic Response in Materials Annual Technical Report
https://resolver.caltech.edu/CaltechASCI:1998.032
Authors: {'items': [{'id': 'Goddard-W-A-III', 'name': {'family': 'Goddard', 'given': 'W. A.'}, 'orcid': '0000-0003-0097-5716'}, {'id': 'Meiron-D-I', 'name': {'family': 'Meiron', 'given': 'D. I.'}, 'orcid': '0000-0003-0397-3775'}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'M.'}, 'orcid': '0000-0001-5877-4824'}, {'id': 'Shepherd-J-E', 'name': {'family': 'Shepherd', 'given': 'J. E.'}, 'orcid': '0000-0003-3181-9310'}]}
Year: 1998
Introduction:
This annual report describes research accomplishments for FY 98 of the Center for Simulation
of Dynamic Response of Materials. The Center is constructing a virtual shock physics facility
in which the full three dimensional response of a variety of target materials can be computed
for a wide range of compressive, tensional, and shear loadings, including those produced by
detonation of energetic materials. The goals are to facilitate computation of a variety of
experiments in which strong shock and detonation waves are made to impinge on targets
consisting of various combinations of materials, compute the subsequent dynamic response
of the target materials, and validate these computations against experimental data.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/sz75e-ve313Quasicontinuum Models of Interfacial Structure and Deformation
https://resolver.caltech.edu/CaltechAUTHORS:SHEprl98
Authors: {'items': [{'id': 'Shenoy-V-B', 'name': {'family': 'Shenoy', 'given': 'V. B.'}}, {'id': 'Miller-R', 'name': {'family': 'Miller', 'given': 'R.'}}, {'id': 'Tadmor-E-B', 'name': {'family': 'Tadmor', 'given': 'E. B.'}}, {'id': 'Phillips-R', 'name': {'family': 'Phillips', 'given': 'R.'}, 'orcid': '0000-0003-3082-2809'}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'M.'}, 'orcid': '0000-0001-5877-4824'}]}
Year: 1998
DOI: 10.1103/PhysRevLett.80.742
Microscopic models of the interaction between grain boundaries (GBs) and both dislocations and cracks are of importance in understanding the role of microstructure in altering the mechanical properties of a material. A recently developed mixed atomistic and continuum method is reformulated to allow for the examination of the interactions between GBs, dislocations, and cracks. These calculations elucidate plausible microscopic mechanisms for these defect interactions and allow for the quantitative evaluation of critical parameters such as the force needed to induce GB migration.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/2ymz7-jfc17Fracture analysis of cellular materials: A strain gradient model
https://resolver.caltech.edu/CaltechAUTHORS:20171213-101038312
Authors: {'items': [{'id': 'Chen-Jun-Yuan', 'name': {'family': 'Chen', 'given': 'J. Y.'}}, {'id': 'Huang-Y', 'name': {'family': 'Huang', 'given': 'Y.'}}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'M.'}, 'orcid': '0000-0001-5877-4824'}]}
Year: 1998
DOI: 10.1016/S0022-5096(98)00006-4
A generalized continuum model is developed for cellular materials based on the equivalence of strain energy at the macro- and microscale. It is rather similar to the strain gradient theory, but has a well-defined characteristic length, namely, the cell size. The continuum model enables one to use powerful analytical methods to investigate fracture of cellular materials. The near-tip asymptotic fields and full-field solutions are obtained for cellular materials with hexagonal, triangular, or square lattice. Using the same strain-energy equivalence at the macro- and microscale, displacements and rotation of discrete cell walls are estimated from the continuum near-tip asymptotic fields. By postulating a maximum-tensile-stress failure criterion of cell walls, the fracture toughness of cellular materials is estimated to be proportional to the thickness h of cell walls and inversely proportional to √L, where L is the cell size. Moreover, the mixed-mode fracture toughness can be simply obtained from the fracture toughness in pure mode 1 and mode II, once the mode mixity is known. It is established that, with the same mass density, the hexagonal or triangular lattice in a cellular material can provide much higher fracture toughness than the square lattice.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/zsd3x-1rb65Quasicontinuum models of fracture and plasticity
https://resolver.caltech.edu/CaltechAUTHORS:20171213-100643529
Authors: {'items': [{'id': 'Miller-R', 'name': {'family': 'Miller', 'given': 'R.'}}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'M.'}, 'orcid': '0000-0001-5877-4824'}, {'id': 'Phillips-R', 'name': {'family': 'Phillips', 'given': 'R.'}, 'orcid': '0000-0003-3082-2809'}, {'id': 'Shenoy-V-B', 'name': {'family': 'Shenoy', 'given': 'V.'}}, {'id': 'Tadmor-E-B', 'name': {'family': 'Tadmor', 'given': 'E. B.'}}]}
Year: 1998
DOI: 10.1016/S0013-7944(98)00047-2
The development of modeling tools which allow for the simultaneous treatment of scales ranging from Ångstroms to microns has stood out as one of the main challenges in materials modeling. In this paper we discuss a formulation of the quasicontinuum (QC) method that allows for a treatment of internal interfaces, opening the possibility of simulating the interactions of cracks, dislocations and grain boundaries. The model is applied to crack tip deformation and is shown to account for both brittle fracture and crack tip dislocation emission. A key example of the method is the treatment of a crack propagating into a grain boundary which reveals both migration of the boundary and that the boundary is a source for the emission of dislocations.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/rv4td-vh423Quasicontinuum simulation of fracture at the atomic scale
https://resolver.caltech.edu/CaltechAUTHORS:MILmsmse98
Authors: {'items': [{'id': 'Miller-R', 'name': {'family': 'Miller', 'given': 'R.'}}, {'id': 'Tadmor-E-B', 'name': {'family': 'Tadmor', 'given': 'E. B.'}}, {'id': 'Phillips-R', 'name': {'family': 'Phillips', 'given': 'R.'}, 'orcid': '0000-0003-3082-2809'}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'M.'}, 'orcid': '0000-0001-5877-4824'}]}
Year: 1998
DOI: 10.1088/0965-0393/6/5/008
We study the problem of atomic scale fracture using the recently developed quasicontinuum method in which there is a systematic thinning of the atomic-level degrees of freedom in regions where they are not needed. Fracture is considered in two distinct settings. First, a study is made of cracks in single crystals, and second, we consider a crack advancing towards a grain boundary (GB) in its path. In the investigation of single crystal fracture, we evaluate the competition between simple cleavage and crack-tip dislocation emission. In addition, we examine the ability of analytic models to correctly predict fracture behaviour, and find that the existing analytical treatments are too restrictive in their treatment of nonlinearity near the crack tip. In the study of GB-crack interactions, we have found a number of interesting deformation mechanisms which attend the advance of the crack. These include the migration of the GB, the emission of dislocations from the GB, and deflection of the crack front along the GB itself. In each case, these mechanisms are rationalized on the basis of continuum mechanics arguments.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/24038-f3c11Energy-based model of compressive splitting in heterogeneous brittle solids
https://resolver.caltech.edu/CaltechAUTHORS:20131007-083528747
Authors: {'items': [{'id': 'Bhattacharya-K', 'name': {'family': 'Bhattacharya', 'given': 'K.'}, 'orcid': '0000-0003-2908-5469'}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'M.'}, 'orcid': '0000-0001-5877-4824'}, {'id': 'Ravichandran-G', 'name': {'family': 'Ravichandran', 'given': 'G.'}, 'orcid': '0000-0002-2912-0001'}]}
Year: 1998
DOI: 10.1016/S0022-5096(98)00026-X
Confined heterogeneous brittle solids loaded under far-field uniaxial compression are often observed to split along the loading axis. We develop a theory which accords this phenomenon an energetic interpretation : the solid splits because in so doing it reduces its total energy, defined as the sum of bulk strain energy and surface energy. The heterogeneous microstructure gives rise to a complex stress distribution in the intact solid. We show that the change in energy due to the release of the microstructural stresses may exceed the cost in fracture energy. Critical conditions for splitting are formulated for polycrystalline solids as a function of readily measurable material properties and applied stresses. The predictions of the theory are found to be in remarkably good agreement with experimental observations in ceramics and rocks.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/pxcgk-t0x90The influence of crack trapping on the toughness of fiber reinforced composites
https://resolver.caltech.edu/CaltechAUTHORS:20171213-095546620
Authors: {'items': [{'id': 'Xu-G', 'name': {'family': 'Xu', 'given': 'G.'}}, {'id': 'Bower-A-F', 'name': {'family': 'Bower', 'given': 'A. F.'}}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'M.'}, 'orcid': '0000-0001-5877-4824'}]}
Year: 1998
DOI: 10.1016/S0022-5096(98)00059-3
Frictional crack bridging is the main mechanism of toughening in brittle fiber\brittle matrix composites. In addition, the fibers may have a second beneficial effect : they tend to trap cracks propagating through the solid, and may cause them to arrest. The effectiveness of crack trapping increases with the fracture toughness of the interface between fibers and matrix. In contrast, crack bridging tends to be more effective if the interface between fibers and matrix has a low fracture toughness. In this paper, we study the competing effects of crack trapping and bridging in a brittle fiber\brittle matrix composite. A numerical method is used to predict in three dimensions the path of a crack as it bypasses rows of fibers in an ideally brittle matrix. The results are used to deduce the influence of crack trapping on the toughness of the composite. In addition, a simple model of frictional crack bridging is used to compare the relative effects of crack trapping and bridging. It is shown that, in general, the influence of bridging greatly exceeds that of trapping. However, if the fibers have a low tensile strength and there is a large resistance to sliding between fibers and matrix, crack trapping can be significant : in this case, the best composite toughness is achieved by using a tough interface between fibers and matrix.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/syf0f-rwq65A non-local formulation of the Peierls dislocation model
https://resolver.caltech.edu/CaltechAUTHORS:20171213-100338338
Authors: {'items': [{'id': 'Miller-R', 'name': {'family': 'Miller', 'given': 'Ron'}}, {'id': 'Phillips-R', 'name': {'family': 'Phillips', 'given': 'Rob'}, 'orcid': '0000-0003-3082-2809'}, {'id': 'Beltz-G', 'name': {'family': 'Beltz', 'given': 'Glen'}}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'Michael'}, 'orcid': '0000-0001-5877-4824'}]}
Year: 1998
DOI: 10.1016/S0022-5096(98)00057-X
Cohesive zone models provide an illuminating and tractable way to include constitutive non-linearity into continuum models of defects. Powerful insights have been gained by studying both dislocations and cracks using such analyses. Recent work has shown that as a result of the locality assumption present in such cohesive zone models, significant errors can be made in the treatment of defect energies. This paper aims to construct a non-local version of the Peierls–Nabarro model in which the atomic level stresses induced at the slip plane depend in a non-local way on the slip degrees of freedom. Our results should be seen as a demonstration in principle of how microscopic calculations can be used to construct insights into constitutive nonlocality. The non-local interplanar kernel used here is computed directly from atomistics and is used to evaluate both the structure and energetics of planar dislocations. The non-local formulation does not significantly change the dislocation core structure from that obtained with the local model, but the new formulation leads to significant improvements in the description of dislocation energetics for dislocations with planar cores.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/0gm5a-3j168Lagrangian finite element analysis of Newtonian fluid flows
https://resolver.caltech.edu/CaltechAUTHORS:20171213-095800584
Authors: {'items': [{'id': 'Radovitzky-R-A', 'name': {'family': 'Radovitzky', 'given': 'R.'}}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'M.'}, 'orcid': '0000-0001-5877-4824'}]}
Year: 1998
DOI: 10.1002/(SICI)1097-0207(19981030)43:4<607::AID-NME399>3.0.CO;2-N
A fully Lagrangian finite element method for the analysis of Newtonian flows is developed. The approach furnishes, in effect, a Lagrangian implementation of the compressible Navier–Stokes equations. As the flow proceeds, the mesh is maintained undistorted through continuous and adaptive remeshing of the fluid mass. The principal advantage of the present approach lies in the treatment of boundary conditions at material surfaces such as free boundaries, fluid/fluid or fluid/solid interfaces. In contrast to Eulerian approaches, boundary conditions are enforced at material surfaces ab initio and therefore require no special attention. Consistent tangents are obtained for Lagrangian implicit analysis of a Newtonian fluid flow which may exhibit compressibility effects. The accuracy of the approach is assessed by comparison of the solution for a sloshing problem with existing numerical results and its versatility demonstrated through a simulation of wave breaking. The finite element mesh is maintained undistorted throughout the computation by recourse to frequent and adaptive remeshing.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/m4mv5-rsz93Solid modeling aspects of three-dimensional fragmentation
https://resolver.caltech.edu/CaltechAUTHORS:20171213-100012816
Authors: {'items': [{'id': 'Pandolfi-A', 'name': {'family': 'Pandolfi', 'given': 'A.'}, 'orcid': '0000-0002-7084-7456'}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'M.'}, 'orcid': '0000-0001-5877-4824'}]}
Year: 1998
DOI: 10.1007/BF01201761
The ways in which the topology and geometry of a three-dimensional finite-element model may evolve as a consequence of fracture and fragmentation are enumerated, and the actions which may be taken in order to update the boundary representation of the solid so as to faithfully reflect that evolution are described. Arbitrary topological and geometrical evolution of a three-dimensional solid, not necessarily restricted to an evolution of its surface, are addressed. Solids are described by their boundary representation (BRep) and a surface and volume triangulation. Fracture processes are modeled by the introduction of cohesive elements at element interfaces. Simple rules are shown to enable the simulation of strikingly complex crack patterns. The scope and versatility of the approach is illustrated with the aid of selected examples of application.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/vfgjm-3ta60Determination of thin-film debonding parameters from telephone-cord measurements
https://resolver.caltech.edu/CaltechAUTHORS:20171213-100854187
Authors: {'items': [{'id': 'Gioia-Gustavo', 'name': {'family': 'Gioia', 'given': 'G.'}}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'M.'}, 'orcid': '0000-0001-5877-4824'}]}
Year: 1998
DOI: 10.1016/S1359-6454(97)00211-5
Methods are put forward for the determination of the fracture energy and kinetic coefficient of thin film/substrate interfaces from measurements performed on telephone cord blisters. This work is based on a previously proposed model for the characterization of debonding features in compressed thin films. The advantages of the proposed methods stem from the following facts concerning telephone cord blisters: (i) they are spontaneous debonding features, and therefore more amenable than artificially contrived features to yield realistic debonding parameters; (ii) they are very commonly observed in compressed thin films; (iii) as revealed by our model, their boundaries are characterized by a constant fracture mode mixity, and (iv) the driving force for debonding equals the fracture energy everywhere on their boundaries.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/cxr9h-fyb67Finite element simulation of ring expansion and fragmentation: The capturing of length and time scales through cohesive models of fracture
https://resolver.caltech.edu/CaltechAUTHORS:20171213-091247239
Authors: {'items': [{'id': 'Pandolfi-A', 'name': {'family': 'Pandolfi', 'given': 'A.'}, 'orcid': '0000-0002-7084-7456'}, {'id': 'Krysl-P', 'name': {'family': 'Krysl', 'given': 'P.'}}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'M.'}, 'orcid': '0000-0001-5877-4824'}]}
Year: 1999
DOI: 10.1023/A:1018672922734
The expanding ring test of Grady and Benson (1983) is taken as a convenient yet challenging validation problem for assessing the fidelity of cohesive models in situations involving ductile dynamical fracture. Attention has been restricted to 1100-0 aluminum samples. Fracture has been modelled by recourse to an irreversible cohesive law embedded into cohesive elements. The finite element model is three-dimensional and fully Lagrangian. In order to limit the extent of deformation-induced distortion, we resort to continuous adaptive remeshing. The cohesive behavior of the material is assumed to be rate independent and, consequently, all rate effects predicted by the calculations are due to inertia and the rate dependency in plastic deformation. The numerical simulations are revealed to be highly predictive of a number of observed features, including: the number of dominant and arrested necks; the fragmentation patterns; the dependence of the number of fragments and the fracture strain on the expansion speed; and the distribution of fragment sizes at fixed expansion speed.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/1qmh3-27d93The 1999 Center for Simulation of Dynamic Response in Materials Annual Technical Report
https://resolver.caltech.edu/CaltechASCI:1999.033
Authors: {'items': [{'id': 'Aivazis-Michael-A-G', 'name': {'family': 'Aivazis', 'given': 'Michael'}}, {'id': 'Goddard-W-A-III', 'name': {'family': 'Goddard', 'given': 'Bill'}, 'orcid': '0000-0003-0097-5716'}, {'id': 'Meiron-D-I', 'name': {'family': 'Meiron', 'given': 'Dan'}, 'orcid': '0000-0003-0397-3775'}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'Michael'}, 'orcid': '0000-0001-5877-4824'}, {'id': 'Pool-James-C-T', 'name': {'family': 'Pool', 'given': 'James C. T.'}}, {'id': 'Shepherd-J-E', 'name': {'family': 'Shepherd', 'given': 'Joe'}, 'orcid': '0000-0003-3181-9310'}]}
Year: 1999
Introduction:
This annual report describes research accomplishments for FY 99 of the Center
for Simulation of Dynamic Response of Materials. The Center is constructing a
virtual shock physics facility in which the full three dimensional response of a
variety of target materials can be computed for a wide range of compressive, ten-
sional, and shear loadings, including those produced by detonation of energetic
materials. The goals are to facilitate computation of a variety of experiments
in which strong shock and detonation waves are made to impinge on targets
consisting of various combinations of materials, compute the subsequent dy-
namic response of the target materials, and validate these computations against
experimental data.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/rx3ef-rng15A Finite Element Study of Electromagnetic Riveting
https://resolver.caltech.edu/CaltechAUTHORS:20171213-090727121
Authors: {'items': [{'id': 'Repetto-E-A', 'name': {'family': 'Repetto', 'given': 'E. A.'}}, {'id': 'Radovitzky-R-A', 'name': {'family': 'Radovitzky', 'given': 'R.'}}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'M.'}, 'orcid': '0000-0001-5877-4824'}, {'id': 'Lundquist-R-C', 'name': {'family': 'Lundquist', 'given': 'R. C.'}}, {'id': 'Sandstrom-D-R', 'name': {'family': 'Sandstrom', 'given': 'D. R.'}}]}
Year: 1999
DOI: 10.1115/1.2830576
Electromagnetic riveting, used in some aerospace assembly processes, involves rapid deformation, leading to the finished rivet configuration. Analysis of this process is described for the case of an aluminum rivet joining typical aluminum structural elements. The analysis is based on a finite element method that includes the effects of heating, due to rapid plastic deformation of the material, on the material properties. Useful details of material deformation and thermal history and the final rivet and structure configuration and states of stress and strain are obtained. These results have significant implications in the design, implementation, and improvement of practical fastening processes in the aerospace industry.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/j0tq6-dm030Nonconvex energy minimization and dislocation structures in ductile single crystals
https://resolver.caltech.edu/CaltechAUTHORS:20171213-092048666
Authors: {'items': [{'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'M.'}, 'orcid': '0000-0001-5877-4824'}, {'id': 'Repetto-E-A', 'name': {'family': 'Repetto', 'given': 'E. A.'}}]}
Year: 1999
DOI: 10.1016/S0022-5096(97)00096-3
Plastically deformed crystals are often observed to develop intricate dislocation patterns such as the labyrinth, mosaic, fence and carpet structures. In this paper, such dislocation structures are given an energetic interpretation with the aid of direct methods of the calculus of variations. We formulate the theory in terms of deformation fields and regard the dislocations as manifestations of the incompatibility of the plastic deformation gradient field. Within this framework, we show that the incremental displacements of inelastic solids follow as minimizers of a suitably defined pseudoelastic energy function. In crystals exhibiting latent hardening, the energy function is nonconvex and has wells corresponding to single-slip deformations. This favors microstructures consisting locally of single slip. Deformation microstructures constructed in accordance with this prescription are shown to be in correspondence with several commonly observed dislocation structures. Finally, we show that a characteristic length scale can be built into the theory by taking into account the self energy of the dislocations. The extended theory leads to scaling laws which appear to be in good qualitative and quantitative agreement with observation.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/t6tsd-qn557A continuum model of kinetic roughening and coarsening in thin films
https://resolver.caltech.edu/CaltechAUTHORS:20171213-091830314
Authors: {'items': [{'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'M.'}, 'orcid': '0000-0001-5877-4824'}, {'id': 'Repetto-E-A', 'name': {'family': 'Repetto', 'given': 'E. A.'}}, {'id': 'Si-H', 'name': {'family': 'Si', 'given': 'H.'}}]}
Year: 1999
DOI: 10.1016/S0022-5096(98)00102-1
We present a phenomenological continuum model of film growth based on a series expansion of the deposition flux in powers of the profile gradient, consideration of the energetics of the film–substrate interface and the enforcement of Onsagers reciprocity relations. The interfacial term, which operates at very small thicknesses, is nonconservative and breaks the ±h symmetry of the remaining terms in the kinetic equation. By virtue of this term, very thin flat films are predicted to be stable within an appropriate range of parameters, and to loose stability and become rough at a well-defined critical thickness. This instability effectively provides an island nucleation mechanism. For thick films, the rate processes envisioned in the model favor a characteristic slope for the film profile, a feature which is in keeping with observation for a number of systems including YBCO films. The enforcement of reciprocity ensures the existance of a kinetic potential and enables the use of direct methods of the calculus of variations. Within this framework, we provide an explicit construction for the coarsening of the film profile based on a sharp interface approximation. The construction predicts characteristic exponents for the evolution of grain size and film roughness which are in close agreement with the observational evidence for YBCO. The predictions of the construction are also born out by numerical tests.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/x3b4w-5md77Finite-deformation irreversible cohesive elements for three-dimensional crack-propagation analysis
https://resolver.caltech.edu/CaltechAUTHORS:20171213-094245696
Authors: {'items': [{'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'M.'}, 'orcid': '0000-0001-5877-4824'}, {'id': 'Pandolfi-A', 'name': {'family': 'Pandolfi', 'given': 'A.'}, 'orcid': '0000-0002-7084-7456'}]}
Year: 1999
DOI: 10.1002/(SICI)1097-0207(19990330)44:9<1267::AID-NME486>3.0.CO;2-7
We develop a three-dimensional finite-deformation cohesive element and a class of irreversible cohesive laws which enable the accurate and efficient tracking of dynamically growing cracks. The cohesive element governs the separation of the crack flanks in accordance with an irreversible cohesive law, eventually leading to the formation of free surfaces, and is compatible with a conventional finite element discretization of the bulk material. The versatility and predictive ability of the method is demonstrated through the simulation of a drop-weight dynamic fracture test similar to those reported by Zehnder and Rosakis. The ability of the method to approximate the experimentally observed crack-tip trajectory is particularly noteworthy.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/pryf8-c1t67A multiscattering series for impedance tomography in layered media
https://resolver.caltech.edu/CaltechAUTHORS:BORip99
Authors: {'items': [{'id': 'Borcea-L', 'name': {'family': 'Borcea', 'given': 'Liliana'}}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'Michael'}, 'orcid': '0000-0001-5877-4824'}]}
Year: 1999
DOI: 10.1088/0266-5611/15/2/011
We introduce an inversion algorithm for tomographic images of layered media. The algorithm is based on a multiscattering series expansion of the Green function that, unlike the Born series, converges unconditionally. Our inversion algorithm obtains images of the medium that improves iteratively as we use more and more terms in the multiscattering series. We present the derivation of the multiscattering series, formulate the inversion algorithm and demonstrate its performance through numerical experiments.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/tktac-0m398The variational formulation of viscoplastic constitutive updates
https://resolver.caltech.edu/CaltechAUTHORS:20171213-091546263
Authors: {'items': [{'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'M.'}, 'orcid': '0000-0001-5877-4824'}, {'id': 'Stainier-Laurent', 'name': {'family': 'Stainier', 'given': 'L.'}, 'orcid': '0000-0001-6719-6616'}]}
Year: 1999
DOI: 10.1016/S0045-7825(98)00219-9
We present a class of constitutive updates for general viscoplastic solids including such aspects of material behavior as finite elastic and plastic deformations, non-Newtonian viscosity, rate-sensitivity and arbitrary flow and hardening rules. The distinguishing characteristic of the proposed constitutive updates is that, by construction, the corresponding incremental stress—strain relations derive from a pseudo-elastic strain-energy density. This, in turn, confers the incremental boundary value problem a variational structure. In particular, the incremental deformation mapping follows from a minimum principle. This minimum principle may conveniently be taken as a basis for error estimation and mesh adaption. The accuracy and robustness of the variational constitutive updates is demonstrated with the aid of convergence tests involving the finitely-deforming Mises solid and ductile single crystals. The ability of the updates to resolve the complex patterns of slip activity which arise in the latter application is particularly noteworthy.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/tdt3n-82b63Error estimation and adaptive meshing in strongly nonlinear dynamic problems
https://resolver.caltech.edu/CaltechAUTHORS:20171213-090926881
Authors: {'items': [{'id': 'Radovitzky-R-A', 'name': {'family': 'Radovitzky', 'given': 'R.'}}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'M.'}, 'orcid': '0000-0001-5877-4824'}]}
Year: 1999
DOI: 10.1016/S0045-7825(98)00230-8
We present work aimed at developing a general framework for mesh adaption in strongly nonlinear, possibly dynamic, problems. We begin by showing that the solutions of the incremental boundary value problem for a wide class of materials, including nonlinear elastic materials, compressible Newtonian fluids and viscoplastic solids, obey a minimum principle, provided that the constitutive updates are formulated appropriately. This minimum principle can be taken as a basis for asymptotic error estimation. In particular, we chose to monitor the error of a lower-order projection of the finite element solution. The optimal mesh size distribution then follows from a posteriori error indicators which are purely local, i.e. can be computed element-by-element. We demonstrate the robustness and versatility of the computational framework with the aid of convergence studies and selected examples of application.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/xr7r2-3es81Elastoplastic finite element analysis of three-dimensional fatigue crack growth in aluminum shafts subjected to axial loading
https://resolver.caltech.edu/CaltechAUTHORS:20171213-094949787
Authors: {'items': [{'id': 'de-Andrés-A', 'name': {'family': 'de-Andrés', 'given': 'A.'}}, {'id': 'Pérez-J-L', 'name': {'family': 'Pérez', 'given': 'J. L.'}}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'M.'}, 'orcid': '0000-0001-5877-4824'}]}
Year: 1999
DOI: 10.1016/S0020-7683(98)00059-6
We have developed a three-dimensional cohesive element and a class of irreversible cohesive laws which enable the accurate and efficient tracking of three-dimensional fatigue crack fronts and the calculation of the attendant fatigue life curves. The cohesive element governs the separation of the crack flanks in accordance with an irreversible cohesive law, eventually leading to the formation of free surfaces, and is compatible with a conventional finite element discretization of the bulk material. The versatility and predictive ability of the method is demonstrated through the simulation of the axial fatigue tests of aluminum shafts of Thompson and Sheppard, 1992a, Thompson and Sheppard, 1992b, Thompson and Sheppard, 1992c . The ability of the method to reproduce the experimentally observed progression of beachmarks and fatigue life curves is particularly noteworthy.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/r1j3p-zp719Plastic Yielding as a Phase Transition
https://resolver.caltech.edu/CaltechAUTHORS:20171213-094627254
Authors: {'items': [{'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'M.'}, 'orcid': '0000-0001-5877-4824'}]}
Year: 1999
DOI: 10.1115/1.2791048
A statistical mechanical theory of forest hardening is developed in which yielding arises as a phase transition. For simplicity, we consider the case of a single dislocation loop moving on a slip plane through randomly distributed forest dislocations, which we treat as point obstacles. The occurrence of slip at the sites occupied by these obstacles is assumed to require the expenditure of a certain amount of work commensurate with the strength of the obstacle. The case of obstacles of infinite strength is treated in detail. We show that the behavior of the dislocation loop as it sweeps the slip plane under the action of a resolved shear stress is identical to that of a lattice gas, or, equivalently, to that of the two-dimensional spin-1/2 Ising model. In particular, there exists a critical temperature T_c below which the system exhibits a yield point, i.e., the slip strain increases sharply when the applied resolved shear stress attains a critical value. Above the critical temperature the yield point disappears and the slip strain depends continuously on the applied stress. The critical exponents, which describe the behavior of the system near the critical temperature, coincide with those of the two-dimensional spin-1/2 Ising model.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/x5n33-wk545Nanoindentation and incipient plasticity
https://resolver.caltech.edu/CaltechAUTHORS:TADjmr99
Authors: {'items': [{'id': 'Tadmor-E-B', 'name': {'family': 'Tadmor', 'given': 'E.B.'}}, {'id': 'Miller-R', 'name': {'family': 'Miller', 'given': 'R.'}}, {'id': 'Phillips-R', 'name': {'family': 'Phillips', 'given': 'R.'}, 'orcid': '0000-0003-3082-2809'}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'M.'}, 'orcid': '0000-0001-5877-4824'}]}
Year: 1999
This paper presents a large-scale atomic resolution simulation of nanoindentation into a thin aluminum film using the recently introduced quasicontinuum method. The purpose of the simulation was to study the initial stages of plastic deformation under the action of an indenter. Two different crystallographic orientations of the film and two different indenter geometries (a rectangular prism and a cylinder) were studied. We obtained both macroscopic load versus indentation depth curves, as well as microscopic quantities, such as the Peierls stress and density of geometrically necessary dislocations beneath the indenter. In addition, we obtain detailed information regarding the atomistic mechanisms responsible for the macroscopic curves. A strong dependence on geometry and orientation is observed. Two different microscopic mechanisms are observed to accommodate the applied loading: (i) nucleation and subsequent propagation into the bulk of edge dislocation dipoles and (ii) deformation twinning.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/agdhm-50x60The atomistic structure and energy of nascent dislocation loops
https://resolver.caltech.edu/CaltechAUTHORS:SHEmsmse99
Authors: {'items': [{'id': 'Shenoy-V-B', 'name': {'family': 'Shenoy', 'given': 'V. B.'}}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'M.'}, 'orcid': '0000-0001-5877-4824'}, {'id': 'Phillips-R', 'name': {'family': 'Phillips', 'given': 'R.'}, 'orcid': '0000-0003-3082-2809'}]}
Year: 1999
DOI: 10.1088/0965-0393/7/4/309
An harmonic lattice theory is used, in conjunction with Mura's theory of eigendistorsions, to study the structure and energetics of nascent dislocation loops in face-centred-cubic (FCC) crystals. An analytical expression for the activation energies of such loops is derived. The results obtained herein indicate that thermal activation of small dislocation loops is possible at high stress levels such as those found in the vicinity of a crack tip. The implications of these results in understanding phenomena such as the brittle-ductile transition are discussed.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/vvwwb-ncj77Symplectic-energy-momentum preserving variational integrators
https://resolver.caltech.edu/CaltechAUTHORS:KANjmp99
Authors: {'items': [{'id': 'Kane-C', 'name': {'family': 'Kane', 'given': 'C.'}}, {'id': 'Marsden-J-E', 'name': {'family': 'Marsden', 'given': 'J. E.'}}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'M.'}, 'orcid': '0000-0001-5877-4824'}]}
Year: 1999
DOI: 10.1063/1.532892
The purpose of this paper is to develop variational integrators for conservative mechanical systems that are symplectic and energy and momentum conserving. To do this, a space–time view of variational integrators is employed and time step adaptation is used to impose the constraint of conservation of energy. Criteria for the solvability of the time steps and some numerical examples are given.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/hhgqy-wmf82Hierarchical models of plasticity: dislocation nucleation and interaction
https://resolver.caltech.edu/CaltechAUTHORS:PHImsmse99
Authors: {'items': [{'id': 'Phillips-R', 'name': {'family': 'Phillips', 'given': 'Rob'}, 'orcid': '0000-0003-3082-2809'}, {'id': 'Rodney-D', 'name': {'family': 'Rodney', 'given': 'David'}}, {'id': 'Shenoy-V-B', 'name': {'family': 'Shenoy', 'given': 'Vivek'}}, {'id': 'Tadmor-E-B', 'name': {'family': 'Tadmor', 'given': 'Ellad'}}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'Michael'}, 'orcid': '0000-0001-5877-4824'}]}
Year: 1999
DOI: 10.1088/0965-0393/7/5/309
One avenue being pursued in the development of dislocation-based models of plasticity is the explicit simulation of the dynamics of dislocations, based on the recognition that such dislocations are the carriers of plasticity. The construction of models of dislocation dynamics requires insights into both the nucleation and interaction of dislocations, many of the details of which fall outside the domain of validity of the linear theory of elasticity. The aim of the present paper is to show how preliminary steps have been made to elucidate the mechanisms of dislocation nucleation and interaction, and to illustrate how such information can be imported into explicit models of dislocation dynamics. This effort reflects, in part, the research program of Gilles Canova, to whom the present volume is dedicated and to whom the authors dedicate this paper.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/b9z9d-qw090Finite element analysis of nonsmooth contact
https://resolver.caltech.edu/CaltechAUTHORS:20100819-144015326
Authors: {'items': [{'id': 'Kane-C', 'name': {'family': 'Kane', 'given': 'C.'}}, {'id': 'Repetto-E-A', 'name': {'family': 'Repetto', 'given': 'E. A.'}}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'M.'}, 'orcid': '0000-0001-5877-4824'}, {'id': 'Marsden-J-E', 'name': {'family': 'Marsden', 'given': 'J. E.'}}]}
Year: 1999
DOI: 10.1016/S0045-7825(99)00034-1
This work develops robust contact algorithms capable of dealing with complex contact situations involving several bodies with corners. Amongst the mathematical tools we bring to bear on the problem is nonsmooth analysis, following Clarke (F.H. Clarke. Optimization and nonsmooth analysis. John Wiley and Sons, New York, 1983.). We specifically address contact geometries for which both the use of normals and gap functions have difficulties and therefore precludes the application of most contact algorithms proposed to date. Such situations arise in applications such as fragmentation, where angular fragments undergo complex collision sequences before they scatter. We demonstrate the robustness and versatility of the nonsmooth contact algorithms developed in this paper with the aid of selected two and three-dimensional applications.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/q4n16-1k168Hierarchical modeling in the mechanics of materials
https://resolver.caltech.edu/CaltechAUTHORS:20171212-153930662
Authors: {'items': [{'id': 'Tadmor-E-B', 'name': {'family': 'Tadmor', 'given': 'E. B.'}}, {'id': 'Phillips-R', 'name': {'family': 'Phillips', 'given': 'R.'}, 'orcid': '0000-0003-3082-2809'}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'M.'}, 'orcid': '0000-0001-5877-4824'}]}
Year: 2000
DOI: 10.1016/S0020-7683(99)00095-5
Many problems in the mechanics of materials involve the operation of either multiple spatial or temporal scales simultaneously. As a result, an important thrust of recent work in this area has been the development of methods allowing for the consideration of multiple scales simultaneously. In this paper, we examine hierarchical approaches to modeling problems of this kind with special reference to the way in which information can be fed from one scale to the next in models of plasticity.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/4b7gy-xfe58Triangular composite finite elements
https://resolver.caltech.edu/CaltechAUTHORS:20171213-090121889
Authors: {'items': [{'id': 'Guo-Y', 'name': {'family': 'Guo', 'given': 'Yong'}}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'Michael'}, 'orcid': '0000-0001-5877-4824'}, {'id': 'Belytschko-T', 'name': {'family': 'Belytschko', 'given': 'Ted'}}, {'id': 'Repetto-E-A', 'name': {'family': 'Repetto', 'given': 'Eduardo A.'}}]}
Year: 2000
DOI: 10.1002/(SICI)1097-0207(20000110/30)47:1/3<287::AID-NME772>3.0.CO;2-M
Composite triangles consisting of four three-node triangles originally proposed by Camacho and Ortiz are studied. It is shown that the original element does not satisfy the Babuška–Brezzi condition nor pass the patch test. Remedies for these shortcomings are described. It is shown that the resulting elements are very robust for large deformation problems. In addition, composite triangular elements generated from four-node quadrilaterals are briefly examined; their accuracy is found to be not as good as the composite triangles.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/dp1tm-5cr37Finite element simulation of dynamic fracture and fragmentation of glass rods
https://resolver.caltech.edu/CaltechAUTHORS:20171212-155115498
Authors: {'items': [{'id': 'Repetto-E-A', 'name': {'family': 'Repetto', 'given': 'E. A.'}}, {'id': 'Radovitzky-R-A', 'name': {'family': 'Radovitzky', 'given': 'R.'}}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'M.'}, 'orcid': '0000-0001-5877-4824'}]}
Year: 2000
DOI: 10.1016/S0045-7825(99)00208-X
The aim of this communication is to provide further illustration of the feasibility of simulating fragmentation explicitly, crack by crack. Cracks are allowed to form and propagate along element boundaries in accordance with a tension-shear cohesive-law model. No topological restrictions are imposed on the cracks, which may nucleate at the surface or in the interior, branch, and link up to form fragments. As the fragments scatter, the complex collisions which they undergo and the attendant frictional interactions are also resolved explicitly by recourse to a contact algorithm. We present a new model of radial cracking which permits the calculation of normal impact to proceed in an axisymmetric mode, without artificially constraining fragment rotation within meridional planes. The scope and versatility of the approach is demonstrated by simulating the propagation of failure waves in glass rods subjected to impact. Key aspects of the observational evidence, such as the failure wave speeds, are correctly predicted by the simulations.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/q8tkw-rfa10A virtual test facility for simulating the dynamic response of materials
https://resolver.caltech.edu/CaltechAUTHORS:20180717-150515004
Authors: {'items': [{'id': 'Aivazis-M', 'name': {'family': 'Aivazis', 'given': 'Michael'}}, {'id': 'Goddard-W-A-III', 'name': {'family': 'Goddard', 'given': 'William A.'}, 'orcid': '0000-0003-0097-5716'}, {'id': 'Meiron-D-I', 'name': {'family': 'Meiron', 'given': 'Dan'}, 'orcid': '0000-0003-0397-3775'}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'Michael'}, 'orcid': '0000-0001-5877-4824'}, {'id': 'Pool-J-C-T', 'name': {'family': 'Pool', 'given': 'James'}}, {'id': 'Shepherd-J-E', 'name': {'family': 'Shepherd', 'given': 'Joseph'}, 'orcid': '0000-0003-3181-9310'}]}
Year: 2000
DOI: 10.1109/5992.825748
The goal of the Caltech Center is to construct a virtual test facility (VTF): a problem solving environment for full 3D parallel simulation of the dynamic response of materials undergoing compression due to shock waves. The objective is to design a software environment that will: facilitate computation in a variety of experiments in which strong shock waves impinge on targets comprising various combinations of materials; compute the target materials' subsequent dynamic response; and validate these computations against experimental data. Successfully constructing such a facility requires modeling of the highest accuracy. We must model at atomistic scales to correctly describe the material properties of the target materials and high explosives; at intermediate (meso) scales to understand the micromechanical response of the target materials; and at continuum scales to capture properly the evolution of macroscopic effects. The article outlines such a test facility. Although it is a very simplified version of the facilities found in a shock-compression laboratory, our VTF includes all the basic features, offering a problem solving environment for validating experiments and facilitating further development of simulation capabilities.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/eatbe-m4m92Subdivision surfaces: a new paradigm for thin-shell finite-element analysis
https://resolver.caltech.edu/CaltechAUTHORS:20171213-090454075
Authors: {'items': [{'id': 'Cirak-F', 'name': {'family': 'Cirak', 'given': 'Fehmi'}}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'Michael'}, 'orcid': '0000-0001-5877-4824'}, {'id': 'Schröder-P', 'name': {'family': 'Schröder', 'given': 'Peter'}, 'orcid': '0000-0002-0323-7674'}]}
Year: 2000
DOI: 10.1002/(SICI)1097-0207(20000430)47:12<2039::AID-NME872>3.0.CO;2-1
We develop a new paradigm for thin-shell finite-element analysis based on the use of subdivision surfaces for (i) describing the geometry of the shell in its undeformed configuration, and (ii) generating smooth interpolated displacement fields possessing bounded energy within the strict framework of the Kirchhoff–Love theory of thin shells. The particular subdivision strategy adopted here is Loop's scheme, with extensions such as required to account for creases and displacement boundary conditions. The displacement fields obtained by subdivision are H2 and, consequently, have a finite Kirchhoff–Love energy. The resulting finite elements contain three nodes and element integrals are computed by a one-point quadrature. The displacement field of the shell is interpolated from nodal displacements only. In particular, no nodal rotations are used in the interpolation. The interpolation scheme induced by subdivision is non-local, i.e. the displacement field over one element depend on the nodal displacements of the element nodes and all nodes of immediately neighbouring elements. However, the use of subdivision surfaces ensures that all the local displacement fields thus constructed combine conformingly to define one single limit surface. Numerical tests, including the Belytschko et al. [10] obstacle course of benchmark problems, demonstrate the high accuracy and optimal convergence of the method.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/kw8e6-wxc29Frictional Collisions Off Sharp Objects
https://resolver.caltech.edu/CaltechAUTHORS:20100819-113606661
Authors: {'items': [{'id': 'Kane-C', 'name': {'family': 'Kane', 'given': 'C.'}}, {'id': 'Marsden-J-E', 'name': {'family': 'Marsden', 'given': 'J. E.'}}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'M.'}, 'orcid': '0000-0001-5877-4824'}, {'id': 'Pandolfi-A', 'name': {'family': 'Pandolfi', 'given': 'A.'}, 'orcid': '0000-0002-7084-7456'}]}
Year: 2000
This work develops robust contact algorithms capable of dealing with multibody nonsmooth contact
geometries for which neither normals nor gap functions can be defined. Such situations arise
in the early stage of fragmentation when a number of angular fragments undergo complex collision
sequences before eventually scattering. Such situations precludes the application of most contact
algorithms proposed to date.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/dfvmy-se793Three dimensional cohesive-element analysis and experiments of dynamic fracture in C300 steel
https://resolver.caltech.edu/CaltechAUTHORS:20171213-085245977
Authors: {'items': [{'id': 'Pandolfi-A', 'name': {'family': 'Pandolfi', 'given': 'A.'}, 'orcid': '0000-0002-7084-7456'}, {'id': 'Guduru-P-R', 'name': {'family': 'Guduru', 'given': 'P. R.'}}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'M.'}, 'orcid': '0000-0001-5877-4824'}, {'id': 'Rosakis-A-J', 'name': {'family': 'Rosakis', 'given': 'A. J.'}, 'orcid': '0000-0003-0559-0794'}]}
Year: 2000
DOI: 10.1016/S0020-7683(99)00155-9
The dynamic drop-weight test is taken as a convenient basis for assessing the fidelity and predictive ability of cohesive models of fracture in applications involving dynamic crack growth. In the experimental phase of the study, coherent gradient sensing (CGS) has been used to study dynamic fracture in C300 maraging steel. The specimens were subjected to three-point bend impact loading under a drop weight tower. High-speed photographs of the CGS interferograms were analyzed to determine the crack tip location, the velocity and the dynamic fracture toughness as a function of time. Post-mortem examination of the specimens revealed the fractography of the fracture surfaces, including the development of shear lips. In a parallel numerical phase of the study, fracture has been modeled by recourse to an irreversible cohesive law embedded into cohesive elements. These cohesive elements govern all aspects of the separation and closure of the incipient cracks. The cohesive behavior of the material is assumed to be rate independent. The finite element model is three dimensional and consists of quadratic ten-noded tetrahedra. The numerical simulations have proven highly predictive of a number of observed features, including: the crack growth initiation time; the trajectory of the propagating crack tip; and the formation of shear lips near the lateral surfaces. The simulations therefore establish the feasibility of using cohesive models of fracture and cohesive elements to predict dynamic crack-growth initiation and propagation in three dimensions.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/ym4hp-s8w59Tetrahedral mesh generation based on node insertion in crystal lattice arrangements and advancing-front-Delaunay triangulation
https://resolver.caltech.edu/CaltechAUTHORS:20171213-084912550
Authors: {'items': [{'id': 'Radovitzky-R-A', 'name': {'family': 'Radovitzky', 'given': 'R.'}}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'M.'}, 'orcid': '0000-0001-5877-4824'}]}
Year: 2000
DOI: 10.1016/S0045-7825(99)00339-4
A method of unstructured technical mesh generation for general three-dimensional domains is presented. A conventional boundary representation is adopted as the basis for the description of solids with evolving geometry and topology. The geometry of the surfaces is represented either analytically or by piecewise polynominal interpolation. A preliminary surface mesh is generated by an advancing-front method, with the nodes inserted by hard-sphere packing in physical space in accordance with a prescribed mesh density. Interior nodes are inserted in a face-centered-cubic (FCC) crystal lattice arrangements coupled to octree spatial subdivision, with the local lattice parameter determined by a prespecified nodal density function. Prior to triangulation of the volume, the preliminary surface mesh is preprocessed by a combination of local transformations and subdivisions in order to guarantee that the surface triangulation be a subcomplex of the volume Delaunay triangulation. A joint Delaunay triangulation of the interior and boundary nodes which preserves the modified surface mesh is then constructed via an advancing-front approach. The resulting mesh is finally improved upon by the application of local transformations. The overall time complexity of the mesher is O(N log N). The robustness and versatility of the approach, as well as the good quality of the resulting meshes, is demostrated with the aid of selected examples.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/ync5y-wc549Three-dimensional finite-element simulation of the dynamic Brazilian tests on concrete cylinders
https://resolver.caltech.edu/CaltechAUTHORS:20171212-154848578
Authors: {'items': [{'id': 'Ruiz-G', 'name': {'family': 'Ruiz', 'given': 'Gonzalo'}}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'Michael'}, 'orcid': '0000-0001-5877-4824'}, {'id': 'Pandolfi-A', 'name': {'family': 'Pandolfi', 'given': 'Anna'}, 'orcid': '0000-0002-7084-7456'}]}
Year: 2000
DOI: 10.1002/(SICI)1097-0207(20000710)48:7<963::AID-NME908>3.0.CO;2-X
We investigate the feasibility of using cohesive theories of fracture, in conjunction with the direct simulation of fracture and fragmentation, in order to describe processes of tensile damage and compressive crushing in concrete specimens subjected to dynamic loading. We account explicitly for microcracking, the development of macroscopic cracks and inertia, and the effective dynamic behaviour of the material is predicted as an outcome of the calculations. The cohesive properties of the material are assumed to be rate-independent and are therefore determined by static properties such as the static tensile strength. The ability of model to predict the dynamic behaviour of concrete may be traced to the fact that cohesive theories endow the material with an intrinsic time scale. The particular configuration contemplated in this study is the Brazilian cylinder test performed in a Hopkinson bar. Our simulations capture closely the experimentally observed rate sensitivity of the dynamic strength of concrete in the form of a nearly linear increase in dynamic strength with strain rate. More generally, our simulations give accurate transmitted loads over a range of strain rates, which attests to the fidelity of the model where rate effects are concerned. The model also predicts key features of the fracture pattern such as the primary lens-shaped cracks parallel to the load plane, as well as the secondary profuse cracking near the supports. The primary cracks are predicted to be nucleated at the centre of the circular bases of the cylinder and to subsequently propagate towards the interior, in accordance with experimental observations. The primary and secondary cracks are responsible for two peaks in the load history, also in keeping with experiment. The results of the simulations also exhibit a size effect. These results validate the theory as it bears on mixed-mode fracture and fragmentation processes in concrete over a range of strain rates.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/qg4mm-06702Variational integrators, the Newmark scheme, and dissipative systems
https://resolver.caltech.edu/CaltechAUTHORS:20100917-084012847
Authors: {'items': [{'id': 'West-M', 'name': {'family': 'West', 'given': 'M.'}}, {'id': 'Kane-C', 'name': {'family': 'Kane', 'given': 'C.'}}, {'id': 'Marsden-J-E', 'name': {'family': 'Marsden', 'given': 'J. E.'}}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'M.'}, 'orcid': '0000-0001-5877-4824'}]}
Year: 2000
Variational methods are a class of symplectic-momentum integrators for ODEs. Using
these schemes, it is shown that the classical Newmark algorithm is structure preserving in a
non-obvious way, thus explaining the observed numerical behavior. Modifications to variational
methods to include forcing and dissipation are also proposed, extending the advantages
of structure preserving integrators to non-conservative systems.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/rjkw8-cfh80A theory of subgrain dislocation structures
https://resolver.caltech.edu/CaltechAUTHORS:20230210-133510000.1
Authors: {'items': [{'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'M.'}, 'orcid': '0000-0001-5877-4824'}, {'id': 'Repetto-Eduardo-A', 'name': {'family': 'Repetto', 'given': 'E. A.'}}, {'id': 'Stainier-Laurent', 'name': {'family': 'Stainier', 'given': 'L.'}, 'orcid': '0000-0001-6719-6616'}]}
Year: 2000
We develop a micromechanical theory of dislocation structures and finite deformation single crystal plasticity based on the direct generation of deformation microstructures and the computation of the attendant effective behavior. Specifically, we aim at describing the lamellar dislocation structures which develop at large strains under monotonic loading. These microstructures are regarded as instances of sequential lamination and treated accordingly. The present approach is based on the explicit construction of microstructures by recursive lamination and their subsequent equilibration in order to relax the incremental constitutive description of the material. The microstructures are permitted to evolve in complexity and fineness with increasing macroscopic deformation. The dislocation structures are deduced from the plastic deformation gradient field by recourse to Kröner's formula for the dislocation density tensor. The theory is rendered nonlocal by the consideration of the self-energy of the dislocations. Selected examples demonstrate the ability of the theory to generate complex microstructures, determine the softening effect which those microstructures have on the effective behavior of the crystal, and account for the dependence of the effective behavior on the size of the crystalline sample, or size effect. In this last regard, the theory predicts the effective behavior of the crystal to stiffen with decreasing sample size, in keeping with experiment. In contrast to strain-gradient theories of plasticity, the size effect occurs for nominally uniform macroscopic deformations. Also in contrast to strain-gradient theories, the dimensions of the microstructure depend sensitively on the loading geometry, the extent of macroscopic deformation and the size of the sample.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/1md8a-azn77A theory of subgrain dislocation structures
https://resolver.caltech.edu/CaltechAUTHORS:20171213-085512032
Authors: {'items': [{'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'M.'}, 'orcid': '0000-0001-5877-4824'}, {'id': 'Repetto-Eduardo-A', 'name': {'family': 'Repetto', 'given': 'E. A.'}}, {'id': 'Stainier-Laurent', 'name': {'family': 'Stainier', 'given': 'L.'}, 'orcid': '0000-0001-6719-6616'}]}
Year: 2000
DOI: 10.1016/S0022-5096(99)00104-0
We develop a micromechanical theory of dislocation structures and finite deformation single crystal plasticity based on the direct generation of deformation microstructures and the computation of the attendant effective behavior. Specifically, we aim at describing the lamellar dislocation structures which develop at large strains under monotonic loading. These microstructures are regarded as instances of sequential lamination and treated accordingly. The present approach is based on the explicit construction of microstructures by recursive lamination and their subsequent equilibration in order to relax the incremental constitutive description of the material. The microstructures are permitted to evolve in complexity and fineness with increasing macroscopic deformation. The dislocation structures are deduced from the plastic deformation gradient field by recourse to Kröner's formula for the dislocation density tensor. The theory is rendered nonlocal by the consideration of the self-energy of the dislocations. Selected examples demonstrate the ability of the theory to generate complex microstructures, determine the softening effect which those microstructures have on the effective behavior of the crystal, and account for the dependence of the effective behavior on the size of the crystalline sample, or size effect. In this last regard, the theory predicts the effective behavior of the crystal to stiffen with decreasing sample size, in keeping with experiment. In contrast to strain-gradient theories of plasticity, the size effect occurs for nominally uniform macroscopic deformations. Also in contrast to strain-gradient theories, the dimensions of the microstructure depend sensitively on the loading geometry, the extent of macroscopic deformation and the size of the sample.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/54fcf-3jv02Mixed Atomistic-Continuum Models of Material Behavior: The Art of Transcending Atomistics and Informing Continua
https://resolver.caltech.edu/CaltechAUTHORS:20230210-231405683
Authors: {'items': [{'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'M.'}, 'orcid': '0000-0001-5877-4824'}, {'id': 'Cuitiño-Alberto-M', 'name': {'family': 'Cuitiño', 'given': 'A. M.'}, 'orcid': '0000-0002-5180-9147'}, {'id': 'Knap-Jaroslaw', 'name': {'family': 'Knap', 'given': 'J.'}}, {'id': 'Koslowski-Marisol', 'name': {'family': 'Koslowski', 'given': 'M.'}, 'orcid': '0000-0001-9650-2168'}]}
Year: 2000
The recent development of microscopes that allow for the examination of defects at the atomic scale has made possible a more direct connection between the defects and the macroscopic response they engender (see, e. g., MRS Bulletin, December 1999). Techniques ranging from high-resolution electron microscopy, which make possible the determination of the atomic-level structure of dislocation cores and grain boundaries, to the atomic force microscopes that bring new meaning to experiments such as those based on nanoindentation, all pose deep challenges as regards the modeling of the mechanics of materials. Each of these experiments calls for renewed efforts to cement the connection between defect mechanics and macroscopic constitutive descriptions. However, the link between the defects themselves and the observed macroscopic behavior is often a difficult one to forge theoretically and remains an active area of research.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/qk400-6e176Variational Integrators and the Newmark Algorithm for Conservative and Dissipative Mechanical Systems
https://resolver.caltech.edu/CaltechAUTHORS:20100819-120143013
Authors: {'items': [{'id': 'Kane-C', 'name': {'family': 'Kane', 'given': 'C.'}}, {'id': 'Marsden-J-E', 'name': {'family': 'Marsden', 'given': 'J. E.'}}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'M.'}, 'orcid': '0000-0001-5877-4824'}, {'id': 'West-M', 'name': {'family': 'West', 'given': 'M.'}}]}
Year: 2000
DOI: 10.1002/1097-0207(20001210)49:10<1295::AID-NME993>3.0.CO;2-W
The purpose of this work is twofold. First, we demonstrate analytically
that the classical Newmark family as well as related integration
algorithms are variational in the sense of the Veselov formulation of
discrete mechanics. Such variational algorithms are well known to be
symplectic and momentum preserving and to often have excellent global
energy behavior. This analytical result is veried through numerical examples
and is believed to be one of the primary reasons that this class
of algorithms performs so well.
Second, we develop algorithms for mechanical systems with forcing,
and in particular, for dissipative systems. In this case, we develop integrators
that are based on a discretization of the Lagrange d'Alembert
principle as well as on a variational formulation of dissipation. It is
demonstrated that these types of structured integrators have good numerical
behavior in terms of obtaining the correct amounts by which
the energy changes over the integration run.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/w1j4g-63r06Finite‐element modeling of dry sliding wear in metals
https://resolver.caltech.edu/CaltechAUTHORS:20171213-085800984
Authors: {'items': [{'id': 'Molinari-J-F', 'name': {'family': 'Molinari', 'given': 'J. F.'}}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'M.'}, 'orcid': '0000-0001-5877-4824'}, {'id': 'Radovitzky-R-A', 'name': {'family': 'Radovitzky', 'given': 'R.'}}, {'id': 'Repetto-E-A', 'name': {'family': 'Repetto', 'given': 'E. A.'}}]}
Year: 2001
DOI: 10.1108/00368790110407257
This paper is concerned with the calibration and validation of a finite‐element model of dry sliding wear in metals. The model is formulated within a Lagrangian framework capable of accounting for large plastic deformations and history‐dependent material behavior. We resort to continuous adaptive meshing as a means of eliminating deformation‐induced element distortion, and of resolving fine features of the wear process such as contact boundary layers. Particular attention is devoted to a generalization of Archard's law in which the hardness of the soft material is allowed to be a function of temperature. This dependence of hardness on temperature provides a means of capturing the observed experimental transition between severe wear rates at low speeds to mild wear rates at high speeds. Other features of the numerical model include: surface evolution due to wear; finite‐deformation J_2 thermoplasticity; heat generation and diffusion in the bulk; non‐equilibrium heat‐transfer across the contact interface; and frictional contact. The model is validated against a conventional test configuration consisting of a brass pin rubbing against a rotating steel plate.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/pfg3f-1e722Tetrahedral composite finite elements
https://resolver.caltech.edu/CaltechAUTHORS:20171128-142213688
Authors: {'items': [{'id': 'Thoutireddy-P', 'name': {'family': 'Thoutireddy', 'given': 'P.'}}, {'id': 'Molinari-J-F', 'name': {'family': 'Molinari', 'given': 'J. F.'}}, {'id': 'Repetto-E-A', 'name': {'family': 'Repetto', 'given': 'E. A.'}}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'M.'}, 'orcid': '0000-0001-5877-4824'}]}
Year: 2001
DOI: 10.1002/nme.337
We develop and analyse a composite 'CT3D' tetrahedral element consisting of an ensemble of 12 four-node linear tetrahedral elements, coupled to a linear assumed deformation defined over the entire domain of the composite element. The element is designed to have well-defined lumped masses and contact tractions in dynamic contact problems while at the same time, minimizing the number of volume constraints per element. The relation between displacements and deformations is enforced weakly by recourse to the Hu–Washizu principle. The element arrays are formulated in accordance with the 'assumed-strain' prescription. The formulation of the element accounts for fully non-linear kinematics. Integrals over the domain of the element are computed by a five-point quadrature rule. The element passes the patch test in arbitrarily distorted configurations. Our numerical tests demonstrate that CT element has been found to possess a convergence rate comparable to those of linear simplicial elements, and that these convergence rates are maintained as the near-incompressible limit is approached. We have also verified that the element satisfies the Babuška–Brezzi condition for a regular mesh configuration. These tests suggest that the CT3D element can indeed be used reliably in calculations involving near-incompressible behaviour which arises, e.g., in the presence of unconfined plastic flow.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/spgca-wb751Mixed Atomistic–Continuum Models of Material Behavior: The Art of Transcending Atomistics and Informing Continua
https://resolver.caltech.edu/CaltechAUTHORS:20171212-142856626
Authors: {'items': [{'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'M.'}, 'orcid': '0000-0001-5877-4824'}, {'id': 'Cuitiño-Alberto-M', 'name': {'family': 'Cuitiño', 'given': 'A. M.'}, 'orcid': '0000-0002-5180-9147'}, {'id': 'Knapp-Jaroslaw', 'name': {'family': 'Knapp', 'given': 'J.'}}, {'id': 'Koslowski-Marisol', 'name': {'family': 'Koslowski', 'given': 'M.'}, 'orcid': '0000-0001-9650-2168'}]}
Year: 2001
DOI: 10.1557/mrs2001.45
The recent development of microscopes that allow for the examination of defects at the atomic scale has made possible a more direct connection between the defects and the macroscopic response they engender (see, e.g., the December 1999 issue of MRS Bulletin).https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/np8ew-b4762Variational Delaunay approach to the generation of tetrahedral finite element meshes
https://resolver.caltech.edu/CaltechAUTHORS:20170408-162713466
Authors: {'items': [{'id': 'Krysl-P', 'name': {'family': 'Krysl', 'given': 'Petr'}}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'Michael'}, 'orcid': '0000-0001-5877-4824'}]}
Year: 2001
DOI: 10.1002/nme.91
We describe an algorithm which generates tetrahedral decomposition of a general solid body, whose surface is given as a collection of triangular facets. The principal idea is to modify the constraints in such a way as to make them appear in an unconstrained triangulation of the vertex set àpriori. The vertex set positions are randomized to guarantee existence of a unique triangulation which satisfies the Delaunay empty-sphere property. (Algorithms for robust, parallelized construction of such triangulations are available.) In order to make the boundary of the solid appear as a collection of tetrahedral faces, we iterate two operations, edge flip and edge split with the insertion of additional vertex, until all of the boundary facets are present in the tetrahedral mesh. The outcome of the vertex insertion is another triangulation of the input surfaces, but one which is represented as a subset of the tetrahedral faces. To determine if a constraining facet is present in the unconstrained Delaunay triangulation of the current vertex set, we use the results of Rajan which re-formulate Delaunay triangulation as a linear programming problem.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/vbnvh-grb88Extraction of boundary representation from surface triangulations
https://resolver.caltech.edu/CaltechAUTHORS:20171212-151905365
Authors: {'items': [{'id': 'Krysl-P', 'name': {'family': 'Krysl', 'given': 'Petr'}}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'Michael'}, 'orcid': '0000-0001-5877-4824'}]}
Year: 2001
DOI: 10.1002/nme.94
Many computational science tools employ finite element meshes as discretizations of the geometrical domains, and automatic mesh generation has become an indispensable part of the discretization process. Boundary representations (BRep) of solids are the means of describing the geometrical model to the mesher, thus enabling the generator to proceed without user intervention. Significant effort has been devoted in the past to BRep construction in the frame-work of solid modelling systems. In this paper we consider the task of converting a tesselation (triangulation) of the surface of a solid into a BRep, and propose a robust and efficient set of algorithms for this purpose. Applications include, among others, remeshing of finite element discretizations during simulations involving not only geometric distortion but also changes in topology (coalescence and fragmentation of solids, flow, and so on).https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/czdyx-9h192A Multiscale Approach for Modeling Crystalline Solids
https://resolver.caltech.edu/CaltechAUTHORS:20230210-354927000.2
Authors: {'items': [{'id': 'Cuitiño-Alberto-M', 'name': {'family': 'Cuitiño', 'given': 'A. M.'}, 'orcid': '0000-0002-5180-9147'}, {'id': 'Stainier-Laurent', 'name': {'family': 'Stainier', 'given': 'L.'}, 'orcid': '0000-0001-6719-6616'}, {'id': 'Wang-Guofeng', 'name': {'family': 'Wang', 'given': 'G.'}, 'orcid': '0000-0001-8249-4101'}, {'id': 'Strachan-Alejandro', 'name': {'family': 'Strachan', 'given': 'A.'}, 'orcid': '0000-0002-4174-9750'}, {'id': 'Çağin-Tahir', 'name': {'family': 'Çağin', 'given': 'T.'}, 'orcid': '0000-0002-3665-0932'}, {'id': 'Goddard-W-A-III', 'name': {'family': 'Goddard', 'given': 'W. A., III'}, 'orcid': '0000-0003-0097-5716'}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'M.'}, 'orcid': '0000-0001-5877-4824'}]}
Year: 2001
In this paper we present a modeling approach to bridge the atomistic with macroscopic scales in crystalline materials. The methodology combines identification and modeling of the controlling unit processes at microscopic level with the direct atomistic determination of fundamental material properties. These properties are computed using a many body Force Field derived from ab initio quantum-mechanical calculations. This approach is exercised to describe the mechanical response of high-purity Tantalum single crystals, including the effect of temperature and strain-rate on the hardening rate. The resulting atomistically informed model is found to capture salient features of the behavior of these crystals such as: the dependence of the initial yield point on temperature and strain rate; the presence of a marked stage I of easy glide, specially at low temperatures and high strain rates; the sharp onset of stage II hardening and its tendency to shift towards lower strains, and eventually disappear, as the temperature increases or the strain rate decreases; the parabolic stage II hardening at low strain rates or high temperatures; the stage II softening at high strain rates or low temperatures; the trend towards saturation at high strains; the temperature and strain-rate dependence of the saturation stress; and the orientation dependence of the hardening rate.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/m0p7y-jsw88An artificial viscosity method for the Lagrangian analysis of shocks in solids with strength on unstructured, arbitrary order tetrahedral meshes
https://resolver.caltech.edu/CaltechAUTHORS:20171212-143743641
Authors: {'items': [{'id': 'Lewis-A-C', 'name': {'family': 'Lewis', 'given': 'A. C.'}}, {'id': 'Radovitzky-R-A', 'name': {'family': 'Radovitzky', 'given': 'R.'}}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'M.'}, 'orcid': '0000-0001-5877-4824'}]}
Year: 2001
DOI: 10.1023/A:1020064403005
We present an artificial viscosity scheme tailored to finite-deformation Lagrangian calculations of shocks in materials with or without strength on unstructured tetrahedral meshes of arbitrary order. The artificial viscous stresses are deviatoric and satisfy material-frame indifference exactly. We have assessed the performance of the method on selected tests, including: a two-dimensional shock tube problem on an ideal gas; a two-dimensional piston problem on tantalum without strength; and a three-dimensional plate impact problem on tantalum with strength. In all cases, the artificial viscosity scheme returns stable and ostensibly oscillation-free solutions on meshes which greatly underresolve the actual shock thickness. The scheme typically spreads the shock over 4 to 6 elements and captures accurately the shock velocities and jump conditions.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/fs4gf-x3w93A multiscale approach for modeling crystalline solids
https://resolver.caltech.edu/CaltechAUTHORS:20171212-152625957
Authors: {'items': [{'id': 'Cuitiño-Alberto-M', 'name': {'family': 'Cuitiño', 'given': 'Alberto M.'}, 'orcid': '0000-0002-5180-9147'}, {'id': 'Stainier-Laurent', 'name': {'family': 'Stainier', 'given': 'Laurent'}, 'orcid': '0000-0001-6719-6616'}, {'id': 'Wang-Guofeng', 'name': {'family': 'Wang', 'given': 'Guofeng'}, 'orcid': '0000-0001-8249-4101'}, {'id': 'Strachan-Alejandro', 'name': {'family': 'Strachan', 'given': 'Alejandro'}, 'orcid': '0000-0002-4174-9750'}, {'id': 'Çağin-Tahir', 'name': {'family': 'Çağin', 'given': 'Tahir'}, 'orcid': '0000-0002-3665-0932'}, {'id': 'Goddard-W-A-III', 'name': {'family': 'Goddard', 'given': 'William A., III'}, 'orcid': '0000-0003-0097-5716'}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'Michael'}, 'orcid': '0000-0001-5877-4824'}]}
Year: 2001
DOI: 10.1023/A:1020012431230
In this paper we present a modeling approach to bridge the atomistic with macroscopic scales in crystalline materials. The methodology combines identification and modeling of the controlling unit processes at microscopic level with the direct atomistic determination of fundamental material properties. These properties are computed using a many body Force Field derived from ab initio quantum-mechanical calculations. This approach is exercised to describe the mechanical response of high-purity Tantalum single crystals, including the effect of temperature and strain-rate on the hardening rate. The resulting atomistically informed model is found to capture salient features of the behavior of these crystals such as: the dependence of the initial yield point on temperature and strain rate; the presence of a marked stage I of easy glide, specially at low temperatures and high strain rates; the sharp onset of stage II hardening and its tendency to shift towards lower strains, and eventually disappear, as the temperature increases or the strain rate decreases; the parabolic stage II hardening at low strain rates or high temperatures; the stage II softening at high strain rates or low temperatures; the trend towards saturation at high strains; the temperature and strain-rate dependence of the saturation stress; and the orientation dependence of the hardening rate.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/tnfe0-sj794An Efficient Adaptive Procedure for Three-Dimensional Fragmentation Simulations
https://resolver.caltech.edu/CaltechAUTHORS:20230210-225443504
Authors: {'items': [{'id': 'Pandolfi-Anna', 'name': {'family': 'Pandolfi', 'given': 'A.'}, 'orcid': '0000-0002-7084-7456'}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'M.'}, 'orcid': '0000-0001-5877-4824'}]}
Year: 2001
We present a simple set of data structures, and a collection of methods for constructing and updating the structures, designed to support the use of cohesive elements in simulations of fracture and fragmentation. Initially, all interior faces in the triangulation are perfectly coherent, i.e. conforming in the usual finite element sense. Cohesive elements are inserted adaptively at interior faces when the effective traction acting on those faces reaches the cohesive strength of the material. The insertion of cohesive elements changes the geometry of the boundary and, frequently, the topology of the model as well. The data structures and methods presented here are straightforward to implement, and enable the efficient tracking of complex fracture and fragmentation processes. The efficiency and versatility of the approach is demonstrated with the aid of two examples of application to dynamic fracture.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/62t2m-kw964Fully C^1‐conforming subdivision elements for finite deformation thin‐shell analysis
https://resolver.caltech.edu/CaltechAUTHORS:20171212-153633409
Authors: {'items': [{'id': 'Cirak-F', 'name': {'family': 'Cirak', 'given': 'Fehmi'}}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'Michael'}, 'orcid': '0000-0001-5877-4824'}]}
Year: 2001
DOI: 10.1002/nme.182
We have extended the subdivision shell elements of Cirak et al. [18] to the finite-deformation range. The assumed finite-deformation kinematics allows for finite membrane and thickness stretching, as well as for large deflections and bending strains. The interpolation of the undeformed and deformed surfaces of the shell is accomplished through the use of subdivision surfaces. The resulting 'subdivision elements' are strictly C1-conforming, contain three nodes and one single quadrature point per element, and carry displacements at the nodes only. The versatility and good performance of the subdivision elements is demonstrated with the aid of a number of test cases, including the stretching of a tension strip; the inflation of a spherical shell under internal pressure; the bending and inflation of a circular plate under the action of uniform pressure; and the inflation of square and circular airbags. In particular, the airbag solutions, while exhibiting intricate folding patterns, appear to converge in certain salient features of the solution, which attests to the robustness of the method.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/kx16t-91h73A Cohesive model of fatigue crack growth
https://resolver.caltech.edu/CaltechAUTHORS:20171212-143333386
Authors: {'items': [{'id': 'Nguyen-O', 'name': {'family': 'Nguyen', 'given': 'O.'}}, {'id': 'Repetto-E-A', 'name': {'family': 'Repetto', 'given': 'E. A.'}}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'M.'}, 'orcid': '0000-0001-5877-4824'}, {'id': 'Radovitzky-R-A', 'name': {'family': 'Radovitzky', 'given': 'R. A.'}}]}
Year: 2001
DOI: 10.1023/A:1010839522926
We investigate the use of cohesive theories of fracture, in conjunction with the explicit resolution of the near-tip plastic fields and the enforcement of closure as a contact constraint, for the purpose of fatigue-life prediction. An important characteristic of the cohesive laws considered here is that they exhibit unloading-reloading hysteresis. This feature has the important consequence of preventing shakedown and allowing for steady crack growth. Our calculations demonstrate that the theory is capable of a unified treatment of long cracks under constant-amplitude loading, short cracks and the effect of overloads, without ad hoc corrections or tuning.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/yt6ph-mbs36An analysis of the quasicontinuum method
https://resolver.caltech.edu/CaltechAUTHORS:20171212-152307212
Authors: {'items': [{'id': 'Knapp-J', 'name': {'family': 'Knapp', 'given': 'J.'}}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'M.'}, 'orcid': '0000-0001-5877-4824'}]}
Year: 2001
DOI: 10.1016/S0022-5096(01)00034-5
The aim of this paper is to present a streamlined and fully three-dimensional version of the quasicontinuum (QC) theory of Tadmor et al. (Philos. Mag. A 73 (1996) 1529; Langmuir 12 (1996) 4529) and to analyze its accuracy and convergence characteristics. Specifically, we assess the effect of the summation rules on accuracy; we determine the rate of convergence of the method in the presence of strong singularities, such as point loads; and we assess the effect of the refinement tolerance, which controls the rate at which new nodes are inserted in the model, on the development of dislocation microstructures.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/sfme6-saj95A computational study of the influence of thermal softening on ballistic penetration in metals
https://resolver.caltech.edu/CaltechAUTHORS:20150227-143957613
Authors: {'items': [{'id': 'Yadav-S', 'name': {'family': 'Yadav', 'given': 'S.'}}, {'id': 'Repetto-E-A', 'name': {'family': 'Repetto', 'given': 'E. A.'}}, {'id': 'Ravichandran-G', 'name': {'family': 'Ravichandran', 'given': 'G.'}, 'orcid': '0000-0002-2912-0001'}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'M.'}, 'orcid': '0000-0001-5877-4824'}]}
Year: 2001
DOI: 10.1016/S0734-743X(01)00008-2
A two-dimensional axisymmetric computational study of the penetration of a tungsten heavy alloy (WHA) rod into a 6061-T6 aluminum target has been performed using a Lagrangian formulation. Adaptive remeshing has been used to alleviate the problem of excessive distortion of elements which occurs during large deformation studies (such as ballistic penetration). Strain hardening, strain-rate hardening and thermal softening in both the penetrator and target materials are taken into full consideration. The computed depth of penetration (DOP), residual penetrator length and maximum crater diameter match very well the experimental results reported by Yadav and Ravichandran (Int. J. Impact Eng., Submitted for publication) for an impact velocity of 1100 m/s. Computer simulations reveal that in the absence of failure mechanisms (such as shear banding), introduction of thermal softening in the penetrator material decreases its depth of penetration in a metal target, when compared to a penetrator material which does not soften thermally. These results are in contrast to the recent work of Rosenberg and Dekel (Int. J. Impact Eng. 21 (1998) 283–296) and a plausible explanation for this discrepancy is presented.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/559vn-a3987Three‐dimensional cohesive modeling of dynamic mixed‐mode fracture
https://resolver.caltech.edu/CaltechAUTHORS:20171128-144716463
Authors: {'items': [{'id': 'Ruiz-G', 'name': {'family': 'Ruiz', 'given': 'Gonzalo'}}, {'id': 'Pandolfi-A', 'name': {'family': 'Pandolfi', 'given': 'Anna'}, 'orcid': '0000-0002-7084-7456'}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'Michael'}, 'orcid': '0000-0001-5877-4824'}]}
Year: 2001
DOI: 10.1002/nme.273
A cohesive formulation of fracture is taken as a basis for the simulation of processes of combined tension-shear damage and mixed-mode fracture in specimens subjected to dynamic loading. Our three-dimensional finite-element calculations account explicitly for crack nucleation, microcracking, the development of macroscopic cracks and inertia. In particular, a tension-shear damage coupling arises as a direct consequence of slanted microcrack formation in the process zone. We validate the model against the three-point-bend concrete beam experiments of Guo et al. (International Journal of Solids and Structures 1995; 32(17/18):2951–2607), John (PhD Thesis, Northwestern University, 1988), and John and Shah (Journal of Structural Engineering 1990; 116(3):585–602) in which a pre-crack is shifted from the central cross-section, leading to asymmetric loading conditions and the development of a mixed-mode process zone. The model accurately captures the experimentally observed fracture patterns and displacement fields, as well as crack paths and crack-tip velocities, as a function of pre-crack geometry and loading conditions. In particular, it correctly accounts for the competition between crack-growth and nucleation mechanisms.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/2sr9p-31t42The computation of the exponential and logarithmic mappings and their first and second linearizations
https://resolver.caltech.edu/CaltechAUTHORS:20171128-144521153
Authors: {'items': [{'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'M.'}, 'orcid': '0000-0001-5877-4824'}, {'id': 'Radovitzky-R-A', 'name': {'family': 'Radovitzky', 'given': 'R. A.'}}, {'id': 'Repetto-E-A', 'name': {'family': 'Repetto', 'given': 'E. A.'}}]}
Year: 2001
DOI: 10.1002/nme.263
We describe two simple methods for the evaluation of the exponential and logarithmic mappings and their first and second linearizations based on the Taylor expansion and the spectral representation. We also provide guidelines for switching between those representations on the basis of the size of the argument. The first and second linearizations of the exponential and logarithmic mappings provided here are based directly on the exponential formula for the solutions of systems of linear ordinary differential equations. This representation does not require the use of perturbation formulae for eigenvalues and eigenvectors. Our approach leads to workable and straightforward expressions for the first and second linearizations of the exponential and logarithmic mappings regardless of degeneracies in the spectral decomposition of the argument.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/8m5ce-byd71Experimental and Numerical Investigation of Shear-dominated Intersonic Crack Growth and Friction in Unidirectional Composites
https://resolver.caltech.edu/CaltechAUTHORS:20200219-114918280
Authors: {'items': [{'id': 'Rosakis-A-J', 'name': {'family': 'Rosakis', 'given': 'A. J.'}, 'orcid': '0000-0003-0559-0794'}, {'id': 'Yu-Chengxiang-Rena', 'name': {'family': 'Yu', 'given': 'C.'}, 'orcid': '0000-0003-4176-0324'}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'M.'}, 'orcid': '0000-0001-5877-4824'}, {'id': 'Coker-D', 'name': {'family': 'Coker', 'given': 'D.'}, 'orcid': '0000-0001-7385-7089'}, {'id': 'Pandolfi-A', 'name': {'family': 'Pandolfi', 'given': 'A.'}, 'orcid': '0000-0002-7084-7456'}]}
Year: 2002
DOI: 10.1007/0-306-48410-2_27
Dynamic crack growth in unidirectional graphite/epoxy composite materials subjected to in-plane impact loading is investigated experimentally and numerically. The experiments are conducted using CGS (Coherent Gradient Sensing) Interferometry in conjunction with high-speed photography to visualize the crack growth events. Cracks are found to propagate at subsonic speeds in the Mode-I case, whereas in both mixed mode and Mode-II the crack tip speed clearly exceeds the shear wave speed of the laminate. For these intersonically growing shear (Mode-II) cracks a shock wave emanating from the crack tip is observed. This provides direct evidence that the cracks propagate faster than the shear wave speed of the composite. The crack tip speed is initally observed to jump to a level close to the axial longitudinal wave speed along the fibers (7500 m/s) and then to stabilize to a lower level of approximately 6500 m/s. This speed corresponds to the speed at which the energy release rate required for shear crack growth is non-zero as determined from asymptotic analysis. The CGS interferograms also reveal the existence of large-scale frictional contact of the crack faces behind the moving shear cracks. In addition high speed thermographic measurements are conducted that show concentrated hot spots behind the crack tip indicating crack face frictional contact. These experiments are modeled by a detailed dynamic finite element calculation involving cohesive elements, adaptive remeshing using subdivision and edge collapse, composite elements, and penalty contact. The numerical calculations are calibrated on the basis of fundamental material properties measured in the laboratory. The computational results are found to be in excellent agreement with the optical experimental measurements (crack speed record and near tip deformation field structure). For shear crack growth, the numerics also confirm the optical observation of large-scale crack face contact.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/fde8n-wwd04Integrated modeling, finite-element analysis, and engineering design for thin-shell structures using subdivision
https://resolver.caltech.edu/CaltechAUTHORS:20171208-164357957
Authors: {'items': [{'id': 'Cirak-F', 'name': {'family': 'Cirak', 'given': 'Fehmi'}}, {'id': 'Scott-M-J', 'name': {'family': 'Scott', 'given': 'Michael J.'}}, {'id': 'Antonsson-E-K', 'name': {'family': 'Antonsson', 'given': 'Erik K.'}}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'Michael'}, 'orcid': '0000-0001-5877-4824'}, {'id': 'Schröder-P', 'name': {'family': 'Schröder', 'given': 'Peter'}, 'orcid': '0000-0002-0323-7674'}]}
Year: 2002
DOI: 10.1016/S0010-4485(01)00061-6
Many engineering design applications require geometric modeling and mechanical simulation of thin flexible structures, such as those found in the automotive and aerospace industries. Traditionally, geometric modeling, mechanical simulation, and engineering design are treated as separate modules requiring different methods and representations. Due to the incompatibility of the involved representations the transition from geometric modeling to mechanical simulation, as well as in the opposite direction, requires substantial effort. However, for engineering design purposes efficient transition between geometric modeling and mechanical simulation is essential. We propose the use of subdivision surfaces as a common foundation for modeling, simulation, and design in a unified framework. Subdivision surfaces provide a flexible and efficient tool for arbitrary topology free-form surface modeling, avoiding many of the problems inherent in traditional spline patch based approaches. The underlying basis functions are also ideally suited for a finite-element treatment of the so-called thin-shell equations, which describe the mechanical behavior of the modeled structures. The resulting solvers are highly scalable, providing an efficient computational foundation for design exploration and optimization. We demonstrate our claims with several design examples, showing the versatility and high accuracy of the proposed method.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/drcyt-3y668The mechanics of deformation-induced subgrain dislocation structures in metallic crystals at large strains
https://resolver.caltech.edu/CaltechAUTHORS:20230210-225845734
Authors: {'items': [{'id': 'Aubry-Sylvie', 'name': {'family': 'Aubry', 'given': 'S.'}, 'orcid': '0000-0002-5123-8655'}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'M.'}, 'orcid': '0000-0001-5877-4824'}]}
Year: 2002
We present a streamlined limiting case of the theory of Oritz & Repetto for crystals with microstructure in which the crystals are assumed to exhibit infinitely strong latent hardening. We take this property to signify that the crystal must necessarily deform in single slip at all material points. This requirement introduces a non–convex constraint that renders the incremental problem non–convex. We have assessed the ability of the theory to predict salient aspects of the body of experimental data compiled by Hansen et al. regarding lamellar dislocation structures in crystals deformed to large strains. Although the comparisons with experiment are somewhat indirect, the theory appears to correctly predict salient aspects of the statistics of misorientation angles and lamellar–boundary spacings, and the scaling of the average misorientation and spacing with increasing macroscopic strain.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/5z6sb-8mt94Three-dimensional adaptive meshing by subdivision and edge-collapse in finite-deformation dynamic-plasticity problems with application to adiabatic shear banding
https://resolver.caltech.edu/CaltechAUTHORS:20171128-141604699
Authors: {'items': [{'id': 'Molinari-J-F', 'name': {'family': 'Molinari', 'given': 'J. F.'}}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'M.'}, 'orcid': '0000-0001-5877-4824'}]}
Year: 2002
DOI: 10.1002/nme.325
This paper is concerned with the development of a general framework for adaptive mesh refinement and coarsening in three-dimensional finite-deformation dynamic–plasticity problems. Mesh adaption is driven by a posteriori global error bounds derived on the basis of a variational formulation of the incremental problem. The particular mesh-refinement strategy adopted is based on Rivara's longest-edge propagation path (LEPP) bisection algorithm. Our strategy for mesh coarsening, or unrefinement, is based on the elimination of elements by edge-collapse. The convergence characteristics of the method in the presence of strong elastic singularities are tested numerically. An application to the three-dimensional simulation of adiabatic shear bands in dynamically loaded tantalum is also presented which demonstrates the robustness and versatility of the method.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/nrbc3-4hw40Time-discretized variational formulation of non-smooth
frictional contact
https://resolver.caltech.edu/CaltechAUTHORS:20100913-101405977
Authors: {'items': [{'id': 'Pandolfi-A', 'name': {'family': 'Pandolfi', 'given': 'A.'}, 'orcid': '0000-0002-7084-7456'}, {'id': 'Kane-C', 'name': {'family': 'Kane', 'given': 'C.'}}, {'id': 'Marsden-J-E', 'name': {'family': 'Marsden', 'given': 'J. E.'}}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'M.'}, 'orcid': '0000-0001-5877-4824'}]}
Year: 2002
DOI: 10.1002/nme.361
The present work extends the non-smooth contact class of algorithms introduced by Kane et al. to the case of friction. The formulation specifically addresses contact geometries, e.g. involving multiple collisions between tightly packed non-smooth bodies, for which neither normals nor gap functions can be properly defined. A key aspect of the approach is that the incremental displacements follow from a minimum principle. The objective function comprises terms which account for inertia, strain energy, contact, friction and external forcing. The Euler–Lagrange equations corresponding to this extended variational principle are shown to be consistent with the equations of motion of solids in frictional contact. In addition to its value as a basis for formulating numerical algorithms, the variational framework offers theoretical advantages as regards the selection of trajectories in cases of non-uniqueness. We present numerical and analytical examples which demonstrate the good momentum and energy conservation characteristics of the numerical algorithms, as well as the ability of the approach to account for stick and slip conditions.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/ad405-4qx81A study of solid-particle erosion of metallic targets
https://resolver.caltech.edu/CaltechAUTHORS:20171208-163608575
Authors: {'items': [{'id': 'Molinari-J-F', 'name': {'family': 'Molinari', 'given': 'J. F.'}}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'M.'}, 'orcid': '0000-0001-5877-4824'}]}
Year: 2002
DOI: 10.1016/S0734-743X(01)00055-0
We perform detailed finite element simulations of impact of metallic plates by spherical particles over a range of impact angles and speeds with a view to develop an insight into the fundamental mechanisms underlying solid-particle erosion. The particular experimental configuration and data set which we analyze corresponds to the experiments of Hutchings (Proc. R. Soc. London, Ser. A 348 (1976) 379), consisting of high-strength steel spherical particles striking mild-steel target plates. The material description used in calculations includes finite deformations, strain hardening, thermal softening, rate sensitivity, frictional contact, heat generation due to plastic working and friction, dynamics and heat conduction. The analysis reveals insights into the relative roles played by plastic flow, friction and adiabatic shearing over the full range of impact angles from glancing to normal impact; and over impact velocities ranging from 141 to 2000 m/s.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/c5mpk-61h18A phase-field theory of dislocation dynamics, strain hardening and hysteresis in ductile single crystals
https://resolver.caltech.edu/CaltechAUTHORS:20230210-232639057
Authors: {'items': [{'id': 'Koslowski-Marisol', 'name': {'family': 'Koslowski', 'given': 'M.'}, 'orcid': '0000-0001-9650-2168'}, {'id': 'Cuitiño-Alberto-M', 'name': {'family': 'Cuitiño', 'given': 'A. M.'}, 'orcid': '0000-0002-5180-9147'}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'M.'}, 'orcid': '0000-0001-5877-4824'}]}
Year: 2002
A phase-field theory of dislocation dynamics, strain hardening and hysteresis in ductile single crystals is developed. The theory accounts for: an arbitrary number and arrangement of dislocation lines over a slip plane; the long-range elastic interactions between dislocation lines; the core structure of the dislocations resulting from a piecewise quadratic Peierls potential; the interaction between the dislocations and an applied resolved shear stress field; and the irreversible interactions with short-range obstacles and lattice friction, resulting in hardening, path dependency and hysteresis. A chief advantage of the present theory is that it is analytically tractable, in the sense that the complexity of the calculations may be reduced, with the aid of closed form analytical solutions, to the determination of the value of the phase field at point-obstacle sites. In particular, no numerical grid is required in calculations. The phase-field representation enables complex geometrical and topological transitions in the dislocation ensemble, including dislocation loop nucleation, bow-out, pinching, and the formation of Orowan loops. The theory also permits the consideration of obstacles of varying strengths and dislocation line-energy anisotropy. The theory predicts a range of behaviors which are in qualitative agreement with observation, including: hardening and dislocation multiplication in single slip under monotonic loading; the Bauschinger effect under reverse loading; the fading memory effect, whereby reverse yielding gradually eliminates the influence of previous loading; the evolution of the dislocation density under cycling loading, leading to characteristic 'butterfly' curves; and others.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/bdcqh-baf67Folding energetics in thin-film diaphragms
https://resolver.caltech.edu/CaltechAUTHORS:20171128-144028971
Authors: {'items': [{'id': 'Gioia-Gustavo', 'name': {'family': 'Gioia', 'given': 'G.'}}, {'id': 'DeSimone-A', 'name': {'family': 'DeSimone', 'given': 'A.'}}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'M.'}, 'orcid': '0000-0001-5877-4824'}, {'id': 'Cuitiño-A-M', 'name': {'family': 'Cuitiño', 'given': 'A. M.'}, 'orcid': '0000-0002-5180-9147'}]}
Year: 2002
DOI: 10.1098/rspa.2001.0921
We perform experiments to elucidate how the folding patterns of thin-film diaphragms subject to in-plane isotropic and anisotropic compressive strains depend on the shape, thickness and size of the diaphragms. We then use a constrained von Kaármaán model to relate the experimental results to the energetics of folding. We show that the differences between the isotropic and the anisotropic cases can be traced back to the structure of the membraneous energy density function. In the isotropic case, we find foldings which satisfy the boundary conditions and minimize the membraneous energy. In the anisotropic case, no such foldings exist, but we are able to construct sequences of increasingly fine foldings which satisfy the boundary conditions and whose membraneous energies converge to the infimum. In both cases, we obtain solutions by allowing bending to select a preferred folding. The solutions compare well with the experimental observations.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/cnf6m-sa481A micromechanical model of hardening, rate sensitivity and thermal softening in BCC single crystals
https://resolver.caltech.edu/CaltechAUTHORS:20171208-155120960
Authors: {'items': [{'id': 'Stainier-Laurent', 'name': {'family': 'Stainier', 'given': 'L.'}, 'orcid': '0000-0001-6719-6616'}, {'id': 'Cuitiño-A-M', 'name': {'family': 'Cuitiño', 'given': 'A. M.'}, 'orcid': '0000-0002-5180-9147'}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'M.'}, 'orcid': '0000-0001-5877-4824'}]}
Year: 2002
DOI: 10.1016/S0022-5096(01)00114-4
The present paper is concerned with the development of a micromechanical model of the hardening, rate-sensitivity and thermal softening of bcc crystals. In formulating the model, we specifically consider the following unit processes: double-kink formation and thermally activated motion of kinks; the close-range interactions between primary and forest dislocations, leading to the formation of jogs; the percolation motion of dislocations through a random array of forest dislocations introducing short-range obstacles of different strengths; dislocation multiplication due to breeding by double cross-slip; and dislocation pair annihilation. The model is found to capture salient features of the behavior of Ta crystals such as: the dependence of the initial yield point on temperature and strain rate; the presence of a marked stage I of easy glide, specially at low temperatures and high strain rates; the sharp onset of stage II hardening and its tendency to shift towards lower strains, and eventually disappear, as the temperature increases or the strain rate decreases; the parabolic stage II hardening at low strain rates or high temperatures; the stage II softening at high strain rates or low temperatures; the trend towards saturation at high strains; the temperature and strain-rate dependence of the saturation stress; and the orientation dependence of the hardening rate.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/rjf4w-1hf60Coarse-graining and renormalization of atomistic binding relations and universal macroscopic cohesive behavior
https://resolver.caltech.edu/CaltechAUTHORS:20171208-163351204
Authors: {'items': [{'id': 'Nguyen-O', 'name': {'family': 'Nguyen', 'given': 'O.'}}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'M.'}, 'orcid': '0000-0001-5877-4824'}]}
Year: 2002
DOI: 10.1016/S0022-5096(01)00133-8
We present two approaches for coarse-graining interplanar potentials and determining the corresponding macroscopic cohesive laws based on energy relaxation and the renormalization group. We analyze the cohesive behavior of a large—but finite—number of interatomic planes and find that the macroscopic cohesive law adopts a universal asymptotic form. The universal form of the macroscopic cohesive law is an attractive fixed point of a suitably-defined renormalization-group transformation.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/9d8y9-hnw68An Efficient Adaptive Procedure for Three-Dimensional Fragmentation Simulations
https://resolver.caltech.edu/CaltechAUTHORS:20171208-163116282
Authors: {'items': [{'id': 'Pandolfi-Anna', 'name': {'family': 'Pandolfi', 'given': 'A.'}, 'orcid': '0000-0002-7084-7456'}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'M.'}, 'orcid': '0000-0001-5877-4824'}]}
Year: 2002
DOI: 10.1007/s003660200013
We present a simple set of data structures, and
a collection of methods for constructing and updating the
structures, designed to support the use of cohesive elements
in simulations of fracture and fragmentation. Initially, all
interior faces in the triangulation are perfectly coherent, i.e.
conforming in the usual finite element sense. Cohesive
elements are inserted adaptively at interior faces when the
effective traction acting on those faces reaches the cohesive
strength of the material. The insertion of cohesive elements
changes the geometry of the boundary and, frequently, the
topology of the model as well. The data structures and
methods presented here are straightforward to implement,
and enable the efficient tracking of complex fracture and
fragmentation processes. The efficiency and versatility of the
approach is demonstrated with the aid of two examples of
application to dynamic fracture.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/dyqr0-wxe86Three-dimensional modeling of intersonic shear-crack growth in asymmetrically loaded unidirectional composite plates
https://resolver.caltech.edu/CaltechAUTHORS:20171208-154753672
Authors: {'items': [{'id': 'Yu-Chengxiang-Rena', 'name': {'family': 'Yu', 'given': 'C.'}, 'orcid': '0000-0003-4176-0324'}, {'id': 'Pandolfi-A', 'name': {'family': 'Pandolfi', 'given': 'A.'}, 'orcid': '0000-0002-7084-7456'}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'M.'}, 'orcid': '0000-0001-5877-4824'}, {'id': 'Coker-Demirkan', 'name': {'family': 'Coker', 'given': 'D.'}, 'orcid': '0000-0001-7385-7089'}, {'id': 'Rosakis-A-J', 'name': {'family': 'Rosakis', 'given': 'A. J.'}, 'orcid': '0000-0003-0559-0794'}]}
Year: 2002
DOI: 10.1016/S0020-7683(02)00466-3
An anisotropic cohesive model of fracture is applied to the numerical simulation of Coker and Rosakis experiments (2001). In these experiments, a unidirectional graphite–epoxy composites plate was impacted with a projectile, resulting in an intersonic shear-dominated crack growth. The simulations account for explicit crack nucleation––through a self-adaptive remeshing procedure––crack closure and frictional sliding. The parameters used in the cohesive model are obtained from quasi-static fracture experiments, and successfully predict the dynamic fracture behavior. In keeping with the experiments, the calculations indicate that there is a preferred intersonic speed for locally steady-state growth of dynamic shear cracks, provided that sufficient energy is supplied to the crack tip. The calculations also show that the crack tip can attain speeds in the vicinity of the longitudinal wave speed in the direction of the fibers, if impacted at higher speeds. In addition, a double-shock which emanates from a finite size contact region behind the crack tip is observed in the simulations. The predicted double-shock structure of the near-tip fields is in close agreement with the experimental observations. The calculations additionally predict the presence of a string of surface hot spots which arise following the passage of the crack tip. The observed and computed hot spot structures agree both in geometry as well as in the magnitude of the temperature elevation. The analysis thus suggests intermittent friction as the origin of the experimentally observed hot spots.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/f2p55-8w991A phase-field theory of dislocation dynamics, strain hardening and hysteresis in ductile single crystals
https://resolver.caltech.edu/CaltechAUTHORS:20171208-164131036
Authors: {'items': [{'id': 'Koslowski-Marisol', 'name': {'family': 'Koslowski', 'given': 'M.'}, 'orcid': '0000-0001-9650-2168'}, {'id': 'Cuitiño-Alberto-M', 'name': {'family': 'Cuitiño', 'given': 'A. M.'}, 'orcid': '0000-0002-5180-9147'}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'M.'}, 'orcid': '0000-0001-5877-4824'}]}
Year: 2002
DOI: 10.1016/S0022-5096(02)00037-6
A phase-field theory of dislocation dynamics, strain hardening and hysteresis in ductile single crystals is developed. The theory accounts for: an arbitrary number and arrangement of dislocation lines over a slip plane; the long-range elastic interactions between dislocation lines; the core structure of the dislocations resulting from a piecewise quadratic Peierls potential; the interaction between the dislocations and an applied resolved shear stress field; and the irreversible interactions with short-range obstacles and lattice friction, resulting in hardening, path dependency and hysteresis. A chief advantage of the present theory is that it is analytically tractable, in the sense that the complexity of the calculations may be reduced, with the aid of closed form analytical solutions, to the determination of the value of the phase field at point-obstacle sites. In particular, no numerical grid is required in calculations. The phase-field representation enables complex geometrical and topological transitions in the dislocation ensemble, including dislocation loop nucleation, bow-out, pinching, and the formation of Orowan loops. The theory also permits the consideration of obstacles of varying strengths and dislocation line-energy anisotropy. The theory predicts a range of behaviors which are in qualitative agreement with observation, including: hardening and dislocation multiplication in single slip under monotonic loading; the Bauschinger effect under reverse loading; the fading memory effect, whereby reverse yielding gradually eliminates the influence of previous loading; the evolution of the dislocation density under cycling loading, leading to characteristic 'butterfly' curves; and others.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/hk1w9-q8p26Variational Methods in Non-Convex Plasticity
https://resolver.caltech.edu/CaltechAUTHORS:20190826-124740658
Authors: {'items': [{'id': 'Aubry-S', 'name': {'family': 'Aubry', 'given': 'S.'}}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'M.'}, 'orcid': '0000-0001-5877-4824'}]}
Year: 2003
DOI: 10.1007/978-94-017-0297-3_5
We show how the theory of crystals with microstructure developed by Ortiz et al. can be applied to predict salient aspects of the body of experimental data compiled by Hughes et al. regarding lamellar dislocation structures in crystals deformed to large strains. The theory correctly predicts the statistics of misorientation angles and lamellar boundary spacings; and the scaling of the average misorientation and spacing with increasing macroscopic strain.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/dksq3-t4x69Nonsmooth Lagrangian mechanics and variational collision integrators
https://resolver.caltech.edu/CaltechAUTHORS:FETsiamjads03
Authors: {'items': [{'id': 'Fetecau-R-C', 'name': {'family': 'Fetecau', 'given': 'R. C.'}}, {'id': 'Marsden-J-E', 'name': {'family': 'Marsden', 'given': 'J. E.'}}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'M.'}, 'orcid': '0000-0001-5877-4824'}, {'id': 'West-M', 'name': {'family': 'West', 'given': 'M.'}}]}
Year: 2003
DOI: 10.1137/S1111111102406038
Variational techniques are used to analyze the problem of rigid-body dynamics with impacts. The theory of smooth Lagrangian mechanics is extended to a nonsmooth context appropriate for collisions, and it is shown in what sense the system is symplectic and satisfies a Noether-style momentum conservation theorem.
Discretizations of this nonsmooth mechanics are developed by using the methodology of variational discrete mechanics. This leads to variational integrators which are symplectic-momentum preserving and are consistent with the jump conditions given in the continuous theory. Specific examples of these methods are tested numerically, and the long-time stable energy behavior typical of variational methods is demonstrated.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/9n8hg-0sa813D Modelling of Impact Failure in Sandwich Structures
https://resolver.caltech.edu/CaltechAUTHORS:20171129-164945762
Authors: {'items': [{'id': 'Yu-Chengxiang-Rena', 'name': {'family': 'Yu', 'given': 'C.'}, 'orcid': '0000-0003-4176-0324'}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'M.'}, 'orcid': '0000-0001-5877-4824'}, {'id': 'Rosakis-A-J', 'name': {'family': 'Rosakis', 'given': 'A. J.'}, 'orcid': '0000-0003-0559-0794'}]}
Year: 2003
DOI: 10.1016/S1566-1369(03)80122-X
Cohesive theories of fracture are applied to simulate the complex failure modes in sandwich structures subjected to low-speed impact. The particular configuration contemplated in this study refers to the experiments performed by Xu and Rosakis [1], where the model specimens involving a compliant polymer core sandwiched between two metal layers, were adopted to simulate failure evolution mechanisms in real sandwich structures. Fracture has been modeled by recourse to an irreversible cohesive law embedded into three-dimensional cohesive elements. These cohesive elements govern all aspects of the separation of the incipient cracks. The cohesive behavior of the material is assumed to be rate independent and, consequently, all rate effects predicted by the calculations are due to inertia. The fidelity of the model has been validated by several previous simulations [2,3]. The numerical simulations have proved highly predictive of a number of observed features, including: the complex sequences of the failure mode, shear-dominated inter-sonic (a speed that is greater than shear wave speed but less than the longitudinal wave speed of the material) inter-layer cracks, the transition from inter-layer crack growth to intra-layer crack formation and the core branching later on.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/6wm47-pf415Multiscale modelling of hardening in BCC crystal plasticity
https://resolver.caltech.edu/CaltechAUTHORS:20171128-115759473
Authors: {'items': [{'id': 'Stainier-Laurent', 'name': {'family': 'Stainier', 'given': 'L.'}, 'orcid': '0000-0001-6719-6616'}, {'id': 'Cuitiño-A-M', 'name': {'family': 'Cuitiño', 'given': 'A. M.'}, 'orcid': '0000-0002-5180-9147'}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'M.'}, 'orcid': '0000-0001-5877-4824'}]}
Year: 2003
DOI: 10.1051/jp4:20030183
The mechanical behavior of polycrystalline metals can be successfully modeled by macroscopic theories, such as Von Mises plasticity. On the other hand, numerous studies can be performed on the atomic scale, either by atomistic or dislocation dynamics models. The proposed model attempts to bridge those two scales by deriving constitutive relations between slip strains, dislocation densities and resolved shear stresses on crystallographic planes, from mechanisms of deformation playing at the level of the dislocation line. The resulting "mesoscopic" hardening relations are controlled by dislocation self energies and junctions strengths. Temperature and strain rate dependence result from the presence of thermally activated mechanisms such as Peierls barriers or pair annihilation by cross slip. A set of material parameters is identified for Tantalum by fitting the numerical stress strain curves from these tests with experimental results gathered in the literature. These parameters prove to be in very good agreement with the values which can be derived from molecular dynamics computations.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/nhsgd-bme02Asynchronous Variational Integrators
https://resolver.caltech.edu/CaltechAUTHORS:20100823-112128812
Authors: {'items': [{'id': 'Lew-A', 'name': {'family': 'Lew', 'given': 'A.'}}, {'id': 'Marsden-J-E', 'name': {'family': 'Marsden', 'given': 'J. E.'}}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'M.'}, 'orcid': '0000-0001-5877-4824'}, {'id': 'West-M', 'name': {'family': 'West', 'given': 'M.'}}]}
Year: 2003
DOI: 10.1007/s00205-002-0212-y
We describe a new class of asynchronous variational integrators (AVI) for nonlinear
elastodynamics. The AVIs are distinguished by the following attributes: (i)
The algorithms permit the selection of independent time steps in each element, and
the local time steps need not bear an integral relation to each other; (ii) the algorithms
derive from a spacetime form of a discrete version of Hamilton's variational
principle. As a consequence of this variational structure, the algorithms conserve
local momenta and a local discrete multisymplectic structure exactly.
To guide the development of the discretizations, a spacetime multisymplectic
formulation of elastodynamics is presented. The variational principle used incorporates
both configuration and spacetime reference variations. This allows a unified
treatment of all the conservation properties of the system.A discrete version of reference
configuration is also considered, providing a natural definition of a discrete
energy. The possibilities for discrete energy conservation are evaluated.
Numerical tests reveal that, even when local energy balance is not enforced
exactly, the global and local energy behavior of the AVIs is quite remarkable, a
property which can probably be traced to the symplectic nature of the algorithmhttps://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/87fjr-qhc90Finite-element simulation of firearm injury to the human cranium
https://resolver.caltech.edu/CaltechAUTHORS:20171128-115541004
Authors: {'items': [{'id': 'Mota-A', 'name': {'family': 'Mota', 'given': 'A.'}}, {'id': 'Klug-W-S', 'name': {'family': 'Klug', 'given': 'W. S.'}}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'M.'}, 'orcid': '0000-0001-5877-4824'}, {'id': 'Pandolfi-A', 'name': {'family': 'Pandolfi', 'given': 'A.'}, 'orcid': '0000-0002-7084-7456'}]}
Year: 2003
DOI: 10.1007/s00466-002-0398-8
An advanced physics-based simulation of firearms injury to the human cranium is presented, modeling by finite elements the collision of a firearm projectile into a human parietal bone. The space-discretized equations of motion are explicitly integrated in time with Newmark's time-stepping algorithm. The impact of the projectile on the skull, as well as the collisions between flying fragments, are controlled through a nonsmooth contact algorithm. Cohesive theories of fracture, in conjunction with adaptive remeshing, control the nucleation and the propagation of fractures. The progressive opening of fracture surfaces is governed by a thermodynamically irreversible cohesive law embedded into cohesive-interface elements. Numerical results compare well with forensic data of actual firearm wounds to human crania.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/7xkqp-ww531Effect of Indenter-Radius Size on Au(001) Nanoindentation
https://resolver.caltech.edu/CaltechAUTHORS:20171128-115314976
Authors: {'items': [{'id': 'Knap-J', 'name': {'family': 'Knap', 'given': 'J.'}}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'M.'}, 'orcid': '0000-0001-5877-4824'}]}
Year: 2003
DOI: 10.1103/PhysRevLett.90.226102
We address the question of whether results obtained for small indenters scale to indenter sizes in the experimental range. The quasicontinuum method is used in order to extend the computational cell size to 2 × 2 × 1 μm^3, nominally containing of order
2.5 × 10^(11) atoms, and in order to permit consideration of indenter radii in the range 70−700 Å. The dislocation structures for the large indenter are found to be less sharp and to extend over a larger region than for the small indenter. In addition, the large-indenter force-displacement curve differs from that corresponding to the small indenter in one important respect, namely, the absence of force drops during indentation, despite profuse dislocation activity. Based on these observations, we conclude that the indenter force is not a reliable indicator of the onset of dislocation activity and plastic deformation for indenter sizes in the experimental range.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/bv15z-xej72Oscillatory Thermomechanical Instability of an Ultrathin Catalyst
https://resolver.caltech.edu/CaltechAUTHORS:20141119-075159032
Authors: {'items': [{'id': 'Cirak-Fehmi', 'name': {'family': 'Cirak', 'given': 'Fehmi'}}, {'id': 'Cisternas-J-E', 'name': {'family': 'Cisternas', 'given': 'Jaime E.'}}, {'id': 'Cuitiño-A-M', 'name': {'family': 'Cuitiño', 'given': 'Alberto M.'}, 'orcid': '0000-0002-5180-9147'}, {'id': 'Ertl-Gerhard', 'name': {'family': 'Ertl', 'given': 'Gerhard'}}, {'id': 'Holmes-P-J', 'name': {'family': 'Holmes', 'given': 'Philip'}}, {'id': 'Kevrekidis-I-G', 'name': {'family': 'Kevrekidis', 'given': 'Ioannis G.'}}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'Michael'}, 'orcid': '0000-0001-5877-4824'}, {'id': 'Rotermund-H-H', 'name': {'family': 'Rotermund', 'given': 'Harm Hinrich'}}, {'id': 'Schunack-Michael', 'name': {'family': 'Schunack', 'given': 'Michael'}}, {'id': 'Wolff-Janpeter', 'name': {'family': 'Wolff', 'given': 'Janpeter'}}]}
Year: 2003
DOI: 10.1126/science.1083909
Because of the small thermal capacity of ultrathin (∼200 nanometers) metal single crystals, it is possible to explore the coupling of catalytic and thermal action at low pressures. We analyzed a chemothermomechanical instability in this regime, in which catalytic reaction kinetics interact with heat transfer and mechanical buckling to create oscillations. These interacting components are separated and explored through experimentation, mathematical modeling, and scientific computation, and an explanation of the phenomenon emerges from their synthesis.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/avmbc-gke75A constrained sequential-lamination algorithm for the simulation of sub-grid microstructure in martensitic materials
https://resolver.caltech.edu/CaltechAUTHORS:20171128-114612180
Authors: {'items': [{'id': 'Aubry-S', 'name': {'family': 'Aubry', 'given': 'Sylvie'}}, {'id': 'Fago-M', 'name': {'family': 'Fago', 'given': 'Matt'}}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'Michael'}, 'orcid': '0000-0001-5877-4824'}]}
Year: 2003
DOI: 10.1016/S0045-7825(03)00260-3
We present a practical algorithm for partially relaxing multiwell energy densities such as pertain to materials undergoing martensitic phase transitions. The algorithm is based on sequential lamination, but the evolution of the microstructure during a deformation process is required to satisfy a continuity constraint, in the sense that the new microstructure should be reachable from the preceding one by a combination of branching and pruning operations. All microstructures generated by the algorithm are in static and configurational equilibrium. Owing to the continuity constraint imposed upon the microstructural evolution, the predicted material behavior may be path-dependent and exhibit hysteresis. In cases in which there is a strict separation of micro- and macrostructural lengthscales, the proposed relaxation algorithm may effectively be integrated into macroscopic finite-element calculations at the sub-grid level. We demonstrate this aspect of the algorithm by means of a numerical example concerned with the indentation of a Cu–Al–Ni shape memory alloy by a spherical indenter.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/b95bw-17e38A director-field model of DNA packaging in viral capsids
https://resolver.caltech.edu/CaltechAUTHORS:20171128-115155193
Authors: {'items': [{'id': 'Klug-W-S', 'name': {'family': 'Klug', 'given': 'W. S.'}}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'M.'}, 'orcid': '0000-0001-5877-4824'}]}
Year: 2003
DOI: 10.1016/S0022-5096(03)00071-1
The present work is concerned with the formulation of a continuum theory of viral DNA packaging based on a director field representation of the encapsidated DNA. The point values of the director field give the local direction and density of the DNA. The continuity of the DNA strand requires that the director field be divergence-free and tangent to the capsid wall. The energy of the DNA is defined as a functional of the director field which accounts for bending, torsion, and for electrostatic interactions through a density-dependent cohesive energy. The operative principle which determines the encapsidated DNA conformation is assumed to be energy minimization. We show that torsionless toroidal solenoids, consisting of planar coils contained within meridional planes and wrapped around a spool core, and fine mixtures of the solenoid and spool phase, beat the inverse spool construction.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/wavry-ss849The mechanics of deformation-induced subgrain-dislocation structures in metallic crystals at large strains
https://resolver.caltech.edu/CaltechAUTHORS:20171128-114743083
Authors: {'items': [{'id': 'Aubry-Sylvie', 'name': {'family': 'Aubry', 'given': 'S.'}, 'orcid': '0000-0002-5123-8655'}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'M.'}, 'orcid': '0000-0001-5877-4824'}]}
Year: 2003
DOI: 10.1098/rspa.2003.1179
We present a streamlined limiting case of the theory of Oritz & Repetto for crystals with microstructure in which the crystals are assumed to exhibit infinitely strong latent hardening. We take this property to signify that the crystal must necessarily deform in single slip at all material points. This requirement introduces a non–convex constraint that renders the incremental problem non–convex. We have assessed the ability of the theory to predict salient aspects of the body of experimental data compiled by Hansen et al. regarding lamellar dislocation structures in crystals deformed to large strains. Although the comparisons with experiment are somewhat indirect, the theory appears to correctly predict salient aspects of the statistics of misorientation angles and lamellar–boundary spacings, and the scaling of the average misorientation and spacing with increasing macroscopic strain.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/ppezt-1h692Optimal BV estimates for a discontinuous Galerkin method for linear elasticity
https://resolver.caltech.edu/CaltechAUTHORS:20110823-091200001
Authors: {'items': [{'id': 'Lew-A', 'name': {'family': 'Lew', 'given': 'Adrian'}}, {'id': 'Neff-P', 'name': {'family': 'Neff', 'given': 'Patrizio'}}, {'id': 'Sulsky-D', 'name': {'family': 'Sulsky', 'given': 'Deborah'}}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'Michael'}, 'orcid': '0000-0001-5877-4824'}]}
Year: 2004
DOI: 10.1155/S1687120004020052
We analyze a discontinuous Galerkin method for linear elasticity. The discrete formulation derives from the Hellinger-Reissner variational principle with the addition of stabilization terms analogous to those previously considered by others for the Navier-Stokes equations and a scalar Poisson equation. For our formulation, we first obtain convergence in a mesh-dependent norm and in the natural mesh-independent BD norm. We then prove a generalization of Korn's second inequality which allows us to strengthen our results to an optimal, mesh-independent BV estimate for the error.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/2tjfm-a4z97An Overview of Variational Integrators
https://resolver.caltech.edu/CaltechAUTHORS:20101005-091206576
Authors: {'items': [{'id': 'Lew-A', 'name': {'family': 'Lew', 'given': 'Adrian'}}, {'id': 'Marsden-J-E', 'name': {'family': 'Marsden', 'given': 'Jerrold E.'}}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'Michael'}, 'orcid': '0000-0001-5877-4824'}, {'id': 'West-M', 'name': {'family': 'West', 'given': 'Matthew'}}]}
Year: 2004
The purpose of this paper is to survey some recent advances in variational
integrators for both finite dimensional mechanical systems as well as continuum
mechanics. These advances include the general development of discrete
mechanics, applications to dissipative systems, collisions, spacetime integration algorithms,
AVI's (Asynchronous Variational Integrators), as well as reduction for
discrete mechanical systems. To keep the article within the set limits, we will only
treat each topic briefly and will not attempt to develop any particular topic in
any depth. We hope, nonetheless, that this paper serves as a useful guide to the
literature as well as to future directions and open problems in the subject.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/30x8v-bnd79Scaling properties of a low-actuation pressure microfluidic valve
https://resolver.caltech.edu/CaltechAUTHORS:STUjap04
Authors: {'items': [{'id': 'Studer-V', 'name': {'family': 'Studer', 'given': 'Vincent'}}, {'id': 'Hang-Giao', 'name': {'family': 'Hang', 'given': 'Giao'}}, {'id': 'Pandolfi-A', 'name': {'family': 'Pandolfi', 'given': 'Anna'}, 'orcid': '0000-0002-7084-7456'}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'Michael'}, 'orcid': '0000-0001-5877-4824'}, {'id': 'Anderson-W-F', 'name': {'family': 'Anderson', 'given': 'W. French'}}, {'id': 'Quake-S-R', 'name': {'family': 'Quake', 'given': 'Stephen R.'}}]}
Year: 2004
DOI: 10.1063/1.1629781
Using basic physical arguments, we present a design and method for the fabrication of microfluidic valves using multilayer soft lithography. These on-off valves have extremely low actuation pressures and can be used to fabricate active functions, such as pumps and mixers in integrated microfluidic chips. We characterized the performance of the valves by measuring both the actuation pressure and flow resistance over a wide range of design parameters, and compared them to both finite element simulations and alternative valve geometries.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/2n2fg-nvd30A Variational r-Adaption and Shape-Optimization Method for Finite-Deformation Elasticity
https://resolver.caltech.edu/CaltechCACR:CACR-2003-206
Authors: {'items': [{'id': 'Thoutireddy-P', 'name': {'family': 'Thoutireddy', 'given': 'P.'}}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'M.'}, 'orcid': '0000-0001-5877-4824'}]}
Year: 2004
This paper is concerned with the formulation of a variational r-adaption method for finite-deformation elastostatic problems. The distinguishing characteristic of the method is that the variational principle simultaneously supplies the solution, the optimal mesh and, in problems of shape optimization, the equilibrium shapes of the system. This is accomplished by minimizing the energy functional with respect to the nodal field values as well as with respect to the triangulation of the domain of analysis. Energy minimization with respect to the referential nodal positions has the effect of equilibrating the energetic or configurational forces acting on the nodes. We derive general expressions for the configuration forces for isoparametric elements and nonlinear, possibly anisotropic, materials under general loading. We illustrate the versatility and convergence characteristics of the method by way of selected numerical tests and applications, including the problem of a semi-infinite crack in linear and nonlinear elastic bodies; and the optimization of the shape of elastic inclusions.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/xszec-cvc22On the Γ-convergence of discrete dynamics and variational integrators
https://resolver.caltech.edu/CaltechAUTHORS:20171128-113838315
Authors: {'items': [{'id': 'Müller-S', 'name': {'family': 'Müller', 'given': 'S.'}}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'M.'}, 'orcid': '0000-0001-5877-4824'}]}
Year: 2004
DOI: 10.1007/BF02666023
For a simple class of Lagrangians and variational integrators, derived by time discretization of the action functional, we establish (i) the Γ-convergence of the discrete action sum to the action functional; (ii) the relation between Γ-convergence and weak* convergence of the discrete trajectories in {itW{su1,℞}}({ofR};{ofr{sun}; and (iii) the relation between Γ-convergence and the convergence of the Fourier transform of the discrete trajectories as measured in the flat norm.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/7vdch-k7c82Universal binding-energy relation for crystals that accounts for surface relaxation
https://resolver.caltech.edu/CaltechAUTHORS:20171128-113554693
Authors: {'items': [{'id': 'Hayes-R-L', 'name': {'family': 'Hayes', 'given': 'Robin L.'}}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'Michael'}, 'orcid': '0000-0001-5877-4824'}, {'id': 'Carter-E-A', 'name': {'family': 'Carter', 'given': 'Emily A.'}, 'orcid': '0000-0001-7330-7554'}]}
Year: 2004
DOI: 10.1103/PhysRevB.69.172104
We present a universal relation for crack surface cohesion including surface relaxation. Specifically, we analyze how N atomic planes respond to an opening displacement at its boundary, producing structurally relaxed surfaces. Via density-functional theory, we verify universality for metals (Al), ceramics (α−Al_2O_3), and semiconductors (Si). When the energy and opening displacement are scaled appropriately with respect to N, the uniaxial elastic constant, the relaxed surface energy, and the equilibrium interlayer spacing, all energy-displacement curves collapse onto a single universal curve.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/vzza8-j8591Variational time integrators
https://resolver.caltech.edu/CaltechAUTHORS:20100824-071747459
Authors: {'items': [{'id': 'Lew-A', 'name': {'family': 'Lew', 'given': 'A.'}}, {'id': 'Marsden-J-E', 'name': {'family': 'Marsden', 'given': 'J. E.'}}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'M.'}, 'orcid': '0000-0001-5877-4824'}, {'id': 'West-M', 'name': {'family': 'West', 'given': 'M.'}}]}
Year: 2004
DOI: 10.1002/nme.958
The purpose of this paper is to review and further develop the subject of variational integration algorithms as it applies to mechanical systems of engineering interest. In particular, the conservation properties of both synchronous and asynchronous variational integrators (AVIs) are discussed in detail. We present selected numerical examples which demonstrate the excellent accuracy, conservation and convergence characteristics of AVIs. In these tests, AVIs are found to result in substantial speed-ups, at equal accuracy, relative to explicit Newmark. A mathematical proof of convergence of the AVIs is also presented in this paper. Finally, we develop the subject of horizontal variations and configurational forces in discrete dynamics. This theory leads to exact path-independent characterizations of the configurational forces acting on discrete systems. Notable examples are the configurational forces acting on material nodes in a finite element discretisation; and the J-integral at the tip of a crack in a finite element mesh.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/t5h7p-yxn29A variational Cam-clay theory of plasticity
https://resolver.caltech.edu/CaltechAUTHORS:20171128-114018119
Authors: {'items': [{'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'M.'}, 'orcid': '0000-0001-5877-4824'}, {'id': 'Pandolfi-A', 'name': {'family': 'Pandolfi', 'given': 'A.'}, 'orcid': '0000-0002-7084-7456'}]}
Year: 2004
DOI: 10.1016/j.cma.2003.08.008
We present a finite deformation constitutive theory for non-cohesive granular media. The material model falls in the family of the so-called Cam-clay theories. As typical of Cam-clay models, soil is assumed to be frictional with a logarithmic-type compression. The same state boundary surface––described by ellipses––is taken as yield and plastic potential surface. Hardening is related only to plastic volumetric strains. The large deformation theory is based on the multiplicative decomposition of the deformation gradient into elastic and inelastic parts. We extend the stress update algorithms from small-strain plasticity to finite plasticity through the logarithmic and exponential mappings and adopt a fully variational characterization of the visco-plastic constitutive updates.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/zfc70-0zg50A cohesive model of fatigue of ferroelectric materials under electro-mechanical cyclic loading
https://resolver.caltech.edu/CaltechAUTHORS:20180709-154444981
Authors: {'items': [{'id': 'Arias-I', 'name': {'family': 'Arias', 'given': 'I.'}}, {'id': 'Serebrinsky-S', 'name': {'family': 'Serebrinsky', 'given': 'S.'}}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'M.'}, 'orcid': '0000-0001-5877-4824'}]}
Year: 2004
DOI: 10.1117/12.540097
A cohesive fatigue-crack nucleation and growth model for ferroelectric materials under electro-mechanical loading is presented. The central feature of the model is a hysteretic cohesive law which couples the mechanical and electrical fields. This law can be used in conjunction with general constitutive relations of bulk behavior, possibly including domain switching, in order to predict fatigue crack growth under arbitrary loading conditions. Another appealing feature of the model is its ability to predict fatigue-crack nucleation. Despite the scarcity and uncertainty of the experimental data, comparisons with PZT fatigue-life data are encouraging.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/64d44-9gx48Density-functional-theory-based local quasicontinuum method: Prediction of dislocation nucleation
https://resolver.caltech.edu/CaltechAUTHORS:20171128-113430030
Authors: {'items': [{'id': 'Fago-M', 'name': {'family': 'Fago', 'given': 'Matt'}}, {'id': 'Hayes-R-L', 'name': {'family': 'Hayes', 'given': 'Robin L.'}}, {'id': 'Carter-E-A', 'name': {'family': 'Carter', 'given': 'Emily A.'}, 'orcid': '0000-0001-7330-7554'}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'Michael'}, 'orcid': '0000-0001-5877-4824'}]}
Year: 2004
DOI: 10.1103/PhysRevB.70.100102
We introduce the density functional theory (DFT) local quasicontinuum method: a first principles multiscale material model that embeds DFT unit cells at the subgrid level of a finite element computation. The method can predict the onset of dislocation nucleation in both single crystals and those with inclusions, although extension to lattice defects awaits new methods. We show that the use of DFT versus embedded-atom method empirical potentials results in different predictions of dislocation nucleation in nanoindented face-centered-cubic aluminum.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/t0bqa-99f42A variational r-adaption and shape-optimization method for finite-deformation elasticity
https://resolver.caltech.edu/CaltechAUTHORS:20171128-114428592
Authors: {'items': [{'id': 'Thoutireddy-P', 'name': {'family': 'Thoutireddy', 'given': 'P.'}}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'M.'}, 'orcid': '0000-0001-5877-4824'}]}
Year: 2004
DOI: 10.1002/nme.1052
This paper is concerned with the formulation of a variational r-adaption method for finite-deformation elastostatic problems. The distinguishing characteristic of the method is that the variational principle simultaneously supplies the solution, the optimal mesh and, in problems of shape optimization, the equilibrium shapes of the system. This is accomplished by minimizing the energy functional with respect to the nodal field values as well as with respect to the triangulation of the domain of analysis. Energy minimization with respect to the referential nodal positions has the effect of equilibrating the energetic or configurational forces acting on the nodes. We derive general expressions for the configurational forces for isoparametric elements and non-linear, possibly anisotropic, materials under general loading. We illustrate the versatility and convergence characteristics of the method by way of selected numerical tests and applications, including the problem of a semi-infinite crack in linear and non-linear elastic bodies; and the optimization of the shape of elastic inclusions.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/pfd4c-b4p89Importance of Shear in the bcc-to-hcp Transformation in Iron
https://resolver.caltech.edu/CaltechAUTHORS:20171128-113250402
Authors: {'items': [{'id': 'Caspersen-K-J', 'name': {'family': 'Caspersen', 'given': 'Kyle J.'}}, {'id': 'Lew-A', 'name': {'family': 'Lew', 'given': 'Adrian'}}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'Michael'}, 'orcid': '0000-0001-5877-4824'}, {'id': 'Carter-E-A', 'name': {'family': 'Carter', 'given': 'Emily A.'}, 'orcid': '0000-0001-7330-7554'}]}
Year: 2004
DOI: 10.1103/PhysRevLett.93.115501
Iron shows a pressure-induced martensitic phase transformation from the ground state ferromagnetic bcc phase to a nonmagnetic hcp phase at ≈13 GPa. The exact transformation pressure (TP) and pathway are not known. Here we present a multiscale model containing a quantum-mechanics-based multiwell energy function accounting for the bcc and hcp phases of Fe and a construction of kinematically compatible and equilibrated mixed phases. This model suggests that shear stresses have a significant influence on the bcc↔hcp transformation. In particular, the presence of modest shear accounts for the scatter in measured TPs. The formation of mixed phases also provides an explanation for the observed hysteresis in TP.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/q44zg-8e091A quantum-mechanically informed continuum model of hydrogen embrittlement
https://resolver.caltech.edu/CaltechAUTHORS:20171128-114149734
Authors: {'items': [{'id': 'Serebrinsky-S', 'name': {'family': 'Serebrinsky', 'given': 'S.'}}, {'id': 'Carter-E-A', 'name': {'family': 'Carter', 'given': 'E. A.'}, 'orcid': '0000-0001-7330-7554'}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'M.'}, 'orcid': '0000-0001-5877-4824'}]}
Year: 2004
DOI: 10.1016/j.jmps.2004.02.010
We present a model of hydrogen embrittlement based upon: (i) a cohesive law dependent on impurity coverage that is calculated from first principles; (ii) a stress-assisted diffusion equation with appropriate boundary conditions accounting for the environment; (iii) a static continuum analysis of crack growth including plasticity; and (iv) the Langmuir relation determining the impurity coverage from its bulk concentration. We consider the effect of the following parameters: yield strength, stress intensity factor, hydrogen concentration in the environment, and temperature. The calculations reproduce the following experimental trends: (i) time to initiation and its dependence on yield strength and stress intensity factor; (ii) finite crack jump at initiation; (iii) intermittent crack growth; (iv) stages I and II of crack growth and their dependence on yield strength; (v) the effect of the environmental impurity concentration on the threshold stress intensity factor; and (vi) the effect of temperature on stage II crack velocity in the low-temperature range. In addition, the theoretically and experimentally observed intermittent cracking may be understood as being due to a time lag in the diffusion of hydrogen towards the cohesive zone, since a buildup of hydrogen is necessary in order for the crack to advance. The predictions of the model are in good quantitative agreement with available measurements, suggesting that hydrogen-induced degradation of cohesion is a likely mechanism for hydrogen-assisted cracking.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/j308h-p3p64Nanovoid Cavitation by Dislocation Emission in Aluminum
https://resolver.caltech.edu/CaltechAUTHORS:20171128-113716219
Authors: {'items': [{'id': 'Marian-J', 'name': {'family': 'Marian', 'given': 'Jaime'}}, {'id': 'Knap-J', 'name': {'family': 'Knap', 'given': 'Jaroslaw'}}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'Michael'}, 'orcid': '0000-0001-5877-4824'}]}
Year: 2004
DOI: 10.1103/PhysRevLett.93.165503
This Letter is concerned with the determination of the transition paths attendant to nanovoid growth in aluminum under hydrostatic tension. The analysis is, therefore, based on energy minimization at 0 K. Aluminum is modeled by the Ercolessi-Adams embedded-atom method, and spurious boundary artifacts are mitigated by the use of the quasicontinuum method. Our analysis reveals several stages of pressure buildup separated by yield points. The first yield point corresponds to the formation of highly stable tetrahedral dislocation junctions around the surfaces of the void. The second yield point is caused by the dissolution of the tetrahedral structures and the emission of conventional 1/2 ⟨110⟩{111} and anomalous 1/2 ⟨110⟩{001} dislocation loops.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/cta69-gf049A multi-phase field model of planar dislocation networks
https://resolver.caltech.edu/CaltechAUTHORS:KOSmsmse04
Authors: {'items': [{'id': 'Koslowski-Marisol', 'name': {'family': 'Koslowski', 'given': 'M.'}}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'M.'}, 'orcid': '0000-0001-5877-4824'}]}
Year: 2004
DOI: 10.1088/0965-0393/12/6/003
In this paper we extend the phase-field model of crystallographic slip of Ortiz (1999 J. Appl. Mech. ASME 66 289–98) and Koslowski et al (2001 J. Mech. Phys. Solids 50 2957–635) to slip processes that require the activation of multiple slip systems, and we apply the resulting model to the investigation of finite twist boundary arrays. The distribution of slip over a slip plane is described by means of multiple integer-valued phase fields. We show how all the terms in the total energy of the crystal, including the long-range elastic energy and the Peierls interplanar energy, can be written explicitly in terms of the multi-phase field. The model is used to ascertain stable dislocation structures arising in an array of finite twist boundaries. These structures are found to consist of regular square or hexagonal dislocation networks separated by complex dislocation pile-ups over the intervening transition layers.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/cq410-eaj82A Model for Kidney Tissue Damage under High Speed Loading
https://resolver.caltech.edu/CaltechAUTHORS:20190718-165126641
Authors: {'items': [{'id': 'Weinberg-K', 'name': {'family': 'Weinberg', 'given': 'Kerstin'}}, {'id': 'Colonius-T', 'name': {'family': 'Colonius', 'given': 'Tim'}, 'orcid': '0000-0003-0326-3909'}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'Michael'}, 'orcid': '0000-0001-5877-4824'}]}
Year: 2004
DOI: 10.1002/pamm.200410098
In a medical procedure to comminute kidney stones the patient is subjected to hypersonic waves focused at the stone. Unfortunately such shock waves also damage the surrounding kidney tissue. We present here a model for the mechanical response of the soft tissue to such a high speed loading regime.
The material model combines shear induced plasticity with irreversible volumetric expansion as induced, e.g., by cavitating bubbles. The theory is based on a multiplicative decomposition of the deformation gradient and on an internal variable formulation of continuum thermodynamics. By the use of logarithmic and exponential mappings the stress update algorithms are extended from small‐strain to the finite deformation range. In that way the time‐discretized version of the porous‐viscoplastic constitutive updates is described in a fully variational manner.
By numerical experiments we study the shock‐wave propagation into the tissue and analyze the resulting stress states. A first finite element simulation shows localized damage in the human kidney.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/fbxcw-3en51Microstructure evolution in the equal channel angular extrusion process
https://resolver.caltech.edu/CaltechAUTHORS:20171128-114315582
Authors: {'items': [{'id': 'Sivakumar-S-M', 'name': {'family': 'Sivakumar', 'given': 'Srinivasan M.'}}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'Michael'}, 'orcid': '0000-0001-5877-4824'}]}
Year: 2004
DOI: 10.1016/j.cma.2004.01.036
We apply a theory of single-crystal plasticity with microstructure to the simulation of the ECAE process. The specific microstructures considered in the simulations are of the sequential lamination type. The size of the microstructure is estimated a posteriori by means of a nonlocal extension of the theory which accounts for dislocation energies. Texture evolution is calculated simply by recourse to Taylor's hypothesis. Calculations concerned with an FCC material (Al–Cu alloy) and 90° ECAE reveal a wealth of information regarding the geometry, size, and texture evolution of subgrain microstructures. The predicted sizes and textures are in good quantitative agreement with the available experimental data.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/txf59-fmg90Prediction of Dislocation Nucleation During Nanoindentation by the Orbital-Free Density Functional Theory Local Quasi-continuum Method
https://resolver.caltech.edu/CaltechAUTHORS:HAYmms05
Authors: {'items': [{'id': 'Hayes-R-L', 'name': {'family': 'Hayes', 'given': 'Robin L.'}}, {'id': 'Fago-M', 'name': {'family': 'Fago', 'given': 'Matt'}}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'Michael'}, 'orcid': '0000-0001-5877-4824'}, {'id': 'Carter-E-A', 'name': {'family': 'Carter', 'given': 'Emily A.'}, 'orcid': '0000-0001-7330-7554'}]}
Year: 2005
DOI: 10.1137/080727531
We introduce the orbital-free density functional theory local quasi-continuum\linebreak (OFDFT-LQC) method: a first-principles-based multiscale material model that embeds OFDFT unit cells at the subgrid level of a finite element computation. Although this method cannot address intermediate length scales such as grain boundary evolution or microtexture, it is well suited to study material phenomena such as continuum level prediction of dislocation nucleation and the effects of varying alloy composition. The model is illustrated with the simulation of dislocation nucleation during indentation into the $(111)$ and $(\overline{1}10)$ surfaces of aluminum and compared against results obtained using an embedded atom method interatomic potential. None of the traditional dislocation nucleation criteria (Hertzian principal shear stress, actual principal shear stress, von Mises strain, or resolved shear stress) correlates with a previously proposed local elastic stability criterion, $\Lambda$. Discrepancies in dislocation nucleation predictions between OFDFT-LQC and other simulations highlight the need for accurate, atomistic constitutive models and the use of realistically sized indenters in the simulations.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/k9qxg-79547Three-dimensional director-field predictions of viral DNA packing arrangements
https://resolver.caltech.edu/CaltechAUTHORS:20170408-154613814
Authors: {'items': [{'id': 'Klug-W-S', 'name': {'family': 'Klug', 'given': 'W. S.'}}, {'id': 'Feldmann-M-T', 'name': {'family': 'Feldmann', 'given': 'M. T.'}}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'M.'}, 'orcid': '0000-0001-5877-4824'}]}
Year: 2005
DOI: 10.1007/s00466-004-0613-x
In this work we develop a discrete director-field model for coarse-grained description of packing arrangements of DNA within bacteriophage virus heads. This computational lattice model allows us to explore the complex energy landscape of fully three-dimensional configurations of packaged DNA. By minimizing the system's free energy by means of the simulated annealing and the conjugate gradient methods, we make predictions about favorable packing conformations. In particular we show that the planar-wrapped inverse spool conformation is stable everywhere inside a virus except in a central core region, where the DNA tends to buckle out of the spooling plane.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/w8vrq-9yk08A class of variational strain-localization finite elements
https://resolver.caltech.edu/CaltechAUTHORS:20171128-113115594
Authors: {'items': [{'id': 'Yang-Qiang', 'name': {'family': 'Yang', 'given': 'Q.'}}, {'id': 'Mota-A', 'name': {'family': 'Mota', 'given': 'A.'}}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'M.'}, 'orcid': '0000-0001-5877-4824'}]}
Year: 2005
DOI: 10.1002/nme.1199
We present a class of finite elements for capturing sub-grid localization processes such as shear bands and void sheets. The elements take the form of a double surface and deform in accordance with an arbitrary constitutive law. In particular they allow for the development of displacement and velocity jumps across volume element boundaries. The thickness of the localized zone is set by an additional field variable which is determined variationally. The localization elements are inserted, and become active, only when localized deformations become energetically favourable. The implementation presented in this work is three-dimensional and allows for finite deformations. The versatility and predictive ability of the method are demonstrated through a simple shear test and the simulation of the dynamic impact of a pre-notched C300 steel sample by a steel projectile.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/veaye-j9h25Shock wave induced damage in kidney tissue
https://resolver.caltech.edu/CaltechAUTHORS:20171128-111255148
Authors: {'items': [{'id': 'Weinberg-K', 'name': {'family': 'Weinberg', 'given': 'K.'}}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'M.'}, 'orcid': '0000-0001-5877-4824'}]}
Year: 2005
DOI: 10.1016/j.commatsci.2004.09.005
In a common medical procedure known as shock-wave lithotripsy hypersonic waves are generated and focused at the kidney stone. These shock waves are thought to fragment the stone but also lead to injuries of the kidney tissue. To predict and estimate this damage we develop here a mechanical model for the response of soft tissue to the exposure of shock waves.
The material model combines shear induced finite plasticity with irreversible volumetric expansion as induced, e.g., by cavitating bubbles. Dynamic effects like micro-inertia and rate sensitivity are included. The time-discretized porous-viscoplastic constitutive updates are described in a fully variational manner. A finite element analysis localizes the damage in the human kidney in good agreement to clinical and experimental studies.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/1561e-qt978Dislocation Microstructures and the Effective Behavior of Single Crystals
https://resolver.caltech.edu/CaltechAUTHORS:20171128-110428097
Authors: {'items': [{'id': 'Conti-S', 'name': {'family': 'Conti', 'given': 'Sergio'}, 'orcid': '0000-0001-7987-9174'}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'Michael'}, 'orcid': '0000-0001-5877-4824'}]}
Year: 2005
DOI: 10.1007/s00205-004-0353-2
We consider single-crystal plasticity in the limiting case of infinite latent hardening, which signifies that the crystal must deform in single slip at all material points. This requirement introduces a nonconvex constraint, and thereby induces the formation of fine-scale structures. We restrict attention throughout to linearized kinematics and deformation theory of plasticity, which is appropriate for monotonic proportional loading and confers the boundary value problem of plasticity a well-defined variational structure analogous to elasticity.
We first study a scale-invariant (local) problem. We show that, by developing microstructures in the form of sequential laminates of finite depth, crystals can beat the single-slip constraint, i.e., the macroscopic (relaxed) constitutive behavior is indistinguishable from multislip ideal plasticity. In a second step, we include dislocation line energies, and hence a length scale, into the model. Different regimes lead to several possible types of microstructure patterns. We present constructions which achieve the various optimal scaling laws, and discuss the relation with experimentally known scalings, such as the Hall-Petch law.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/jywmb-bte12Nanovoid deformation in aluminum under simple shear
https://resolver.caltech.edu/CaltechAUTHORS:20171128-110626684
Authors: {'items': [{'id': 'Marian-J', 'name': {'family': 'Marian', 'given': 'Jaime'}}, {'id': 'Knap-J', 'name': {'family': 'Knap', 'given': 'Jaroslaw'}}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'Michael'}, 'orcid': '0000-0001-5877-4824'}]}
Year: 2005
DOI: 10.1016/j.actamat.2005.02.046
We analyze the mechanisms underlying the deformation of a nanovoid in an Al crystal subjected to cyclic shear deformation using numerical simulations. Boundary and cell-size effects have been minimized by means of the quasicontinuum method. The deformation of the void entails a noticeable reduction in volume. During the loading phase, our analysis reveals several stages of stress buildup separated by yield points. The main mechanisms underlying the deformation of the crystal are: glide of primary and secondary partial dislocation loops with mixed edge-screw character; intersection of primary and secondary loops to form jogs and junctions; cross-slip; and dislocation multiplication and annihilation. Cross-slip occurs by the Fleischer mechanism and not by the more commonly assumed Friedel–Escaig mechanism. During unloading, most of the dislocation population and void volume reduction is recovered by re-absorption of dislocation loops and annihilation mediated by cross slip. However, a residual dislocation density remains around the void at the end of the unloading process.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/sakgp-w6m43A cohesive approach to thin-shell fracture and fragmentation
https://resolver.caltech.edu/CaltechAUTHORS:20171128-110244891
Authors: {'items': [{'id': 'Cirak-F', 'name': {'family': 'Cirak', 'given': 'Fehmi'}}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'Michael'}, 'orcid': '0000-0001-5877-4824'}, {'id': 'Pandolfi-A', 'name': {'family': 'Pandolfi', 'given': 'Anna'}, 'orcid': '0000-0002-7084-7456'}]}
Year: 2005
DOI: 10.1016/j.cma.2004.07.048
We develop a finite-element method for the simulation of dynamic fracture and fragmentation of thin-shells. The shell is spatially discretized with subdivision shell elements and the fracture along the element edges is modeled with a cohesive law. In order to follow the propagation and branching of cracks, subdivision shell elements are pre-fractured ab initio and the crack opening is constrained prior to crack nucleation. This approach allows for shell fracture in an in-plane tearing mode, a shearing mode, or a bending of hinge mode. The good performance of the method is demonstrated through the simulation of petalling failure experiments in aluminum plates.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/mhsn2-7x760Discrete Crystal Elasticity and Discrete Dislocations in Crystals
https://resolver.caltech.edu/CaltechAUTHORS:20171128-110029910
Authors: {'items': [{'id': 'Ariza-M-P', 'name': {'family': 'Ariza', 'given': 'M. P.'}, 'orcid': '0000-0003-0266-0216'}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'M.'}, 'orcid': '0000-0001-5877-4824'}]}
Year: 2005
DOI: 10.1007/s00205-005-0391-4
This article is concerned with the development of a discrete theory of crystal elasticity and dislocations in crystals. The theory is founded upon suitable adaptations to crystal lattices of elements of algebraic topology and differential calculus such as chain complexes and homology groups, differential forms and operators, and a theory of integration of forms. In particular, we define the lattice complex of a number of commonly encountered lattices, including body-centered cubic and face-centered cubic lattices. We show that material frame indifference naturally leads to discrete notions of stress and strain in lattices. Lattice defects such as dislocations are introduced by means of locally lattice-invariant (but globally incompatible) eigendeformations. The geometrical framework affords discrete analogs of fundamental objects and relations of the theory of linear elastic dislocations, such as the dislocation density tensor, the equation of conservation of Burgers vector, Kröner's relation and Mura's formula for the stored energy. We additionally supply conditions for the existence of equilibrium displacement fields; we show that linear elasticity is recovered as the Γ-limit of harmonic lattice statics as the lattice parameter becomes vanishingly small; we compute the Γ-limit of dilute dislocation distributions of dislocations; and we show that the theory of continuously distributed linear elastic dislocations is recovered as the Γ-limit of the stored energy as the lattice parameter and Burgers vectors become vanishingly small.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/1bb7c-t4c42A hysteretic cohesive-law model of fatigue-crack nucleation
https://resolver.caltech.edu/CaltechAUTHORS:20171128-110948068
Authors: {'items': [{'id': 'Serebrinsky-S', 'name': {'family': 'Serebrinsky', 'given': 'S.'}}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'M.'}, 'orcid': '0000-0001-5877-4824'}]}
Year: 2005
DOI: 10.1016/j.scriptamat.2005.07.015
We assess the ability of a hysteretic cohesive-law model to predict the number of cycles to fatigue-crack initiation. Comparisons with experimental data for a 2048-T851 aluminum alloy, 300 M steel and AISI 4340 steel suggest that the approach captures salient aspects of the observed behavior.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/98m3r-t3v70Validation of large scale simulations of dynamic fracture
https://resolver.caltech.edu/CaltechAUTHORS:20200609-095317554
Authors: {'items': [{'id': 'Arias-I', 'name': {'family': 'Arias', 'given': 'Irene'}}, {'id': 'Knap-J', 'name': {'family': 'Knap', 'given': 'Jaroslaw'}}, {'id': 'Chalivendra-V-B', 'name': {'family': 'Chalivendra', 'given': 'Vijaya B.'}}, {'id': 'Hong-Soonsung', 'name': {'family': 'Hong', 'given': 'Soonsung'}}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'Michael'}, 'orcid': '0000-0001-5877-4824'}, {'id': 'Rosakis-A-J', 'name': {'family': 'Rosakis', 'given': 'Ares J.'}, 'orcid': '0000-0003-0559-0794'}]}
Year: 2006
DOI: 10.1007/1-4020-5370-3_252
A novel integrated approach is developed for a systematic validation of large-scale finite element simulations on dynamic crack propagations along a weak plane [1]. A set of well-controlled experimental scheme is specifically designed to provide accurate input data for the numerical simulations as well as to provide metrics for quantitative comparisons between experimental and numerical results. Dynamic photoelasticity with high-speed photography is used to capture experimental records of dynamic crack propagations along a weak plane and to provide the crack propagation history. In the dynamic experiments, a modified Hopkinson bar setup with a notch-face loading configuration is used to obtain controlled loading conditions for the dynamic fracture problem. Also an inverse-problem approach of cohesive zone model is employed to obtain a realistic cohesive law, i.e. a traction-separation law, of the weak plane, from independently measured crack-tip deformation fields using speckle interferometry technique. The experimentally collected data, the loading conditions and the cohesive law, are considered as input for the finite element simulations [2]. We employ finite-deformation cohesive elements to account for crack initiation and growth in bulk finite-element discretizations of the experimental sample. As it is well know, the cohesive elements introduce an additional material-dependent length-scale into the finite element model. The demand of accurately resolving this length-scale by the finite-element discretization, as required for truly mesh-independent results, may often lead to discretizations containing several millions of elements. We therefore resort to massively parallel computing.
A comparison of the metrics from the numerical simulations with those from the experimental measurements is performed to validate the large-scale simulations. The numerical results show good agreements with the experimental results, leading to a successful validation of the large scale simulations of the dynamic crack propagations along the weak plane.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/pjwqf-qv757Three-dimensional fracture and fragmentation of artificial kidney stones
https://resolver.caltech.edu/CaltechAUTHORS:MOTjpcs06
Authors: {'items': [{'id': 'Mota-A', 'name': {'family': 'Mota', 'given': 'Alejandro'}}, {'id': 'Knap-J', 'name': {'family': 'Knap', 'given': 'Jaroslaw'}}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'Michael'}, 'orcid': '0000-0001-5877-4824'}]}
Year: 2006
DOI: 10.1088/1742-6596/46/1/041
The brittle fracture of a gypsum cylinder, which is used as an artificial kidney stone in lithotripsy research, is simulated by the use of the finite element method. The cylinder is submerged in water and is subjected to a pressure front parallel to one of its planar faces. The stresses induced by the pressure wave lead to fracture in the interior of the cylinder, with the formation of a spall plane located about 2/3 of the length from the face on which the pressure is applied. We show that the simulation reproduces the salient features of experimental observations.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/ngwjs-zfv66Finite strain r-adaption based on a fully variational framework
https://resolver.caltech.edu/CaltechAUTHORS:20191008-153941494
Authors: {'items': [{'id': 'Mosler-J', 'name': {'family': 'Mosler', 'given': 'J.'}}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'M.'}, 'orcid': '0000-0001-5877-4824'}]}
Year: 2006
DOI: 10.1007/1-4020-5370-3_407
A novel r-adaptive finite element strategy based on a fully variational framework is presented. Provided the underlying physical problem is characterized by means of a minimization principle, the proposed method seeks, for a fixed number of nodes, for the best finite element interpolation depending on the nodal positions with respect to the deformed (x) as well as the undeformed (X) configuration, cf. [1]. The existence of a minimization problem does not represent a very strong restriction, since for many physical problems such as standard dissipative media an incremental potential can also be recast, cf. [2]. While minimizing the potential considered by fixing the nodes within the undeformed configuration corresponds to classical NEWTONian mechanics, a variation with respect to (X) is associated with ESHELBY mechanics, cf. [3]. However, in contrast to the simplicity of the concept, its numerical implementation is far away from being straightforward. According to [4], the resulting system of equations is highly singular and hence, standard optimization strategies cannot be applied. In this paper, a viscous regularization is used. This approach is designed to render the minimization problem well-posed while leaving its solutions unchanged. Obviously, relocating the nodes within the undeformed configuration by fixing the triangulation (the connectivity) may lead to strong topological constraints. As a consequence, an energy based re-meshing strategy is advocated. Contrary to classical mesh-improvement methods based on geometrical quality measures, the novel concepts identifies local energy minimizers. That is, the energy of the new triangulation is always lower than that of the initial discretization. The performance of the resulting finite element model is demonstrated by fully three-dimensional examples.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/v6y7r-45c96Cohesive Model of Electromechanical Fatigue for Ferroelectric Materials and Structures
https://resolver.caltech.edu/CaltechAUTHORS:20190821-105957679
Authors: {'items': [{'id': 'Arias-I', 'name': {'family': 'Arias', 'given': 'Irene'}}, {'id': 'Serebrinsky-S', 'name': {'family': 'Serebrinsky', 'given': 'Santiago'}}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'Michael'}, 'orcid': '0000-0001-5877-4824'}]}
Year: 2006
DOI: 10.1007/1-4020-5370-3_158
Ferroelectric materials are extensively used in a variety of sensor and actuator applications, where the non-linear coupling between mechanical and electrical fields are of primary interest. They are also a promising set of materials for improved dynamic as well as non-volatile memory devices, where only the electrical properties are directly exploited. However, ferroelectrics are brittle, and their low fracture toughness (in the order of 1MPam1/2) makes them susceptible to cracking. In addition, ferroelectric materials exhibit electrical fatigue (loss of switchable polarization) under cyclic electrical loading and, due to the strong electro-mechanical coupling, sometimes mechanical fatigue as well. Conversely, the propagation of fatigue cracks hinders the performance of the devices and raises serious reliability concerns.
Despite recent experimental and modelling advances, the precise nature of the interactions between fracture, deformation and defect structures underlying ferroelectric fatigue is in need of further elucidation, and a physics-based multiscale model enabling the prediction of the fatigue life of ferroelectric devices is yet to emerge. Therefore, there remains a need for phenomenological and empirical models that can be experimentally validated and used in engineering design.
We present a model of electro-mechanical ferroelectric fatigue based on the postulate of a ferroelectric cohesive law that: couples mechanical displacement and electric-potential discontinuity to mechanical tractions and surface-charge density; and exhibits a monotonic envelope and loading-unloading hysteresis [1]. The model is applicable whenever the changes in properties leading to fatigue are localized in one or more planar-like regions, modelled by the cohesive surfaces. We validate the model against experimental data for a simple test configuration consisting of an infinite slab acted upon by an oscillatory voltage differential across the slab and otherwise stress free. The model captures salient features of the experimental record including: the existence of a threshold nominal field for the onset of fatigue; the dependence of the threshold on the applied-field frequency; the dependence of fatigue life on the amplitude of the nominal field; and the dependence of the coercive field on the size of the component, or size effect. Our results, although not conclusive, indicate that planar-like regions affected by cycling may lead to the observed fatigue in tetragonal PZT.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/wppwn-yq492A variational constitutive model for porous metal plasticity
https://resolver.caltech.edu/CaltechAUTHORS:20171128-111130155
Authors: {'items': [{'id': 'Weinberg-K', 'name': {'family': 'Weinberg', 'given': 'K.'}}, {'id': 'Mota-A', 'name': {'family': 'Mota', 'given': 'A.'}}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'M.'}, 'orcid': '0000-0001-5877-4824'}]}
Year: 2006
DOI: 10.1007/s00466-005-0685-2
This paper presents a variational formulation of viscoplastic constitutive updates for porous elastoplastic materials. The material model combines von Mises plasticity with volumetric plastic expansion as induced, e.g., by the growth of voids and defects in metals. The finite deformation theory is based on the multiplicative decomposition of the deformation gradient and an internal variable formulation of continuum thermodynamics. By the use of logarithmic and exponential mappings the stress update algorithms are extended from small strains to finite deformations. Thus the time-discretized version of the porous-viscoplastic constitutive updates is described in a fully variational manner. The range of behavior predicted by the model and the performance of the variational update are demonstrated by its application to the forced expansion and fragmentation of U-6%Nb rings.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/rs6et-rmr28A Finite-Deformation Constitutive Model of Bulk Metallic Glass Plasticity
https://resolver.caltech.edu/CaltechAUTHORS:20171128-103311936
Authors: {'items': [{'id': 'Yang-Qiang', 'name': {'family': 'Yang', 'given': 'Q.'}}, {'id': 'Mota-A', 'name': {'family': 'Mota', 'given': 'A.'}}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'M.'}, 'orcid': '0000-0001-5877-4824'}]}
Year: 2006
DOI: 10.1007/s00466-005-0690-5
A constitutive model of bulk metallic glass (BMG) plasticity is developed which accounts for finitedeformation kinematics, the kinetics of free volume, strain hardening, thermal softening, rate-dependency and non-Newtonian viscosity. The model has been validated against uniaxial compression test data; and against plate bending experiments. The model captures accurately salient aspects of the material behavior including: the viscosity of Vitreloy 1 as a function of temperature and strain rate; the temperature and strain-rate dependence of the equilibrium free-volume concentration; the uniaxial compression stress-strain curves as a function of strain rate and temperature; and the dependence of shear-band spacing on plate thickness. Calculations suggest that, under adiabatic conditions, strain softening and localization in BMGs is due both to an increase in free volume and to the rise in temperature within the band. The calculations also suggest that the shear band spacing in plate-bending specimens is controlled by the stress relaxation in the vicinity of the shear bands.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/gfc23-gmj11A variational formulation of the coupled thermo-mechanical boundary-value problem for general dissipative solids
https://resolver.caltech.edu/CaltechAUTHORS:20171128-103435161
Authors: {'items': [{'id': 'Yang-Qiang', 'name': {'family': 'Yang', 'given': 'Q.'}}, {'id': 'Stainier-Laurent', 'name': {'family': 'Stainier', 'given': 'L.'}, 'orcid': '0000-0001-6719-6616'}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'M.'}, 'orcid': '0000-0001-5877-4824'}]}
Year: 2006
DOI: 10.1016/j.jmps.2005.08.010
A variational formulation of the coupled thermo-mechanical boundary-value problem for general dissipative solids is presented. The coupled thermo-mechanical boundary-value problem under consideration consists of the equilibrium problem for a deformable, inelastic and dissipative solid with the heat conduction problem appended in addition. The variational formulation allows for general dissipative solids, including finite elastic and plastic deformations, non-Newtonian viscosity, rate sensitivity, arbitrary flow and hardening rules, as well as heat conduction. We show that a joint potential function exists such that both the conservation of energy and the balance of linear momentum equations follow as Euler–Lagrange equations. The identification of the joint potential requires a careful distinction between equilibrium and external temperatures, which are equal at equilibrium. The variational framework predicts the fraction of dissipated energy that is converted to heat. A comparison of this prediction and experimental data suggests that α-titanium and Al2024-T conform to the variational framework.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/1br8c-y3653A phenomenological cohesive model of ferroelectric fatigue
https://resolver.caltech.edu/CaltechAUTHORS:20191018-114729501
Authors: {'items': [{'id': 'Arias-I', 'name': {'family': 'Arias', 'given': 'I.'}}, {'id': 'Serebrinsky-S', 'name': {'family': 'Serebrinsky', 'given': 'S.'}}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'M.'}, 'orcid': '0000-0001-5877-4824'}]}
Year: 2006
DOI: 10.1016/j.actamat.2005.10.035
We develop a phenomenological model of electro-mechanical ferroelectric fatigue based on a ferroelectric cohesive law that couples mechanical displacement and electric-potential discontinuity to mechanical tractions and surface-charge density. The ferroelectric cohesive law exhibits a monotonic envelope and loading–unloading hysteresis. The model is applicable whenever the changes in properties leading to fatigue are localized in one or more planar-like regions, modeled by the cohesive surfaces. We validate the model against experimental data for a simple test configuration consisting of an infinite slab acted upon by an oscillatory voltage differential across the slab and otherwise stress free. The model captures salient features of the experimental record including: the existence of a threshold nominal field for the onset of fatigue; the dependence of the threshold on the applied-field frequency; the dependence of fatigue life on the amplitude of the nominal field; and the dependence of the coercive field on the size of the component, or size effect. Our results, although not conclusive, indicate that planar-like regions affected by cycling may lead to the observed fatigue in tetragonal PZT.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/kg0df-qg663Local maximum-entropy approximation schemes: a seamless bridge between finite elements and meshfree methods
https://resolver.caltech.edu/CaltechAUTHORS:20171128-101329930
Authors: {'items': [{'id': 'Arroyo-M', 'name': {'family': 'Arroyo', 'given': 'M.'}}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'M.'}, 'orcid': '0000-0001-5877-4824'}]}
Year: 2006
DOI: 10.1002/nme.1534
We present a one-parameter family of approximation schemes, which we refer to as local maximum-entropy approximation schemes, that bridges continuously two important limits: Delaunay triangulation and maximum-entropy (max-ent) statistical inference. Local max-ent approximation schemes represent a compromise—in the sense of Pareto optimality—between the competing objectives of unbiased statistical inference from the nodal data and the definition of local shape functions of least width. Local max-ent approximation schemes are entirely defined by the node set and the domain of analysis, and the shape functions are positive, interpolate affine functions exactly, and have a weak Kronecker-delta property at the boundary. Local max-ent approximation may be regarded as a regularization, or thermalization, of Delaunay triangulation which effectively resolves the degenerate cases resulting from the lack or uniqueness of the triangulation. Local max-ent approximation schemes can be taken as a convenient basis for the numerical solution of PDEs in the style of meshfree Galerkin methods. In test cases characterized by smooth solutions we find that the accuracy of local max-ent approximation schemes is vastly superior to that of finite elements.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/e2913-7r808On spatial and material covariant balance laws in elasticity
https://resolver.caltech.edu/CaltechAUTHORS:YAVjmp06
Authors: {'items': [{'id': 'Yavari-A', 'name': {'family': 'Yavari', 'given': 'Arash'}}, {'id': 'Marsden-J-E', 'name': {'family': 'Marsden', 'given': 'Jerrold E.'}}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'Michael'}, 'orcid': '0000-0001-5877-4824'}]}
Year: 2006
DOI: 10.1063/1.2190827
This paper presents some developments related to the idea of covariance in elasticity. The geometric point of view in continuum mechanics is briefly reviewed. Building on this, regarding the reference configuration and the ambient space as Riemannian manifolds with their own metrics, a Lagrangian field theory of elastic bodies with evolving reference configurations is developed. It is shown that even in this general setting, the Euler-Lagrange equations resulting from horizontal (referential) variations are equivalent to those resulting from vertical (spatial) variations. The classical Green-Naghdi-Rivilin theorem is revisited and a material version of it is discussed. It is shown that energy balance, in general, cannot be invariant under isometries of the reference configuration, which in this case is identified with a subset of [openface R]3. Transformation properties of balance of energy under rigid translations and rotations of the reference configuration is obtained. The spatial covariant theory of elasticity is also revisited. The transformation of balance of energy under an arbitrary diffeomorphism of the reference configuration is obtained and it is shown that some nonstandard terms appear in the transformed balance of energy. Then conditions under which energy balance is materially covariant are obtained. It is seen that material covariance of energy balance is equivalent to conservation of mass, isotropy, material Doyle-Ericksen formula and an extra condition that we call configurational inviscidity. In the last part of the paper, the connection between Noether's theorem and covariance is investigated. It is shown that the Doyle-Ericksen formula can be obtained as a consequence of spatial covariance of Lagrangian density. Similarly, it is shown that the material Doyle-Ericksen formula can be obtained from material covariance of Lagrangian density.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/edp5p-tzy15Effective Cohesive Behavior of Layers of Interatomic Planes
https://resolver.caltech.edu/CaltechAUTHORS:20171128-101614160
Authors: {'items': [{'id': 'Braides-A', 'name': {'family': 'Braides', 'given': 'Andrea'}}, {'id': 'Lew-A-J', 'name': {'family': 'Lew', 'given': 'Adrian J.'}}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'Michael'}, 'orcid': '0000-0001-5877-4824'}]}
Year: 2006
DOI: 10.1007/s00205-005-0399-9
A simple model of cleavage in brittle crystals consists of a layer of material containing N atomic planes separating in accordance with an interplanar potential under the action of an opening displacement δ prescribed on the boundary of the layer. The problem addressed in this work concerns the characterization of the constrained minima of the energy E_N of the layer as a function of δ as N becomes large. These minima determine the effective or macroscopic cohesive law of the crystal. The main results presented in this communication are: (i) the computation of the Γ limit E_0 of E_N as N → ∞; (ii) the characterization of the minimum values of E_0 as a function of the macroscopic opening displacement; (iii) a proof of uniform convergence of the minima of E_N for the case of nearest-neighbor interactions; and (iv) a proof of uniform convergence of the derivatives of E_N, or tractions, in the same case. The scaling on which the present Γ-convergence analysis is based has the effect of separating the bulk and surface contributions to the energy. It differs crucially from other scalings employed in the past in that it renders both contributions of the same order.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/y19rn-b5d26Quantum mechanics based multiscale modeling of stress-induced phase transformations in iron
https://resolver.caltech.edu/CaltechAUTHORS:20171128-102325449
Authors: {'items': [{'id': 'Lew-A', 'name': {'family': 'Lew', 'given': 'A.'}}, {'id': 'Caspersen-K-J', 'name': {'family': 'Caspersen', 'given': 'K.'}}, {'id': 'Carter-E-A', 'name': {'family': 'Carter', 'given': 'E. A.'}, 'orcid': '0000-0001-7330-7554'}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'M.'}, 'orcid': '0000-0001-5877-4824'}]}
Year: 2006
DOI: 10.1016/j.jmps.2005.11.009
The ground state crystal structure of Fe, ferromagnetic body-centered cubic (bcc), undergoes a stress-induced martensitic phase transformation to a hexagonally close-packed (hcp) structure. Both bcc and hcp have been observed to coexist over a large range deformations, such that the nonlinearities in the constitutive behavior of each phase need to be included for an accurate description. We present herein a methodology to construct high-fidelity quantum mechanics based nonlinear elastic energy densities, amenable to be included in microstructural optimization procedures like sequential lamination. We use the model to show that the transition pressure (TP) has a strong dependence on relatively small amounts of shear deformation, and to investigate the value of the TP under uniaxial compressions, presumably found in shock-loaded materials. Results hint that more complex deformation patterns may need be present to be consistent with measured experimental values.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/5sxbd-wbq80Prediction of dislocation nucleation during nanoindentation of Al_3Mg by the orbital-free density functional theory local quasicontinuum method
https://resolver.caltech.edu/CaltechAUTHORS:20171128-102135095
Authors: {'items': [{'id': 'Hayes-R-L', 'name': {'family': 'Hayes', 'given': 'Robin L.'}}, {'id': 'Ho-Gregory', 'name': {'family': 'Ho', 'given': 'Gregory'}}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'Michael'}, 'orcid': '0000-0001-5877-4824'}, {'id': 'Carter-E-A', 'name': {'family': 'Carter', 'given': 'Emily A.'}, 'orcid': '0000-0001-7330-7554'}]}
Year: 2006
DOI: 10.1080/14786430500525829
The first-principles prediction of dislocation nucleation in metallic systems subject to realistically sized indenters requires a multiscale approach due to the prohibitive computational expense. The largest empirical atomistic simulations include at most a billion atoms, at the same time requiring the parameterization of new interactions whenever an additional species or crystal structure is added. The multiscale orbital-free density functional theory–local quasicontinuum (OFDFT-LQC) method overcomes these problems by using first-principles OFDFT to capture the atomic interactions while relying upon LQC to evolve the macroscopic system. We use this method to indent the (111) surface of a 2×2×1μm piece of L1_2 Al_3Mg. Using a localization criterion, the first dislocation is predicted to form off-axis on the slip plane in the direction after the indenter has penetrated 70 nm. Other popular dislocation nucleation criteria give different predictions. These results are strikingly similar to those for indentation into the (111) surface of Al, indicating that the underlying crystal structure, not the atomic identity, is the most important factor in determining the onset of plasticity.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/8t74q-bak81BV estimates for mortar methods in linear elasticity
https://resolver.caltech.edu/CaltechAUTHORS:20171128-101948445
Authors: {'items': [{'id': 'Hauret-P', 'name': {'family': 'Hauret', 'given': 'Patrice'}}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'Michael'}, 'orcid': '0000-0001-5877-4824'}]}
Year: 2006
DOI: 10.1016/j.cma.2005.09.021
This paper is concerned with the convergence of mortar methods applied to linear elasticity. We prove that the conventional mesh-dependent norms used in the analysis of mortar methods are bounded below by the BV norm. When combined with standard results, this bound establishes a decomposition-independent and mesh-independent proof of the convergence of mortar methods in linear elasticity.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/eerx7-pv778On the numerical implementation of variational arbitrary Lagrangian–Eulerian (VALE) formulations
https://resolver.caltech.edu/CaltechAUTHORS:20171128-102503230
Authors: {'items': [{'id': 'Mosler-J', 'name': {'family': 'Mosler', 'given': 'J.'}}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'M.'}, 'orcid': '0000-0001-5877-4824'}]}
Year: 2006
DOI: 10.1002/nme.1621
This paper is concerned with the implementation of variational arbitrary Lagrangian–Eulerian formulations, also known as variational r-adaption methods. These methods seek to minimize the energy function with respect to the finite-element mesh over the reference configuration of the body. We propose a solution strategy based on a viscous regularization of the configurational forces. This procedure eliminates the ill-posedness of the problem without changing its solutions, i.e. the minimizers of the regularized problems are also minimizers of the original functional. We also develop strategies for optimizing the triangulation, or mesh connectivity, and for allowing nodes to migrate in and out of the boundary of the domain. Selected numerical examples demonstrate the robustness of the solution procedures and their ability to produce highly anisotropic mesh refinement in regions of high energy density.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/g23gb-6rh44A recursive-faulting model of distributed damage in confined brittle materials
https://resolver.caltech.edu/CaltechAUTHORS:20110715-150624112
Authors: {'items': [{'id': 'Pandolfi-A', 'name': {'family': 'Pandolfi', 'given': 'A.'}, 'orcid': '0000-0002-7084-7456'}, {'id': 'Conti-S', 'name': {'family': 'Conti', 'given': 'S.'}, 'orcid': '0000-0001-7987-9174'}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'M.'}, 'orcid': '0000-0001-5877-4824'}]}
Year: 2006
DOI: 10.1016/j.jmps.2006.02.003
We develop a model of distributed damage in brittle materials deforming in triaxial compression based on the explicit construction of special microstructures obtained by recursive faulting. The model aims to predict the effective or macroscopic behavior of the material from its elastic and fracture properties; and to predict the microstructures underlying the microscopic behavior. The model accounts for the elasticity of the matrix, fault nucleation and the cohesive and frictional behavior of the faults. We analyze the resulting quasistatic boundary value problem and determine the relaxation of the potential energy, which describes the macroscopic material behavior averaged over all possible fine-scale structures. Finally, we present numerical calculations of the dynamic multi-axial compression experiments on sintered aluminum nitride of Chen and Ravichandran [1994. Dynamic compressive behavior of ceramics under lateral confinement. J. Phys. IV 4, 177–182; 1996a. Static and dynamic compressive behavior of aluminum nitride under moderate confinement. J. Am. Soc. Ceramics 79(3), 579–584; 1996b. An experimental technique for imposing dynamic multiaxial compression with mechanical confinement. Exp. Mech. 36(2), 155–158; 2000. Failure mode transition in ceramics under dynamic multiaxial compression. Int. J. Fracture 101, 141–159]. The model correctly predicts the general trends regarding the observed damage patterns; and the brittle-to-ductile transition resulting under increasing confinement.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/7jjhx-nzp67A 3D Cohesive Investigation on Branching for Brittle Materials
https://resolver.caltech.edu/CaltechAUTHORS:20200604-144115576
Authors: {'items': [{'id': 'Yu-Rena-C', 'name': {'family': 'Yu', 'given': 'Rena C.'}, 'orcid': '0000-0003-4176-0324'}, {'id': 'Pandolfi-A', 'name': {'family': 'Pandolfi', 'given': 'Anna'}, 'orcid': '0000-0002-7084-7456'}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'Michael'}, 'orcid': '0000-0001-5877-4824'}]}
Year: 2007
DOI: 10.1007/978-1-4020-6530-9_8
Recently, Fineberg and Sharon conducted dynamic crack propagation experiments in PMMA and soda lime glass [1, 2, 3, 4, 5, 6, 7]. They pointed out some notable features of micro-branching instabilities in brittle materials, and their experiments raised a considerable interest for the brittle fracture dynamics. In this paper we present some numerical results on brittle fracture obtained by using cohesive theories of fracture. In the numerical calculations, the branching instability is a natural outcome of the explicit formulation. The cohesive model captures the basic features of experiments, such as the transition of the crack surface from smooth to hackled with increasing energy flux, and the power-law functional form of the profile of the crack branches.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/c17q0-vxx53A theory of anharmonic lattice statics for analysis of defective crystals
https://resolver.caltech.edu/CaltechAUTHORS:20131009-090857631
Authors: {'items': [{'id': 'Yavari-A', 'name': {'family': 'Yavari', 'given': 'Arash'}}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'Michael'}, 'orcid': '0000-0001-5877-4824'}, {'id': 'Bhattacharya-K', 'name': {'family': 'Bhattacharya', 'given': 'Kaushik'}, 'orcid': '0000-0003-2908-5469'}]}
Year: 2007
DOI: 10.1007/s10659-006-9079-8
This paper develops a theory of anharmonic lattice statics for the analysis of defective complex lattices. This theory differs from the classical treatments of defects in lattice statics in that it does not rely on harmonic and homogenous force constants. Instead, it starts with an interatomic potential, possibly with infinite range as appropriate for situations with electrostatics, and calculates the equilibrium states of defects. In particular, the present theory accounts for the differences in the force constants near defects and in the bulk. The present formulation reduces the analysis of defective crystals to the solution of a system of nonlinear difference equations with appropriate boundary conditions. A harmonic problem is obtained by linearizing the nonlinear equations, and a method for obtaining analytical solutions is described in situations where one can exploit symmetry. It is then extended to the anharmonic problem using modified Newton–Raphson iteration. The method is demonstrated for model problems motivated by domain walls in ferroelectric materials.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/7qryr-3vt64A discrete mechanics approach to dislocation dynamics in BCC crystals
https://resolver.caltech.edu/CaltechAUTHORS:20171121-135628923
Authors: {'items': [{'id': 'Ramasubramaniam-A', 'name': {'family': 'Ramasubramaniam', 'given': 'A.'}}, {'id': 'Ariza-M-P', 'name': {'family': 'Ariza', 'given': 'M. P.'}, 'orcid': '0000-0003-0266-0216'}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'M.'}, 'orcid': '0000-0001-5877-4824'}]}
Year: 2007
DOI: 10.1016/j.jmps.2006.08.005
A discrete mechanics approach to modeling the dynamics of dislocations in BCC single crystals is presented. Ideas are borrowed from discrete differential calculus and algebraic topology and suitably adapted to crystal lattices. In particular, the extension of a crystal lattice to a CW complex allows for convenient manipulation of forms and fields defined over the crystal. Dislocations are treated within the theory as energy-minimizing structures that lead to locally lattice-invariant but globally incompatible eigendeformations. The discrete nature of the theory eliminates the need for regularization of the core singularity and inherently allows for dislocation reactions and complicated topological transitions. The quantization of slip to integer multiples of the Burgers' vector leads to a large integer optimization problem. A novel approach to solving this NP-hard problem based on considerations of metastability is proposed. A numerical example that applies the method to study the emanation of dislocation loops from a point source of dilatation in a large BCC crystal is presented. The structure and energetics of BCC screw dislocation cores, as obtained via the present formulation, are also considered and shown to be in good agreement with available atomistic studies. The method thus provides a realistic avenue for mesoscale simulations of dislocation based crystal plasticity with fully atomistic resolution.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/bcbhq-vy878Concurrent Multiscale Computing of Deformation Microstructure by Relaxation and Local Enrichment with Application to Single-Crystal Plasticity
https://resolver.caltech.edu/CaltechAUTHORS:CONmms07
Authors: {'items': [{'id': 'Conti-S', 'name': {'family': 'Conti', 'given': 'Sergio'}, 'orcid': '0000-0001-7987-9174'}, {'id': 'Hauret-P', 'name': {'family': 'Hauret', 'given': 'Patrice'}}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'Michael'}, 'orcid': '0000-0001-5877-4824'}]}
Year: 2007
DOI: 10.1137/060662332
This paper is concerned with the effective modeling of deformation microstructures within a concurrent multiscale computing framework. We present a rigorous formulation of concurrent multiscale computing based on relaxation; we establish the connection between concurrent multiscale computing and enhanced-strain elements; and we illustrate the approach in an important area of application, namely, single-crystal plasticity, for which the explicit relaxation of the problem is derived analytically. This example demonstrates the vast effect of microstructure formation on the macroscopic behavior of the sample, e.g., on the force/travel curve of a rigid indentor. Thus, whereas the unrelaxed model results in an overly stiff response, the relaxed model exhibits a proper limit load, as expected. Our numerical examples additionally illustrate that ad hoc element enhancements, e.g., based on polynomial, trigonometric, or similar representations, are unlikely to result in any significant relaxation in general.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/d2sp0-24539Quasi-continuum orbital-free density-functional theory: A route to multi-million atom non-periodic DFT calculation
https://resolver.caltech.edu/CaltechAUTHORS:20131007-153105987
Authors: {'items': [{'id': 'Gavini-V', 'name': {'family': 'Gavini', 'given': 'Vikram'}}, {'id': 'Bhattacharya-K', 'name': {'family': 'Bhattacharya', 'given': 'Kaushik'}, 'orcid': '0000-0003-2908-5469'}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'Michael'}, 'orcid': '0000-0001-5877-4824'}]}
Year: 2007
DOI: 10.1016/j.jmps.2007.01.012
Density-functional theory (DFT) has provided insights into various materials properties in the recent decade. However, its computational complexity has made other aspects, especially those involving defects, beyond reach. Here, we present a method that enables the study of multi-million atom clusters using orbital-free density-functional theory (OFDFT) with no spurious physics or restrictions on geometry. The key ideas are: (i) a real-space formulation; (ii) a nested finite-element implementation of the formulation and (iii) a systematic means of adaptive coarse-graining retaining full resolution where necessary and coarsening elsewhere with no patches, assumptions or structure. We demonstrate the method, its accuracy under modest computational cost and the physical insights it offers by studying one and two vacancies in aluminum crystals consisting of millions of atoms.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/had6d-4zn49Non-periodic finite-element formulation of orbital-free density functional theory
https://resolver.caltech.edu/CaltechAUTHORS:20101213-152730530
Authors: {'items': [{'id': 'Gavini-V', 'name': {'family': 'Gavini', 'given': 'Vikram'}}, {'id': 'Knap-J', 'name': {'family': 'Knap', 'given': 'Jaroslaw'}}, {'id': 'Bhattacharya-K', 'name': {'family': 'Bhattacharya', 'given': 'Kaushik'}, 'orcid': '0000-0003-2908-5469'}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'Michael'}, 'orcid': '0000-0001-5877-4824'}]}
Year: 2007
DOI: 10.1016/j.jmps.2006.09.011
We propose an approach to perform orbital-free density functional theory calculations in a non-periodic setting using the finite-element method. We consider this a step towards constructing a seamless multi-scale approach for studying defects like vacancies, dislocations and cracks that require quantum mechanical resolution at the core and are sensitive to long range continuum stresses. In this paper, we describe a local real-space variational formulation for orbital-free density functional theory, including the electrostatic terms and prove existence results. We prove the convergence of the finite-element approximation including numerical quadratures for our variational formulation. Finally, we demonstrate our method using examples.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/5p4s5-bkb13Improved design of low-pressure fluidic microvalves
https://resolver.caltech.edu/CaltechAUTHORS:PANjmm07
Authors: {'items': [{'id': 'Pandolfi-A', 'name': {'family': 'Pandolfi', 'given': 'Anna'}, 'orcid': '0000-0002-7084-7456'}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'Michael'}, 'orcid': '0000-0001-5877-4824'}]}
Year: 2007
DOI: 10.1088/0960-1317/17/8/010
Multilayer soft lithography (MSL) is used to fabricate monolithic elastomeric on-off microvalves by adopting a two-layer cross-channel architecture. The performance of microvalves is strongly dependent on the two-channel geometry (width, height and shape) and on the thickness of the interlayer membrane. Using a finite element model previously validated against experiments, we propose a new fluidic microvalve design, based on the concept of chemically swelling the thin interlayer membrane so as to induce two stable equilibrium configurations. The complete closure of the new valve may then be achieved by applying a much reduced actuation pressure, down to 1/4 of the pressure needed by the standard monostable design. The maximum stress in the interlayer membrane of the bistable valve also drops to 1/3 of the value corresponding to the standard design.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/b5hpy-8b395Numerical modelling and experimental validation of dynamic fracture events along weak planes
https://resolver.caltech.edu/CaltechAUTHORS:20171121-100722120
Authors: {'items': [{'id': 'Arias-I', 'name': {'family': 'Arias', 'given': 'Irene'}}, {'id': 'Knap-J', 'name': {'family': 'Knap', 'given': 'Jaroslaw'}}, {'id': 'Chalivendra-V-B', 'name': {'family': 'Chalivendra', 'given': 'Vijaya B.'}}, {'id': 'Hong-Soonsung', 'name': {'family': 'Hong', 'given': 'Soonsung'}}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'Michael'}, 'orcid': '0000-0001-5877-4824'}, {'id': 'Rosakis-A-J', 'name': {'family': 'Rosakis', 'given': 'Ares J.'}, 'orcid': '0000-0003-0559-0794'}]}
Year: 2007
DOI: 10.1016/j.cma.2006.10.052
The conceptual simplicity and the ability of cohesive finite element models to describe complex fracture phenomena makes them often the approach of choice to study dynamic fracture. These models have proven to reproduce some experimental features, but to this point, no systematic study has validated their predictive ability; the difficulty in producing a sufficiently complete experimental record, and the intensive computational requirements needed to obtain converged simulations are possible causes. Here, we present a systematic integrated numerical–experimental approach to the verification and validation (V&V) of simulations of dynamic fracture along weak planes. We describe the intertwined computational and the experimental sides of the work, present the V&V results, and extract general conclusions about this kind of integrative approach.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/8qbb1-64n80Anharmonic lattice statics analysis of 180º and 90º ferroelectric domain walls in PbTiO_3
https://resolver.caltech.edu/CaltechAUTHORS:20131008-142756092
Authors: {'items': [{'id': 'Yavari-A', 'name': {'family': 'Yavari', 'given': 'A.'}}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'M.'}, 'orcid': '0000-0001-5877-4824'}, {'id': 'Bhattacharya-K', 'name': {'family': 'Bhattacharya', 'given': 'K.'}, 'orcid': '0000-0003-2908-5469'}]}
Year: 2007
DOI: 10.1080/14786430701418956
This paper presents an anharmonic lattice statics analysis of 180 ° and 90 ° domain walls in tetragonal ferroelectric perovskites. We present all the calculations and numerical examples for the technologically important ferroelectric material PbTiO_3. We use shell potentials that are fitted to quantum mechanics calculations. Our formulation places no restrictions on the range of the interactions. This formulation of lattice statics is inhomogeneous and accounts for the variation of the force constants near defects. The discrete governing equations for perfect domain walls are reduced using symmetry conditions. We solve the linearized discrete governing equations directly using a novel method in the setting of the theory of difference equations. We calculate the fully nonlinear solutions using modified Newton–Raphson iterations.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/65md6-9am55Constitutive model for plasticity in an amorphous polycarbonate
https://resolver.caltech.edu/CaltechAUTHORS:FORpre07
Authors: {'items': [{'id': 'Fortunelli-A', 'name': {'family': 'Fortunelli', 'given': 'A.'}, 'orcid': '0000-0001-5337-4450'}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'M.'}, 'orcid': '0000-0001-5877-4824'}]}
Year: 2007
DOI: 10.1103/PhysRevE.76.041806
A constitutive model for describing the mechanical response of an amorphous glassy polycarbonate is proposed. The model is based on an isotropic elastic phase surrounded by an SO(3) continuum of plastic phases onto which the elastic phase can collapse under strain. An approximate relaxed energy is developed for this model on the basis of physical considerations and extensive numerical testing, and it is shown that it corresponds to an ideal elastic-plastic behavior. Kinetic effects are introduced as rate-independent viscoplasticity, and a comparison with experimental data is presented, showing that the proposed model is able to capture the main features of the plastic behavior of amophous glassy polycarbonate.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/3cz52-wd413Diamond elements: a finite element/discrete-mechanics approximation scheme with guaranteed optimal convergence in incompressible elasticity
https://resolver.caltech.edu/CaltechAUTHORS:20171121-135247808
Authors: {'items': [{'id': 'Hauret-P', 'name': {'family': 'Hauret', 'given': 'P.'}}, {'id': 'Kuhl-E', 'name': {'family': 'Kuhl', 'given': 'E.'}}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'M.'}, 'orcid': '0000-0001-5877-4824'}]}
Year: 2007
DOI: 10.1002/nme.1992
We present a finite element discretization scheme for the compressible and incompressible elasticity problems that possess the following properties: (i) the discretization scheme is defined on a triangulation of the domain; (ii) the discretization scheme is defined—and is identical—in all spatial dimensions; (iii) the displacement field converges optimally with mesh refinement; and (iv) the inf–sup condition is automatically satisfied. The discretization scheme is motivated both by considerations of topology and analysis, and it consists of the combination of a certain mesh pattern and a choice of interpolation that guarantees optimal convergence of displacements and pressures. Rigorous proofs of the satisfaction of the inf–sup condition are presented for the problem of linearized incompressible elasticity. We additionally show that the discretization schemes can be given a compelling interpretation in terms of discrete differential operators. In particular, we develop a discrete analogue of the classical tensor differential complex in terms of which the discrete and continuous boundary-value problems are formally identical. We also present numerical tests that demonstrate the dimension-independent scope of the scheme and its good performance in problems of finite elasticity.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/2dw5z-qfv38Variational h-adaption in finite deformation elasticity and plasticity
https://resolver.caltech.edu/CaltechAUTHORS:20171121-135438429
Authors: {'items': [{'id': 'Mosler-J', 'name': {'family': 'Mosler', 'given': 'J.'}}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'M.'}, 'orcid': '0000-0001-5877-4824'}]}
Year: 2007
DOI: 10.1002/nme.2011
We propose a variational h-adaption strategy in which the evolution of the mesh is driven directly by the governing minimum principle. This minimum principle is the principle of minimum potential energy in the case of elastostatics; and a minimum principle for the incremental static problem of elasto-viscoplasticity. In particular, the mesh is refined locally when the resulting energy or incremental pseudo-energy released exceeds a certain threshold value. In order to avoid global recomputes, we estimate the local energy released by mesh refinement by means of a lower bound obtained by relaxing a local patch of elements. This bound can be computed locally, which reduces the complexity of the refinement algorithm to O(N). We also demonstrate how variational h-refinement can be combined with variational r-refinement to obtain a variational hr-refinement algorithm. Because of the strict variational nature of the h-refinement algorithm, the resulting meshes are anisotropic and outperform other refinement strategies based on aspect ratio or other purely geometrical measures of mesh quality. The versatility and rate of convergence of the resulting approach are illustrated by means of selected numerical examples.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/y8zb6-vhs56Vacancy clustering and prismatic dislocation loop formation in aluminum
https://resolver.caltech.edu/CaltechAUTHORS:GAVprb07
Authors: {'items': [{'id': 'Gavirini-V', 'name': {'family': 'Gavirini', 'given': 'Vikram'}}, {'id': 'Bhattacharya-K', 'name': {'family': 'Bhattacharya', 'given': 'Kaushik'}, 'orcid': '0000-0003-2908-5469'}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'Michael'}, 'orcid': '0000-0001-5877-4824'}]}
Year: 2007
DOI: 10.1103/PhysRevB.76.180101
The formation of prismatic dislocation loops is an important factor leading to radiation damage of metals. However, the formation mechanism and the size of the smallest stable loop has remained unclear. In this Rapid Communication, we use electronic structure calculations with millions of atoms to address this problem in aluminum. Our results show that there is a cascade of larger and larger vacancy clusters with smaller and smaller energy. Further, the results show that a seven vacancy cluster on the (111) plane can collapse into a stable prismatic loop. This supports the long-standing hypothesis that vacancy clustering leads to a prismatic loop, and that these loops can be stable at extremely small sizes. Finally our results show that it is important to conduct calculations using realistic concentrations (computational cell size) to obtain physically meaningful results.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/dkmmq-hez16Finite Element Analysis of Nonsmooth Frictional Contact
https://resolver.caltech.edu/CaltechAUTHORS:20200603-101544417
Authors: {'items': [{'id': 'Pandolfi-A', 'name': {'family': 'Pandolfi', 'given': 'Anna'}, 'orcid': '0000-0002-7084-7456'}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'Michael'}, 'orcid': '0000-0001-5877-4824'}]}
Year: 2007
DOI: 10.1007/978-1-4020-6405-0_4
A nonsmooth contact class of algorithms were introduced by Kane et al. [1] and extended to the case of friction by Pandolfi et. al [2]. The formulation specifically addresses geometries for which neither normals nor gap functions can be properly defined, e.g. bodies with corners. The formulation provides the incremental displacements in variational form, following from a minimum principle. Selected numerical examples of application of the algorithm are presented here.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/vjdwn-che80Discrete mechanics and optimal control for constrained systems
https://resolver.caltech.edu/CaltechAUTHORS:20101005-084114302
Authors: {'items': [{'id': 'Leyendecker-S', 'name': {'family': 'Leyendecker', 'given': 'Sigrid'}}, {'id': 'Ober-Blŏbaum-S', 'name': {'family': 'Ober-Blŏbaum', 'given': 'S.'}}, {'id': 'Marsden-J-E', 'name': {'family': 'Marsden', 'given': 'Jerrold E.'}}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'Michael'}, 'orcid': '0000-0001-5877-4824'}]}
Year: 2008
DOI: 10.1002/oca.912
The equations of motion of a controlled mechanical system subject to holonomic constraints may be formulated in terms
of the states and controls by applying a constrained version of the Lagrange-d'Alembert principle. This paper derives a
structure-preserving scheme for the optimal control of such systems using, as one of the key ingredients, a discrete analogue
of that principle. This property is inherited when the system is reduced to its minimal dimension by the discrete null
space method. Together with initial and final conditions on the configuration and conjugate momentum, the reduced discrete
equations serve as nonlinear equality constraints for the minimization of a given objective functional. The algorithm yields
a sequence of discrete configurations together with a sequence of actuating forces, optimally guiding the system from the
initial to the desired final state. In particular, for the optimal control of multibody systems, a force formulation consistent
with the joint constraints is introduced. This enables one to prove the consistency of the evolution of momentum maps.
Using a two-link pendulum, the method is compared with existing methods. Further, it is applied to a satellite reorientation
maneuver and a biomotion problem.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/w035t-37v48Discrete Dislocation Dynamics in Crystals
https://resolver.caltech.edu/CaltechAUTHORS:20200603-083049889
Authors: {'items': [{'id': 'Ariza-M-P', 'name': {'family': 'Ariza', 'given': 'M. P.'}, 'orcid': '0000-0003-0266-0216'}, {'id': 'Ramasubramaniam-A', 'name': {'family': 'Ramasubramaniam', 'given': 'A.'}}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'M.'}, 'orcid': '0000-0001-5877-4824'}]}
Year: 2008
DOI: 10.1007/978-3-540-71992-2_58
We present a study of 3D dislocation dynamics in BCC crystals based on discrete crystal elasticity. Ideas are borrowed from discrete differential calculus and algebraic geometry to construct a mechanics of discrete lattices. The notion of lattice complexes provides a convenient means of manipulating forms and fields defined over the crystal. Atomic interactions are accounted for via linearized embedded atom potentials thus allowing for the application of efficient fast Fourier transforms. Dislocations are treated within the theory as energy minimizing structures that lead to locally lattice-invariant but globally incompatible eigendeformations. The discrete nature of the theory automatically eliminates the need for core cutoffs. The quantization of slip to integer multiples of the Burgers vector along each slip system leads to a large integer optimization problem. We suggest a new method for solving this NP-hard optimization problem and the simulation of large 3D systems.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/8cgf8-z0521A variational constitutive model for soft biological tissues
https://resolver.caltech.edu/CaltechAUTHORS:20180112-160452524
Authors: {'items': [{'id': 'El-Sayed-T', 'name': {'family': 'El Sayed', 'given': 'Tamer'}}, {'id': 'Mota-A', 'name': {'family': 'Mota', 'given': 'Alejandro'}}, {'id': 'Fraternali-F', 'name': {'family': 'Fraternali', 'given': 'Fernando'}, 'orcid': '0000-0002-7549-6405'}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'Michael'}, 'orcid': '0000-0001-5877-4824'}]}
Year: 2008
DOI: 10.1016/j.jbiomech.2008.02.023
In this paper, a fully variational constitutive model of soft biological tissues is formulated in the finite strain regime. The model includes Ogden-type hyperelasticity, finite viscosity, deviatoric and volumetric plasticity, rate and microinertia effects. Variational updates are obtained via time discretization and pre-minimization of a suitable objective function with respect to internal variables. Genetic algorithms are used for model parameter identification due to their suitability for non-convex, high dimensional optimization problems. The material behavior predicted by the model is compared to available tests on swine and human brain tissue. The ability of the model to predict a wide range of experimentally observed behavior, including hysteresis, cyclic softening, rate effects, and plastic deformation is demonstrated.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/9hvwd-48g33Numerical Analysis of Elastomeric Fluidic Microvalves
https://resolver.caltech.edu/CaltechAUTHORS:20110511-082733397
Authors: {'items': [{'id': 'Pandolfi-A', 'name': {'family': 'Pandolfi', 'given': 'Anna'}, 'orcid': '0000-0002-7084-7456'}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'Michael'}, 'orcid': '0000-0001-5877-4824'}]}
Year: 2008
DOI: 10.1166/sl.2008.002
We present a finite element model of polydimethylsiloxane (PDMS) fluidic microvalves. A valve is fabricated by assembling two patterned layers in a two-channel crossed architecture. The valve closes as a consequence of the motion of the interlayer membrane. The membrane is deformed by the pressure of the actuation fluid, flowing in one of the two channels. By using a soft rubber material model, we setup a numerical model of the microvalve and validate it against experiments. The numerical model allows to evaluate the mechanical engagement of commonly used microvalve architectures and to analyze the performance of alternative geometries.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/d5q5b-fbe56Fracture and fragmentation of simplicial finite element meshes using graphs
https://resolver.caltech.edu/CaltechAUTHORS:20171121-095741576
Authors: {'items': [{'id': 'Mota-A', 'name': {'family': 'Mota', 'given': 'Alejandro'}}, {'id': 'Knap-J', 'name': {'family': 'Knap', 'given': 'Jaroslaw'}}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'Michael'}, 'orcid': '0000-0001-5877-4824'}]}
Year: 2008
DOI: 10.1002/nme.2135
An approach for the topological representation of simplicial finite element meshes as graphs is presented. It is shown that by using a graph, the topological changes induced by fracture reduce to a few, local kernel operations. The performance of the graph representation is demonstrated and analyzed, using as reference the three-dimensional fracture algorithm by Pandolfi and Ortiz (Eng. Comput. 1998; 14(4):287–308). It is shown that the graph representation initializes in O(N^(1.1)_E) time and fractures in O(N^(1.0)_I) time, while the reference implementation requires O(N^(2.1)_E) time to initialize and O(N^(1.9)_I) time to fracture, where N_E is the number of elements in the mesh and N_I is the number of interfaces to fracture.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/ypkyc-kg435A variational approach to coarse graining of equilibrium and non-equilibrium atomistic description at finite temperature
https://resolver.caltech.edu/CaltechAUTHORS:20171121-095259651
Authors: {'items': [{'id': 'Kulkarni-Y', 'name': {'family': 'Kulkarni', 'given': 'Yashashree'}}, {'id': 'Knapp-J', 'name': {'family': 'Knapp', 'given': 'Jaroslaw'}}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'Michael'}, 'orcid': '0000-0001-5877-4824'}]}
Year: 2008
DOI: 10.1016/j.jmps.2007.09.005
The aim of this paper is the development of equilibrium and non-equilibrium extensions of the quasicontinuum (QC) method. We first use variational mean-field theory and the maximum-entropy (max-ent) formalism for deriving approximate probability distribution and partition functions for the system. The resulting probability distribution depends locally on atomic temperatures defined for every atom and the corresponding thermodynamic potentials are explicit and local in nature. The method requires an interatomic potential as the sole empirical input. Numerical validation is performed by simulating thermal equilibrium properties of selected materials using the Lennard–Jones (LJ) pair potential and the embedded-atom method (EAM) potential and comparing with molecular dynamics results as well as experimental data. The max-ent variational approach is then taken as a basis for developing a three-dimensional non-equilibrium finite-temperature extension of the QC method. This extension is accomplished by coupling the local temperature-dependent free energy furnished by the max-ent approximation scheme to the heat equation in a joint thermo-mechanical variational setting. Results for finite-temperature nanoindentation tests demonstrate the ability of the method to capture non-equilibrium transport properties and differentiate between slow and fast indentation.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/h5k6x-nh873Minimum principles for the trajectories of systems governed by rate problems
https://resolver.caltech.edu/CaltechAUTHORS:20171117-152209057
Authors: {'items': [{'id': 'Conti-S', 'name': {'family': 'Conti', 'given': 'S.'}, 'orcid': '0000-0001-7987-9174'}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'M.'}, 'orcid': '0000-0001-5877-4824'}]}
Year: 2008
DOI: 10.1016/j.jmps.2007.11.006
Recently, Mielke and Ortiz [2007. A class of minimum principles for characterizing the trajectories of dissipative systems, ESAIM Control Optim. Calc. Var., in press] have proposed a variational reformulation of evolutionary problems that characterizes entire trajectories of a system as minimizers of certain energy–dissipation functionals. In this paper we present two examples of energy–dissipation functionals for which relaxations and optimal scalings can be rigorously derived. The first example concerns a one-dimensional bar characterized by a quadratic dissipation function and a bistable energy density; the second example concerns the coarsening kinetics of island growth in thin films exhibiting a preferred slope. In both cases, we present closed-form relaxations in the local limit of the problem and optimal scaling relations for the nonlocal problems. The relaxations rigorously characterize macroscopic properties of complex microstructural evolution by means of well-posed effective problems. The scaling relations rigorously characterize some average properties of the coarsening kinetics of the systems and lead to predictions on the growth exponents.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/ewc6h-0t345Variational r-adaption in elastodynamics
https://resolver.caltech.edu/CaltechAUTHORS:20100917-153815166
Authors: {'items': [{'id': 'Zielonka-M-G', 'name': {'family': 'Zielonka', 'given': 'M. G.'}}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'M.'}, 'orcid': '0000-0001-5877-4824'}, {'id': 'Marsden-J-E', 'name': {'family': 'Marsden', 'given': 'J. E.'}}]}
Year: 2008
DOI: 10.1002/nme.2205
We develop a variational r-adaptive finite element framework for solid dynamic applications and explore
its conceptual links with the theory of dynamic configurational forces. The central idea underlying the
proposed approach is to allow Hamilton's principle of stationary action to determine jointly the evolution of
the displacement field and the discretization of the reference configuration of the body. This is accomplished
by rendering the action stationary with respect to the material and spatial nodal coordinates simultaneously.
However, we find that a naive consistent Galerkin discretization of the action leads to intrinsically unstable
solutions. Remarkably, we also find that this unstable behavior is eliminated when a mixed, multifield
version of Hamilton's principle is adopted. Additional features of the proposed numerical implementation
include the use of uncoupled space and time discretizations; the use of independent space interpolations for
velocities and deformations; the application of these interpolations over a continuously varying adaptive
mesh; and the application of mixed variational integrators with independent time interpolations for
velocities and nodal parameters. The accuracy, robustness and versatility of the approach are assessed and
demonstrated by way of convergence tests and selected examples.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/ddsdd-qet45A class of minimum principles for characterizing the trajectories and the relaxation of dissipative systems
https://resolver.caltech.edu/CaltechAUTHORS:20171121-095528613
Authors: {'items': [{'id': 'Mielke-A', 'name': {'family': 'Mielke', 'given': 'Alexander'}}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'Michael'}, 'orcid': '0000-0001-5877-4824'}]}
Year: 2008
DOI: 10.1051/cocv:2007064
This work is concerned with the reformulation of evolutionary problems in a weak form enabling consideration of solutions that may exhibit evolving microstructures. This reformulation is accomplished by expressing the evolutionary problem in variational form, i.e., by identifying a functional whose minimizers represent entire trajectories of the system. The particular class of functionals under consideration is derived by first defining a sequence of time-discretized minimum problems and subsequently formally passing to the limit of continuous time. The resulting functionals may be regarded as a weighted dissipation-energy functional with a weight decaying with a rate . The corresponding Euler-Lagrange equation leads to an elliptic regularization of the original evolutionary problem. The Γ-limit of these functionals for is highly degenerate and provides limited information regarding the limiting trajectories of the system. Instead we seek to characterize the minimizing trajectories directly. The special class of problems characterized by a rate-independent dissipation functional is amenable to a particularly illuminating analysis. For these systems it is possible to derive a priori bounds that are independent of the regularizing parameter, whence it is possible to extract convergent subsequences and find the limiting trajectories. Under general assumptions on the functionals, we show that all such limits satisfy the energetic formulation (S) & (E) for rate-independent systems. Moreover, we show that the accumulation points of the regularized solutions solve the associated limiting energetic formulation.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/qvq0p-q7v75Variational integrators for constrained dynamical systems
https://resolver.caltech.edu/CaltechAUTHORS:LEYzamm08
Authors: {'items': [{'id': 'Leyendecker-S', 'name': {'family': 'Leyendecker', 'given': 'Sigrid'}}, {'id': 'Marsden-J-E', 'name': {'family': 'Marsden', 'given': 'Jerrold E.'}}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'Michael'}, 'orcid': '0000-0001-5877-4824'}]}
Year: 2008
DOI: 10.1002/zamm.200700173
A variational formulation of constrained dynamics is presented in the continuous and in the discrete setting. The existing theory on variational integration of constrained problems is extended by aspects on the initialization of simulations, the discrete Legendre transform and certain postprocessing steps. Furthermore, the discrete null space method which has been introduced in the framework of energy-momentum conserving integration of constrained systems is adapted to the framework of variational integrators. It eliminates the constraint forces (including the Lagrange multipliers) from the timestepping scheme and subsequently reduces its dimension to the minimal possible number. While retaining the structure preserving properties of the specific integrator, the solution of the smaller dimensional system saves computational costs and does not suffer from conditioning problems. The performance of the variational discrete null space method is illustrated by numerical examples dealing with mass point systems, a closed kinematic chain of rigid bodies and flexible multibody dynamics and the solutions are compared to those obtained by an energy-momentum scheme.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/cjm35-0e711Effect of atomic scale plasticity on hydrogen diffusion in iron: Quantum mechanically informed and on-the-fly kinetic Monte Carlo simulations
https://resolver.caltech.edu/CaltechAUTHORS:RAMjmr08
Authors: {'items': [{'id': 'Ramasubramaniam-A', 'name': {'family': 'Ramasubramaniam', 'given': 'A.'}}, {'id': 'Itakura-M', 'name': {'family': 'Itakura', 'given': 'M.'}}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'M.'}, 'orcid': '0000-0001-5877-4824'}, {'id': 'Carter-E-A', 'name': {'family': 'Carter', 'given': 'E. A.'}, 'orcid': '0000-0001-7330-7554'}]}
Year: 2008
DOI: 10.1557/JMR.2008.0340
We present an off-lattice, on-the-fly kinetic Monte Carlo (KMC) model for simulating stress-assisted diffusion and trapping of hydrogen by crystalline defects in iron. Given an embedded atom (EAM) potential as input, energy barriers for diffusion are ascertained on the fly from the local environments of H atoms. To reduce computational cost, on-the-fly calculations are supplemented with precomputed strain-dependent energy barriers in defect-free parts of the crystal. These precomputed barriers, obtained with high-accuracy density functional theory calculations, are used to ascertain the veracity of the EAM barriers and correct them when necessary. Examples of bulk diffusion in crystals containing a screw dipole and vacancies are presented. Effective diffusivities obtained from KMC simulations are found to be in good agreement with theory. Our model provides an avenue for simulating the interaction of hydrogen with cracks, dislocations, grain boundaries, and other lattice defects, over extended time scales, albeit at atomistic length scales.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/3fbde-xtw73Rigorous verification, validation, uncertainty quantification and certification through concentration-of-measure inequalities
https://resolver.caltech.edu/CaltechAUTHORS:LUCcmame08
Authors: {'items': [{'id': 'Lucas-L-J', 'name': {'family': 'Lucas', 'given': 'L. J.'}}, {'id': 'Owhadi-H', 'name': {'family': 'Owhadi', 'given': 'H.'}, 'orcid': '0000-0002-5677-1600'}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'M.'}, 'orcid': '0000-0001-5877-4824'}]}
Year: 2008
DOI: 10.1016/j.cma.2008.06.008
We apply concentration-of-measure inequalities to the quantification of uncertainties in the performance of engineering systems. Specifically, we envision uncertainty quantification in the context of certification, i.e., as a tool for deciding whether a system is likely to perform safely and reliably within design specifications. We show that concentration-of-measure inequalities rigorously bound probabilities of failure and thus supply conservative certification criteria. In addition, they supply unambiguous quantitative definitions of terms such as margins, epistemic and aleatoric uncertainties, verification and validation measures, confidence factors, and others, as well as providing clear procedures for computing these quantities by means of concerted simulation and experimental campaigns. We also investigate numerically the tightness of concentration-of-measure inequalities with the aid of an imploding ring example. Our numerical tests establish the robustness and viability of concentration-of-measure inequalities as a basis for certification in that particular example of application.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/1hmsk-wkd20Rigorous verification, validation, uncertainty quantification and certification through concentration-of-measure inequalities
https://resolver.caltech.edu/CaltechAUTHORS:LUCcmame08
Authors: {'items': [{'id': 'Lucas-L-J', 'name': {'family': 'Lucas', 'given': 'L. J.'}}, {'id': 'Owhadi-H', 'name': {'family': 'Owhadi', 'given': 'H.'}, 'orcid': '0000-0002-5677-1600'}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'M.'}, 'orcid': '0000-0001-5877-4824'}]}
Year: 2008
DOI: 10.1016/j.cma.2008.06.008
We apply concentration-of-measure inequalities to the quantification of uncertainties in the performance of engineering systems. Specifically, we envision uncertainty quantification in the context of certification, i.e., as a tool for deciding whether a system is likely to perform safely and reliably within design specifications. We show that concentration-of-measure inequalities rigorously bound probabilities of failure and thus supply conservative certification criteria. In addition, they supply unambiguous quantitative definitions of terms such as margins, epistemic and aleatoric uncertainties, verification and validation measures, confidence factors, and others, as well as providing clear procedures for computing these quantities by means of concerted simulation and experimental campaigns. We also investigate numerically the tightness of concentration-of-measure inequalities with the aid of an imploding ring example. Our numerical tests establish the robustness and viability of concentration-of-measure inequalities as a basis for certification in that particular example of application.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/webek-nxp44Biomechanics of traumatic brain injury
https://resolver.caltech.edu/CaltechAUTHORS:ELScmame08
Authors: {'items': [{'id': 'El-Sayed-T', 'name': {'family': 'El Sayed', 'given': 'Tamer'}}, {'id': 'Mota-A', 'name': {'family': 'Mota', 'given': 'Alejandro'}}, {'id': 'Fraternali-F', 'name': {'family': 'Fraternali', 'given': 'Fernando'}, 'orcid': '0000-0002-7549-6405'}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'Michael'}, 'orcid': '0000-0001-5877-4824'}]}
Year: 2008
DOI: 10.1016/j.cma.2008.06.006
A biomechanical model for traumatic brain injury and soft tissue damage is presented. A variational constitutive model for soft biological tissues is utilized to reproduce axonal damage and cavitation injury through inelastic deformation. The material response is split into elastoplastic and viscoelastic components, including rate effects, shear and porous plasticity, and finite viscoelasticity. Mechanical damage of brain tissue is classified as volumetric (compression/tension) and shear-type. Finite element simulations of brain injuries are presented, examining frontal and oblique head impacts with external objects. Localization, extension, intensity and reversibility/irreversibility of tissue damage are predicted. Future directions of this work, relating mechanical damage and physiological brain dysfunction, and application to relevant medical and engineering problems are discussed.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/nxwmn-yka05An error-estimate-free and remapping-free variational mesh refinement and coarsening method for dissipative solids at finite strains
https://resolver.caltech.edu/CaltechAUTHORS:MOSijnme09
Authors: {'items': [{'id': 'Mosler-J', 'name': {'family': 'Mosler', 'given': 'J.'}}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'M.'}, 'orcid': '0000-0001-5877-4824'}]}
Year: 2009
DOI: 10.1002/nme.2428
A variational h-adaptive finite element formulation is proposed. The distinguishing feature of this method
is that mesh refinement and coarsening are governed by the same minimization principle characterizing the
underlying physical problem. Hence, no error estimates are invoked at any stage of the adaption procedure.
As a consequence, linearity of the problem and a corresponding Hilbert-space functional framework are
not required and the proposed formulation can be applied to highly non-linear phenomena. The basic strategy is to refine (respectively, unrefine) the spatial discretization locally if such refinement (respectively, unrefinement) results in a sufficiently large reduction (respectively, sufficiently small increase) in the energy. This strategy leads to an adaption algorithm having O(N) complexity. Local refinement is effected by edge-bisection and local unrefinement by the deletion of terminal vertices. Dissipation is accounted for within a time-discretized variational framework resulting in an incremental potential energy. In addition, the entire hierarchy of successive refinements is stored and the internal state of parent elements is updated so that no mesh-transfer operator is required upon unrefinement. The versatility and robustness of the resulting variational adaptive finite element formulation is illustrated by means of selected numerical
examples.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/jwn26-g9k59Eigenfracture: An Eigendeformation Approach to Variational Fracture
https://resolver.caltech.edu/CaltechAUTHORS:SCHMmms09
Authors: {'items': [{'id': 'Schmidt-B', 'name': {'family': 'Schmidt', 'given': 'Bernd'}}, {'id': 'Fraternali-F', 'name': {'family': 'Fraternali', 'given': 'Fernando'}, 'orcid': '0000-0002-7549-6405'}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'Michael'}, 'orcid': '0000-0001-5877-4824'}]}
Year: 2009
DOI: 10.1137/080712568
We propose an approximation scheme for a variational theory of brittle fracture. In this scheme, the energy functional is approximated by a family of functionals depending on a small parameter and on two fields: the displacement field and an eigendeformation field that describes the fractures that occur in the body. Specifically, the eigendeformations allow the displacement field to develop jumps that cost no local elastic energy. However, this local relaxation requires the expenditure of a certain amount of fracture energy. We provide a construction, based on the consideration of ε-neighborhoods of the support of the eigendeformation field, for calculating the right amount of fracture energy associated with the eigendeformation field. We prove the Γ-convergence of the eigendeformation functional sequence, and of finite element approximations of the eigendeformation functionals, to the Griffith-type energy functional introduced in Francfort and Marigo [J. Mech. Phys. Solids, 46 (1998), pp. 1319–1342]. This type of convergence ensures the convergence of eigendeformation solutions, and of finite element approximations thereof, to brittle-fracture solutions. Numerical examples concerned with quasi-static mixed-mode crack propagation illustrate the versatility and robustness of the approach and its ability to predict crack-growth patterns in brittle solids.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/49y34-et543Computational assessment of ballistic impact on a high strength structural steel/polyurea composite plate
https://resolver.caltech.edu/CaltechAUTHORS:20090807-150328529
Authors: {'items': [{'id': 'El-Sayed-T', 'name': {'family': 'El Sayed', 'given': 'T.'}}, {'id': 'Mock-W-Jr', 'name': {'family': 'Mock', 'given': 'Willis, Jr.'}}, {'id': 'Mota-A', 'name': {'family': 'Mota', 'given': 'Alejandro'}}, {'id': 'Fraternali-F', 'name': {'family': 'Fraternali', 'given': 'Fernando'}, 'orcid': '0000-0002-7549-6405'}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'Michael'}, 'orcid': '0000-0001-5877-4824'}]}
Year: 2009
DOI: 10.1007/s00466-008-0327-6
Ballistic impact on a polyurea retrofitted high strength structural steel plate is simulated and validated. A soft material model for polyurea, which is capable of capturing complex mechanical behavior characterized by large strains, hysteresis, rate sensitivity, stress softening (Mullins effect), and deviatoric and volumetric plasticity, is calibrated against several uniaxial tension experiments and a three-dimensional release wave experiment to capture both the material point and bulk behaviors. A porous plasticity model is employed to model the high strength structural steel and localization elements are included to capture adiabatic shear bands and strain localization. The computational capabilities of these models are demonstrated by the prediction of the target plate displacement, which shows excellent agreement with experiments.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/549gd-nrc25Γ-convergence of Variational Integrators for Constrained Systems
https://resolver.caltech.edu/CaltechAUTHORS:20090914-142014445
Authors: {'items': [{'id': 'Schmidt-B', 'name': {'family': 'Schmidt', 'given': 'Bernd'}}, {'id': 'Leyendecker-S', 'name': {'family': 'Leyendecker', 'given': 'Sigrid'}}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'Michael'}, 'orcid': '0000-0001-5877-4824'}]}
Year: 2009
DOI: 10.1007/s00332-008-9030-1
For a physical system described by a motion in an energy landscape under holonomic constraints, we study the Γ-convergence of variational integrators to the corresponding continuum action functional and the convergence properties of solutions of the discrete Euler–Lagrange equations to stationary points of the continuum problem. This extends the results in Müller and Ortiz (J. Nonlinear Sci. 14:279–296, 2004) to constrained systems. The convergence result is illustrated with examples of mass point systems and flexible multibody dynamics.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/m9d9c-fg636A numerical model of light adjustable lens
https://resolver.caltech.edu/CaltechAUTHORS:20090624-131751374
Authors: {'items': [{'id': 'Pandolfi-A', 'name': {'family': 'Pandolfi', 'given': 'Anna'}, 'orcid': '0000-0002-7084-7456'}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'Michael'}, 'orcid': '0000-0001-5877-4824'}]}
Year: 2009
DOI: 10.1007/s00466-008-0361-4
We model numerically the mechanical effects of UV induced photo-polymerization in elastomeric artificial lens. The elastomer is originated upon cross-linking of a silicone matrix. UV irradiation of one side of the lens polymerizes selectively a photosensitive macromer, causing local variations of its concentration. The subsequent diffusion of macromers from high concentration to low concentration zones modifies the shape of the lens and thus its dioptric power. In vitro experiments on artificial lens showed that the power change is dependent on UV exposure time, irradiation intensity and light pattern. With the aim to define a numerical tool able to predict the dioptric power adjustment as a function of the UV irradiation parameters, we setup a purely mechanic finite element model of the lens, adopting a hyperelastic material model embedded with eigen-deformations. Numerical simulations of axis-symmetric irradiation closely reproduced the experimental results, in terms of both lens geometry and dioptric power, for positive, negative and lock-in corrections.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/mjqnb-thg34On the behavior of dissipative systems in contact with a heat bath: Application to Andrade creep
https://resolver.caltech.edu/CaltechAUTHORS:20090904-125145240
Authors: {'items': [{'id': 'Sullivan-T', 'name': {'family': 'Sullivan', 'given': 'T.'}}, {'id': 'Koslowski-Marisol', 'name': {'family': 'Koslowski', 'given': 'M.'}}, {'id': 'Theil-Florian', 'name': {'family': 'Theil', 'given': 'F.'}}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'M.'}, 'orcid': '0000-0001-5877-4824'}]}
Year: 2009
DOI: 10.1016/j.jmps.2009.03.006
We develop a theory of statistical mechanics for dissipative systems governed by equations of evolution that assigns probabilities to individual trajectories of the system. The theory is made mathematically rigorous and leads to precise predictions regarding the behavior of dissipative systems at finite temperature. Such predictions include the effect of temperature on yield phenomena and rheological time exponents. The particular case of an ensemble of dislocations moving in a slip plane through a random array of obstacles is studied numerically in detail. The numerical results bear out the analytical predictions regarding the mean response of the system, which exhibits Andrade creep.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/34a79-7b165Experimental validation of large-scale simulations of dynamic fracture along weak planes
https://resolver.caltech.edu/CaltechAUTHORS:20090430-111534836
Authors: {'items': [{'id': 'Chalivendra-V-B', 'name': {'family': 'Chalivendra', 'given': 'Vijaya B.'}}, {'id': 'Hong-Soosung', 'name': {'family': 'Hong', 'given': 'Soosung'}}, {'id': 'Arias-I', 'name': {'family': 'Arias', 'given': 'Irene'}}, {'id': 'Knap-J', 'name': {'family': 'Knap', 'given': 'Jaroslaw'}}, {'id': 'Rosakis-A-J', 'name': {'family': 'Rosakis', 'given': 'Ares'}, 'orcid': '0000-0003-0559-0794'}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'Michael'}, 'orcid': '0000-0001-5877-4824'}]}
Year: 2009
DOI: 10.1016/j.ijimpeng.2008.11.009
A well-controlled and minimal experimental scheme for dynamic fracture along weak planes is specifically designed for the validation of large-scale simulations using cohesive finite elements. The role of the experiments in the integrated approach is two-fold. On the one hand, careful measurements provide accurate boundary conditions and material parameters for a complete setup of the simulations without free parameters. On the other hand, quantitative performance metrics are provided by the experiments, which are compared a posteriori with the results of the simulations. A modified Hopkinson bar setup in association with notch-face loading is used to obtain controlled loading of the fracture specimens. An inverse problem of cohesive zone modeling is performed to obtain accurate mode-I cohesive zone laws from experimentally measured deformation fields. The speckle interferometry technique is employed to obtain the experimentally measured deformation field. Dynamic photoelasticity in conjunction with high-speed photography is used to capture experimental records of crack propagation. The comparison shows that both the experiments and the numerical simulations result in very similar crack initiation times and produce crack tip velocities which differ by less than 6%. The results also confirm that the detailed shape of the non-linear cohesive zone law has no significant influence on the numerical results.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/q6wv0-50a75Kidney damage in extracorporeal shock wave lithotripsy: a numerical approach for different shock profiles
https://resolver.caltech.edu/CaltechAUTHORS:20090808-142504866
Authors: {'items': [{'id': 'Weinberg-Kerstin', 'name': {'family': 'Weinberg', 'given': 'Kerstin'}}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'Michael'}, 'orcid': '0000-0001-5877-4824'}]}
Year: 2009
DOI: 10.1007/s10237-008-0135-0
In shock-wave lithotripsy—a medical procedure to fragment kidney stones—the patient is subjected to hypersonic waves focused at the kidney stone. Although this procedure is widely applied, the physics behind this medical treatment, in particular the question of how the injuries to the surrounding kidney tissue arise, is still under investigation. To contribute to the solution of this problem, two- and three-dimensional numerical simulations of a human kidney under shock-wave loading are presented. For this purpose a constitutive model of the bio-mechanical system kidney is introduced, which is able to map large visco-elastic deformations and, in particular, material damage. The specific phenomena of cavitation induced oscillating bubbles is modeled here as an evolution of spherical pores within the soft kidney tissue. By means of large scale finite element simulations, we study the shock-wave propagation into the kidney tissue, adapt unknown material parameters and analyze the resulting stress states. The simulations predict localized damage in the human kidney in the same regions as observed in animal experiments. Furthermore, the numerical results suggest that in first instance the pressure amplitude of the shock wave impulse (and not so much its exact time-pressure profile) is responsible for damaging the kidney tissue.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/2p9s5-3cx15Fracture Paths from Front Kinetics: Relaxation and Rate Independence
https://resolver.caltech.edu/CaltechAUTHORS:20090904-105348917
Authors: {'items': [{'id': 'Larsen-C-J', 'name': {'family': 'Larsen', 'given': 'C. J.'}}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'M.'}, 'orcid': '0000-0001-5877-4824'}, {'id': 'Richardson-C-L', 'name': {'family': 'Richardson', 'given': 'C. L.'}}]}
Year: 2009
DOI: 10.1007/s00205-009-0216-y
Crack fronts play a fundamental role in engineering models for fracture: they are the location of both crack growth and the energy dissipation due to growth. However, there has not been a rigorous mathematical definition of crack front, nor rigorous mathematical analysis predicting fracture paths using these fronts as the location of growth and dissipation. Here, we give a natural weak definition of crack front and front speed, and consider models of crack growth in which the energy dissipation is a function of the front speed, that is, the dissipation rate at time t is of the form $$\int_{F(t)}\psi(v(x, t)) {\rm d}{\mathcal {H}^{N - 2}}(x)$$ where F(t) is the front at time t and v is the front speed. We show how this dissipation can be used within existing models of quasi-static fracture, as well as in the new dissipation functionals of Mielke–Ortiz. An example of a constrained problem for which there is existence is shown, but in general, if there are no constraints or other energy penalties, this dissipation must be relaxed. We prove a general relaxation formula that gives the surprising result that the effective dissipation is always rate-independent.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/addr0-fks84Atmospheric effects on extensive air showers observed with the surface detector of the Pierre Auger observatory
https://resolver.caltech.edu/CaltechAUTHORS:20091201-094133422
Authors: {'items': [{'id': 'Abraham-J', 'name': {'family': 'Abraham', 'given': 'J.'}}, {'id': 'Abreu-P', 'name': {'family': 'Abreu', 'given': 'P.'}}, {'id': 'Aglietta-M', 'name': {'family': 'Aglietta', 'given': 'M.'}}, {'id': 'Aguirre-C', 'name': {'family': 'Aguirre', 'given': 'C.'}}, {'id': 'Ahn-E-J', 'name': {'family': 'Ahn', 'given': 'E. J.'}}, {'id': 'Allard-D', 'name': {'family': 'Allard', 'given': 'D.'}}, {'id': 'Allekotte-I', 'name': {'family': 'Allekotte', 'given': 'I.'}}, {'id': 'Allen-J', 'name': {'family': 'Allen', 'given': 'J.'}}, {'id': 'Allison-P', 'name': {'family': 'Allison', 'given': 'P.'}}, {'id': 'Alvarez-Muñiz-J', 'name': {'family': 'Alvarez-Muñiz', 'given': 'J.'}}, {'id': 'Ambrosio-M', 'name': {'family': 'Ambrosio', 'given': 'M.'}}, {'id': 'Anchordoqui-L', 'name': {'family': 'Anchordoqui', 'given': 'L.'}}, {'id': 'Andringa-S', 'name': {'family': 'Andringa', 'given': 'S.'}}, {'id': 'Anzalone-A', 'name': {'family': 'Anzalone', 'given': 'A.'}}, {'id': 'Aramo-C', 'name': {'family': 'Aramo', 'given': 'C.'}}, {'id': 'Arganda-E', 'name': {'family': 'Arganda', 'given': 'E.'}}, {'id': 'Argirò-S', 'name': {'family': 'Argirò', 'given': 'S.'}}, {'id': 'Arisaka-K', 'name': {'family': 'Arisaka', 'given': 'K.'}}, {'id': 'Arneodo-F', 'name': {'family': 'Arneodo', 'given': 'F.'}}, {'id': 'Arqueros-F', 'name': {'family': 'Arqueros', 'given': 'F.'}}, {'id': 'Asch-T', 'name': {'family': 'Asch', 'given': 'T.'}}, {'id': 'Asorey-H', 'name': {'family': 'Asorey', 'given': 'H.'}}, {'id': 'Assis-P', 'name': {'family': 'Assis', 'given': 'P.'}}, {'id': 'Aublin-J', 'name': {'family': 'Aublin', 'given': 'J.'}}, {'id': 'Ave-M', 'name': {'family': 'Ave', 'given': 'M.'}}, {'id': 'Avila-G', 'name': {'family': 'Avila', 'given': 'G.'}}, {'id': 'Bäcker-T', 'name': {'family': 'Bäcker', 'given': 'T.'}}, {'id': 'Badagnani-D', 'name': {'family': 'Badagnani', 'given': 'D.'}}, {'id': 'Barber-K-B', 'name': {'family': 'Barber', 'given': 'K. B.'}}, {'id': 'Barbosa-A-F', 'name': {'family': 'Barbosa', 'given': 'A. F.'}}, {'id': 'Barroso-S-L-C', 'name': {'family': 'Barroso', 'given': 'S. L. C.'}}, {'id': 'Baughman-B', 'name': {'family': 'Baughman', 'given': 'B.'}}, {'id': 'Bauleo-P', 'name': {'family': 'Bauleo', 'given': 'P.'}}, {'id': 'Beatty-J-J', 'name': {'family': 'Beatty', 'given': 'J. J.'}}, {'id': 'Beau-T', 'name': {'family': 'Beau', 'given': 'T.'}}, {'id': 'Becker-B-R', 'name': {'family': 'Becker', 'given': 'B. R.'}}, {'id': 'Becker-K-H', 'name': {'family': 'Becker', 'given': 'K. H.'}}, {'id': 'Bellétoile-A', 'name': {'family': 'Bellétoile', 'given': 'A.'}}, {'id': 'Bellido-J-A', 'name': {'family': 'Bellido', 'given': 'J. A.'}}, {'id': 'BenZvi-S', 'name': {'family': 'BenZvi', 'given': 'S.'}}, {'id': 'Berat-C', 'name': {'family': 'Berat', 'given': 'C.'}}, {'id': 'Bernardini-Paolo', 'name': {'family': 'Bernardini', 'given': 'P.'}}, {'id': 'Bertou-X', 'name': {'family': 'Bertou', 'given': 'X.'}}, {'id': 'Biermann-P-L', 'name': {'family': 'Biermann', 'given': 'P. L.'}}, {'id': 'Billoir-P', 'name': {'family': 'Billoir', 'given': 'P.'}}, {'id': 'Blanch-Bigas-O', 'name': {'family': 'Blanch-Bigas', 'given': 'O.'}}, {'id': 'Blanco-F', 'name': {'family': 'Blanco', 'given': 'F.'}}, {'id': 'Bleve-C', 'name': {'family': 'Bleve', 'given': 'C.'}}, {'id': 'Blümer-H', 'name': {'family': 'Blümer', 'given': 'H.'}}, {'id': 'Boháčová-M', 'name': {'family': 'Boháčová', 'given': 'M.'}}, {'id': 'Bonifazi-C', 'name': {'family': 'Bonifazi', 'given': 'C.'}}, {'id': 'Bonino-R', 'name': {'family': 'Bonino', 'given': 'R.'}}, {'id': 'Borodai-N', 'name': {'family': 'Borodai', 'given': 'N.'}}, {'id': 'Brack-J', 'name': {'family': 'Brack', 'given': 'J.'}}, {'id': 'Brogueira-P', 'name': {'family': 'Brogueira', 'given': 'P.'}}, {'id': 'Brown-William-C-Physics', 'name': {'family': 'Brown', 'given': 'W. C.'}}, {'id': 'Bruijn-R', 'name': {'family': 'Bruijn', 'given': 'R.'}}, {'id': 'Buchholz-P', 'name': {'family': 'Buchholz', 'given': 'P.'}}, {'id': 'Bueno-A', 'name': {'family': 'Bueno', 'given': 'A.'}}, {'id': 'Burton-R-E', 'name': {'family': 'Burton', 'given': 'R. E.'}}, {'id': 'Busca-N-G', 'name': {'family': 'Busca', 'given': 'N. G.'}}, {'id': 'Caballero-Mora-K-S', 'name': {'family': 'Caballero-Mora', 'given': 'K. S.'}}, {'id': 'Caramete-L', 'name': {'family': 'Caramete', 'given': 'L.'}}, {'id': 'Caruso-R', 'name': {'family': 'Caruso', 'given': 'R.'}}, {'id': 'Carvalho-W', 'name': {'family': 'Carvalho', 'given': 'W.'}}, {'id': 'Castellina-A', 'name': {'family': 'Castellina', 'given': 'A.'}}, {'id': 'Catalano-O', 'name': {'family': 'Catalano', 'given': 'O.'}}, {'id': 'Cazon-L', 'name': {'family': 'Cazon', 'given': 'L.'}}, {'id': 'Cester-R', 'name': {'family': 'Cester', 'given': 'R.'}}, {'id': 'Chauvin-J', 'name': {'family': 'Chauvin', 'given': 'J.'}}, {'id': 'Chiavassa-A', 'name': {'family': 'Chiavassa', 'given': 'A.'}}, {'id': 'Chinellato-J-A', 'name': {'family': 'Chinellato', 'given': 'J. A.'}}, {'id': 'Chou-Aaron-S', 'name': {'family': 'Chou', 'given': 'A.'}}, {'id': 'Chudoba-J', 'name': {'family': 'Chudoba', 'given': 'J.'}}, {'id': 'Chye-J', 'name': {'family': 'Chye', 'given': 'J.'}}, {'id': 'Clay-R-W', 'name': {'family': 'Clay', 'given': 'R. W.'}}, {'id': 'Colombo-E', 'name': {'family': 'Colombo', 'given': 'E.'}}, {'id': 'Conceição-R', 'name': {'family': 'Conceição', 'given': 'R.'}}, {'id': 'Connolly-B', 'name': {'family': 'Connolly', 'given': 'B.'}}, {'id': 'Contreras-F', 'name': {'family': 'Contreras', 'given': 'F.'}}, {'id': 'Coppens-J', 'name': {'family': 'Coppens', 'given': 'J.'}}, {'id': 'Cordier-A', 'name': {'family': 'Cordier', 'given': 'A.'}}, {'id': 'Cotti-U', 'name': {'family': 'Cotti', 'given': 'U.'}}, {'id': 'Coutu-S', 'name': {'family': 'Coutu', 'given': 'S.'}}, {'id': 'Covault-C-E', 'name': {'family': 'Covault', 'given': 'C. E.'}}, {'id': 'Creusot-A', 'name': {'family': 'Creusot', 'given': 'A.'}}, {'id': 'Criss-A', 'name': {'family': 'Criss', 'given': 'A.'}}, {'id': 'Cronin-J', 'name': {'family': 'Cronin', 'given': 'J.'}}, {'id': 'Curutiu-A', 'name': {'family': 'Curutiu', 'given': 'A.'}}, {'id': 'Dagoret-Campagne-S', 'name': {'family': 'Dagoret-Campagne', 'given': 'S.'}}, {'id': 'Dallier-R', 'name': {'family': 'Dallier', 'given': 'R.'}}, {'id': 'Daumiller-K', 'name': {'family': 'Daumiller', 'given': 'K.'}}, {'id': 'Dawson-B-R', 'name': {'family': 'Dawson', 'given': 'B. R.'}}, {'id': 'de-Almeida-R-M', 'name': {'family': 'de Almeida', 'given': 'R. M.'}}, {'id': 'De-Domenico-M', 'name': {'family': 'De Domenico', 'given': 'M.'}}, {'id': 'De-Donato-C', 'name': {'family': 'De Donato', 'given': 'C.'}}, {'id': 'De-Jong-S-J', 'name': {'family': 'De Jong', 'given': 'S. J.'}}, {'id': 'De-La-Vega-G', 'name': {'family': 'De La Vega', 'given': 'G.'}}, {'id': 'de-Mello-Junior-W-J-M', 'name': {'family': 'de Mello Junior', 'given': 'W. J. M.'}}, {'id': 'de-Mello-Neto-J-R-T', 'name': {'family': 'de Mello Neto', 'given': 'J. R. T.'}}, {'id': 'De-Mitri-I', 'name': {'family': 'De Mitri', 'given': 'I.'}}, {'id': 'de-Souza-V', 'name': {'family': 'de Souza', 'given': 'V.'}}, {'id': 'de-Vries-K-D', 'name': {'family': 'de Vries', 'given': 'K. D.'}}, {'id': 'Decerprit-G', 'name': {'family': 'Decerprit', 'given': 'G.'}}, {'id': 'del-Peral-L', 'name': {'family': 'del Peral', 'given': 'L.'}}, {'id': 'Deligny-O', 'name': {'family': 'Deligny', 'given': 'O.'}}, {'id': 'Della-Selva-A', 'name': {'family': 'Della Selva', 'given': 'A.'}}, {'id': 'Delle-Fratte-C', 'name': {'family': 'Delle Fratte', 'given': 'C.'}}, {'id': 'Dembinski-H', 'name': {'family': 'Dembinski', 'given': 'H.'}}, {'id': 'Di-Giulio-C', 'name': {'family': 'Di Giulio', 'given': 'C.'}}, {'id': 'Diaz-J-C', 'name': {'family': 'Diaz', 'given': 'J. C.'}}, {'id': 'Diep-P-N', 'name': {'family': 'Diep', 'given': 'P. N.'}}, {'id': 'Dobrigkeit-C', 'name': {'family': 'Dobrigkeit', 'given': 'C.'}}, {'id': "D'Olivo-J-C", 'name': {'family': "D'Olivo", 'given': 'J. C.'}}, {'id': 'Dong-P-N', 'name': {'family': 'Dong', 'given': 'P. N.'}}, {'id': 'Dornic-D', 'name': {'family': 'Dornic', 'given': 'D.'}}, {'id': 'Dorofeev-A', 'name': {'family': 'Dorofeev', 'given': 'A.'}}, {'id': 'dos-Anjos-J-C', 'name': {'family': 'dos Anjos', 'given': 'J. C.'}}, {'id': 'Dova-M-T', 'name': {'family': 'Dova', 'given': 'M. T.'}}, {'id': "D'Urso-D", 'name': {'family': "D'Urso", 'given': 'D.'}}, {'id': 'Dutan-I', 'name': {'family': 'Dutan', 'given': 'I.'}}, {'id': 'DuVernois-M-A', 'name': {'family': 'DuVernois', 'given': 'M. A.'}}, {'id': 'Engel-R', 'name': {'family': 'Engel', 'given': 'R.'}}, {'id': 'Erdmann-M', 'name': {'family': 'Erdmann', 'given': 'M.'}}, {'id': 'Escobar-C-O', 'name': {'family': 'Escobar', 'given': 'C. O.'}}, {'id': 'Etchegoyen-A', 'name': {'family': 'Etchegoyen', 'given': 'A.'}}, {'id': 'Facal-San-Luis-P', 'name': {'family': 'Facal San Luis', 'given': 'P.'}}, {'id': 'Falcke-H', 'name': {'family': 'Falcke', 'given': 'H.'}}, {'id': 'Farrar-G', 'name': {'family': 'Farrar', 'given': 'G.'}}, {'id': 'Fauth-A-C', 'name': {'family': 'Fauth', 'given': 'A. C.'}}, {'id': 'Fazzini-N', 'name': {'family': 'Fazzini', 'given': 'N.'}}, {'id': 'Ferrer-F', 'name': {'family': 'Ferrer', 'given': 'F.'}}, {'id': 'Ferrero-A', 'name': {'family': 'Ferrero', 'given': 'A.'}}, {'id': 'Fick-B', 'name': {'family': 'Fick', 'given': 'B.'}}, {'id': 'Filevich-A', 'name': {'family': 'Filevich', 'given': 'A.'}}, {'id': 'Filipčič-A', 'name': {'family': 'Filipčič', 'given': 'A.'}}, {'id': 'Fleck-I', 'name': {'family': 'Fleck', 'given': 'I.'}}, {'id': 'Fliescher-S', 'name': {'family': 'Fliescher', 'given': 'S.'}}, {'id': 'Fracchiolla-C-E', 'name': {'family': 'Fracchiolla', 'given': 'C. E.'}}, {'id': 'Fraenkel-E-D', 'name': {'family': 'Fraenkel', 'given': 'E. D.'}}, {'id': 'Fulgione-W', 'name': {'family': 'Fulgione', 'given': 'W.'}}, {'id': 'Gamarra-R-F', 'name': {'family': 'Gamarra', 'given': 'R. F.'}}, {'id': 'Gambetta-S', 'name': {'family': 'Gambetta', 'given': 'S.'}}, {'id': 'García-B', 'name': {'family': 'García', 'given': 'B.'}}, {'id': 'García-Gámez-D', 'name': {'family': 'García-Gámez', 'given': 'D.'}}, {'id': 'Garcia-Pinto-D', 'name': {'family': 'Garcia-Pinto', 'given': 'D.'}}, {'id': 'Garrido-X', 'name': {'family': 'Garrido', 'given': 'X.'}}, {'id': 'Gelmini-G', 'name': {'family': 'Gelmini', 'given': 'G.'}}, {'id': 'Gemmeke-H', 'name': {'family': 'Gemmeke', 'given': 'H.'}}, {'id': 'Ghia-P-L', 'name': {'family': 'Ghia', 'given': 'P. 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J.'}}, {'id': 'Scuderi-M', 'name': {'family': 'Scuderi', 'given': 'M.'}}, {'id': 'Segreto-A', 'name': {'family': 'Segreto', 'given': 'A.'}}, {'id': 'Semikoz-D', 'name': {'family': 'Semikoz', 'given': 'D.'}}, {'id': 'Settimo-M', 'name': {'family': 'Settimo', 'given': 'M.'}}, {'id': 'Shellard-R-C', 'name': {'family': 'Shellard', 'given': 'R. C.'}}, {'id': 'Sidelnik-I', 'name': {'family': 'Sidelnik', 'given': 'I.'}}, {'id': 'Siffert-B-B', 'name': {'family': 'Siffert', 'given': 'B. B.'}}, {'id': 'Smiałkowski-A', 'name': {'family': 'Smiałkowski', 'given': 'A.'}}, {'id': 'Šmída-R', 'name': {'family': 'Šmída', 'given': 'R.'}}, {'id': 'Smith-B-E', 'name': {'family': 'Smith', 'given': 'B. E.'}}, {'id': 'Snow-G-R', 'name': {'family': 'Snow', 'given': 'G. R.'}}, {'id': 'Sommers-P', 'name': {'family': 'Sommers', 'given': 'P.'}}, {'id': 'Sorokin-J', 'name': {'family': 'Sorokin', 'given': 'J.'}}, {'id': 'Spinka-H-M', 'name': {'family': 'Spinka', 'given': 'H.'}}, {'id': 'Squartini-R', 'name': {'family': 'Squartini', 'given': 'R.'}}, {'id': 'Strazzeri-E', 'name': {'family': 'Strazzeri', 'given': 'E.'}}, {'id': 'Stutz-A-M', 'name': {'family': 'Stutz', 'given': 'A.'}, 'orcid': '0000-0003-2300-8200'}, {'id': 'Suarez-F', 'name': {'family': 'Suarez', 'given': 'F.'}}, {'id': 'Suomijärvi-T', 'name': {'family': 'Suomijärvi', 'given': 'T.'}}, {'id': 'Supanitsky-A-D', 'name': {'family': 'Supanitsky', 'given': 'A. D.'}}, {'id': 'Sutherland-M-S', 'name': {'family': 'Sutherland', 'given': 'M. S.'}}, {'id': 'Swain-J', 'name': {'family': 'Swain', 'given': 'J.'}}, {'id': 'Szadkowski-Z', 'name': {'family': 'Szadkowski', 'given': 'Z.'}}, {'id': 'Tamashiro-A', 'name': {'family': 'Tamashiro', 'given': 'A.'}}, {'id': 'Tamburro-A', 'name': {'family': 'Tamburro', 'given': 'A.'}}, {'id': 'Tarutina-T', 'name': {'family': 'Tarutina', 'given': 'T.'}}, {'id': 'Taşcău-O', 'name': {'family': 'Taşcău', 'given': 'O.'}}, {'id': 'Tcaciuc-R', 'name': {'family': 'Tcaciuc', 'given': 'R.'}}, {'id': 'Tcherniakhovski-D', 'name': {'family': 'Tcherniakhovski', 'given': 'D.'}}, {'id': 'Thao-N-T', 'name': {'family': 'Thao', 'given': 'N. T.'}}, {'id': 'Thomas-D', 'name': {'family': 'Thomas', 'given': 'D.'}}, {'id': 'Ticona-R', 'name': {'family': 'Ticona', 'given': 'R.'}}, {'id': 'Tiffenberg-J', 'name': {'family': 'Tiffenberg', 'given': 'J.'}}, {'id': 'Timmermans-C', 'name': {'family': 'Timmermans', 'given': 'C.'}}, {'id': 'Tkaczyk-W', 'name': {'family': 'Tkaczyk', 'given': 'W.'}}, {'id': 'Todero-Peixoto-C-J', 'name': {'family': 'Todero-Peixoto', 'given': 'C. J.'}}, {'id': 'Tomé-B', 'name': {'family': 'Tomé', 'given': 'B.'}}, {'id': 'Tonachini-A', 'name': {'family': 'Tonachini', 'given': 'A.'}}, {'id': 'Torres-I', 'name': {'family': 'Torres', 'given': 'I.'}}, {'id': 'Travnicek-P', 'name': {'family': 'Travnicek', 'given': 'P.'}}, {'id': 'Tridapalli-D-B', 'name': {'family': 'Tridapalli', 'given': 'D. B.'}}, {'id': 'Tristram-G', 'name': {'family': 'Tristram', 'given': 'G.'}}, {'id': 'Trovato-E', 'name': {'family': 'Trovato', 'given': 'E.'}}, {'id': 'Tuci-V', 'name': {'family': 'Tuci', 'given': 'V.'}}, {'id': 'Tueros-M', 'name': {'family': 'Tueros', 'given': 'M.'}}, {'id': 'Ulrich-R', 'name': {'family': 'Ulrich', 'given': 'R.'}}, {'id': 'Unger-M', 'name': {'family': 'Unger', 'given': 'M.'}}, {'id': 'Urban-M', 'name': {'family': 'Urban', 'given': 'M.'}}, {'id': 'Valdés-Galicia-J-F', 'name': {'family': 'Valdés-Galicia', 'given': 'J. F.'}}, {'id': 'Valiño-I', 'name': {'family': 'Valiño', 'given': 'I.'}}, {'id': 'Valore-L', 'name': {'family': 'Valore', 'given': 'L.'}}, {'id': 'van-den-Berg-A-M', 'name': {'family': 'van den Berg', 'given': 'A. M.'}}, {'id': 'Vázquez-J-R', 'name': {'family': 'Vázquez', 'given': 'J. R.'}}, {'id': 'Vázquez-R-A', 'name': {'family': 'Vázquez', 'given': 'R. A.'}}, {'id': 'Veberič-D', 'name': {'family': 'Veberič', 'given': 'D.'}}, {'id': 'Velarde-A', 'name': {'family': 'Velarde', 'given': 'A.'}}, {'id': 'Venters-T', 'name': {'family': 'Venters', 'given': 'T.'}}, {'id': 'Verzi-V', 'name': {'family': 'Verzi', 'given': 'V.'}}, {'id': 'Videla-M', 'name': {'family': 'Videla', 'given': 'M.'}}, {'id': 'Villaseñor-L', 'name': {'family': 'Villaseñor', 'given': 'L.'}}, {'id': 'Vorobiov-S', 'name': {'family': 'Vorobiov', 'given': 'S.'}}, {'id': 'Voyvodic-L', 'name': {'family': 'Voyvodic', 'given': 'L.'}}, {'id': 'Wahlberg-H', 'name': {'family': 'Wahlberg', 'given': 'H.'}}, {'id': 'Wahrlich-P', 'name': {'family': 'Wahrlich', 'given': 'P.'}}, {'id': 'Wainberg-O', 'name': {'family': 'Wainberg', 'given': 'O.'}}, {'id': 'Warner-D', 'name': {'family': 'Warner', 'given': 'D.'}}, {'id': 'Watson-A-A', 'name': {'family': 'Watson', 'given': 'A. A.'}}, {'id': 'Westerhoff-S', 'name': {'family': 'Westerhoff', 'given': 'S.'}}, {'id': 'Whelan-B-J', 'name': {'family': 'Whelan', 'given': 'B. J.'}}, {'id': 'Wieczorek-G', 'name': {'family': 'Wieczorek', 'given': 'G.'}}, {'id': 'Wiencke-L', 'name': {'family': 'Wiencke', 'given': 'L.'}}, {'id': 'Wilczyńska-B', 'name': {'family': 'Wilczyńska', 'given': 'B.'}}, {'id': 'Wilczyński-H', 'name': {'family': 'Wilczyński', 'given': 'H.'}}, {'id': 'Wileman-C', 'name': {'family': 'Wileman', 'given': 'C.'}}, {'id': 'Winnick-M-G', 'name': {'family': 'Winnick', 'given': 'M. G.'}}, {'id': 'Wu-H', 'name': {'family': 'Wu', 'given': 'H.'}}, {'id': 'Wundheiler-B', 'name': {'family': 'Wundheiler', 'given': 'B.'}}, {'id': 'Yamamoto-T', 'name': {'family': 'Yamamoto', 'given': 'T.'}}, {'id': 'Younk-P', 'name': {'family': 'Younk', 'given': 'P.'}}, {'id': 'Yuan-G', 'name': {'family': 'Yuan', 'given': 'G.'}}, {'id': 'Zas-E', 'name': {'family': 'Zas', 'given': 'E.'}}, {'id': 'Zavrtanik-D', 'name': {'family': 'Zavrtanik', 'given': 'D.'}}, {'id': 'Zavrtanik-M', 'name': {'family': 'Zavrtanik', 'given': 'M.'}}, {'id': 'Zaw-I', 'name': {'family': 'Zaw', 'given': 'I.'}}, {'id': 'Zepeda-A', 'name': {'family': 'Zepeda', 'given': 'A.'}}, {'id': 'Ziolkowski-M', 'name': {'family': 'Ziolkowski', 'given': 'M.'}}]}
Year: 2009
DOI: 10.1016/j.astropartphys.2009.06.004
Atmospheric parameters, such as pressure (P), temperature (T) and density (ρ∝P/T), affect the development of extensive air showers initiated by energetic cosmic rays. We have studied the impact of atmospheric variations on extensive air showers by means of the surface detector of the Pierre Auger Observatory. The rate of events shows a not, vert, similar 10% seasonal modulation and not, vert, similar 2% diurnal one. We find that the observed behaviour is explained by a model including the effects associated with the variations of P and ρ. The former affects the longitudinal development of air showers while the latter influences the Molière radius and hence the lateral distribution of the shower particles. The model is validated with full simulations of extensive air showers using atmospheric profiles measured at the site of the Pierre Auger Observatory.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/6cp43-5zg55Smooth, second order, non-negative meshfree approximants selected by maximum entropy
https://resolver.caltech.edu/CaltechAUTHORS:20091022-115918749
Authors: {'items': [{'id': 'Cyron-C-J', 'name': {'family': 'Cyron', 'given': 'C. J.'}}, {'id': 'Arroyo-M', 'name': {'family': 'Arroyo', 'given': 'M.'}}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'M.'}, 'orcid': '0000-0001-5877-4824'}]}
Year: 2009
DOI: 10.1002/nme.2597
We present a family of approximation schemes, which we refer to as second-order maximum-entropy (max-ent) approximation schemes, that extends the first-order local max-ent approximation schemes to second-order consistency. This method retains the fundamental properties of first-order max-ent schemes, namely the shape functions are smooth, non-negative, and satisfy a weak Kronecker-delta property at the boundary. This last property makes the imposition of essential boundary conditions in the numerical solution of partial differential equations trivial. The evaluation of the shape functions is not explicit, but it is very efficient and robust. To our knowledge, the proposed method is the first higher-order scheme for function approximation from unstructured data in arbitrary dimensions with non-negative shape functions. As a consequence, the approximants exhibit variation diminishing properties, as well as an excellent behavior in structural vibrations problems as compared with the Lagrange finite elements, MLS-based meshfree methods and even B-Spline approximations, as shown through numerical experiments. When compared with usual MLS-based second-order meshfree methods, the shape functions presented here are much easier to integrate in a Galerkin approach, as illustrated by the standard benchmark problems.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/xfwgw-xjt84A three-dimensional multiscale model of intergranular hydrogen-assisted cracking
https://resolver.caltech.edu/CaltechAUTHORS:20100624-085532611
Authors: {'items': [{'id': 'Rimoli-J-J', 'name': {'family': 'Rimoli', 'given': 'J. J.'}, 'orcid': '0000-0002-8707-2968'}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'M.'}, 'orcid': '0000-0001-5877-4824'}]}
Year: 2010
DOI: 10.1080/14786431003752134
We present a three-dimensional model of intergranular hydrogen-embrittlement (HE) that accounts for: (i) the degradation of grain-boundary strength that arises from hydrogen coverage; (ii) grain-boundary diffusion of hydrogen; and (iii) a continuum model of plastic deformation that explicitly resolves the three-dimensional polycrystalline structure of the material. The polycrystalline structure of the specimen along the crack propagation path is resolved explicitly by the computational mesh. The texture of the polycrystal is assumed to be random and the grains are elastically anisotropic and deform plastically by crystallographic slip. We use the impurity-dependent cohesive model in order to account for the embrittling of grain boundaries due to hydrogen coverage. We have carried out three-dimensional finite-element calculations of crack-growth initiation and propagation in AISI 4340 steel double-cantilever specimens in contact with an aggressive environment and compared the predicted initiation times and crack-growth curves with the experimental data. The calculated crack-growth curves exhibit a number of qualitative features that are in keeping with observation, including: an incubation time followed by a well-defined crack-growth initiation transition for sufficiently large loading; the existence of a threshold intensity factor K_(Iscc) below which there is no crack propagation; a subsequent steeply rising part of the curve known as stage I; a plateau, or stage II, characterized by a load-insensitive crack-growth rate; and a limiting stress-intensity factor K_(Ic), or toughness, at which pure mechanical failure occurs. The calculated dependence of the crack-growth initiation time on applied stress-intensity factor exhibits power-law behavior and the corresponding characteristic exponents are in the ball-park of experimental observation. The stage-II calculated crack-growth rates are in good overall agreement with experimental measurements.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/a82fm-wfh57Shock-induced subgrain microstructures as possible homogenous sources of hot spots and initiation sites in energetic polycrystals
https://resolver.caltech.edu/CaltechAUTHORS:20100216-152951955
Authors: {'items': [{'id': 'Rimoli-J-J', 'name': {'family': 'Rimoli', 'given': 'J. J.'}, 'orcid': '0000-0002-8707-2968'}, {'id': 'Gürses-E', 'name': {'family': 'Gürses', 'given': 'E.'}}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'M.'}, 'orcid': '0000-0001-5877-4824'}]}
Year: 2010
DOI: 10.1103/PhysRevB.81.014112
The purpose of this work is to assess the feasibility of a homogeneous—or defect-free—initiation mechanism for high energetic materials in which initiation is a direct consequence of the heterogeneity of crystal plasticity at the subgrain scale. In order to assess the feasibility of these mechanisms, we develop a multiscale model that explicitly accounts for three scales: (i) the polycrystalline structure at the macroscale, (ii) single-crystal plasticity—including subgrain microstructure formation—at the mesoscale, and (iii) chemical kinetics at the molecular scale. An explicit construction gives the effective or macroscopic behavior of plastically deforming crystals with microstructure, and enables the reconstruction of optimal microstructures from the computed macroscopic averages. An intrinsic feature of the optimal deformation microstructures is the presence of highly localized regions of plastic deformation or slip lines. Temperatures, strain rates, and pressures in these slip lines rise well in excess of the average or macroscopic values. Slip lines thus provide a plentiful supply of likely initiation sites, or hotspots, in defect-free crystals. We have assessed this initiation mechanism by simulating a PETN plate impact experiment and comparing the resulting predictions with experimental pop-plot data. The computed characteristic exponents are in the ballpark of experimental observationhttps://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/7smrv-x1g75Finite-temperature extension of the quasicontinuum method using Langevin dynamics: entropy losses and analysis of errors
https://resolver.caltech.edu/CaltechAUTHORS:20100121-141104452
Authors: {'items': [{'id': 'Marian-J', 'name': {'family': 'Marian', 'given': 'J.'}}, {'id': 'Venturini-Gabriela-N', 'name': {'family': 'Venturini', 'given': 'G.'}}, {'id': 'Hansen-B-L', 'name': {'family': 'Hansen', 'given': 'B. L.'}}, {'id': 'Knapp-J', 'name': {'family': 'Knapp', 'given': 'J.'}}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'M.'}, 'orcid': '0000-0001-5877-4824'}, {'id': 'Campbell-G-H', 'name': {'family': 'Campbell', 'given': 'G. H.'}}]}
Year: 2010
DOI: 10.1088/0965-0393/18/1/015003
The concurrent bridging of molecular dynamics and continuum thermodynamics presents a number of challenges, mostly associated with energy transmission and changes in the constitutive description of a material across domain boundaries. In this paper, we propose a framework for simulating coarse dynamic systems in the canonical ensemble using the quasicontinuum method (QC). The equations of motion are expressed in reduced QC coordinates and are strictly derived from dissipative Lagrangian mechanics. The derivation naturally leads to a classical Langevin implementation where the timescale is governed by vibrations emanating from the finest length scale occurring in the computational cell. The equations of motion are integrated explicitly via Newmark's (β = 0; γ = 1/2) method, which is parametrized to ensure overdamped dynamics. In this fashion, spurious heating due to reflected vibrations is suppressed, leading to stable canonical trajectories. To estimate the errors introduced by the QC reduction in the resulting dynamics, we have quantified the vibrational entropy losses in Al uniform meshes by calculating the thermal expansion coefficient for a number of conditions. We find that the entropic depletion introduced by coarsening varies linearly with the element size and is independent of the nodal cluster diameter. We rationalize the results in terms of the system, mesh and cluster sizes within the framework of the quasiharmonic approximation. The limitations of the method and alternatives to mitigate the errors introduced by coarsening are discussed. This work represents the first of a series of studies aimed at developing a fully non-equilibrium finite-temperature extension of QC.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/p8nc4-1f205Non-periodic finite-element formulation of Kohn–Sham density functional theory
https://resolver.caltech.edu/CaltechAUTHORS:20100302-131546235
Authors: {'items': [{'id': 'Suryanarayana-P', 'name': {'family': 'Suryanarayana', 'given': 'Phanish'}, 'orcid': '0000-0001-5172-0049'}, {'id': 'Vikram-G', 'name': {'family': 'Vikram', 'given': 'Gavini'}}, {'id': 'Blesgen-T', 'name': {'family': 'Blesgen', 'given': 'Thomas'}}, {'id': 'Bhattacharya-K', 'name': {'family': 'Bhattacharya', 'given': 'Kaushik'}, 'orcid': '0000-0003-2908-5469'}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'Michael'}, 'orcid': '0000-0001-5877-4824'}]}
Year: 2010
DOI: 10.1016/j.jmps.2009.10.002
We present a real-space, non-periodic, finite-element formulation for Kohn–Sham density functional theory (KS-DFT). We transform the original variational problem into a local saddle-point problem, and show its well-posedness by proving the existence of minimizers. Further, we prove the convergence of finite-element approximations including numerical quadratures. Based on domain decomposition, we develop a parallel finite-element implementation of this formulation capable of performing both all-electron and pseudopotential calculations. We assess the accuracy of the formulation through selected test cases and demonstrate good agreement with the literature. We also evaluate the numerical performance of the implementation with regard to its scalability and convergence rates. We view this work as a step towards developing a method that can accurately study defects like vacancies, dislocations and crack tips using density functional theory (DFT) at reasonable computational cost by retaining electronic resolution where it is necessary and seamlessly coarse-graining far away.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/jya74-xk759Study and validation of a variational theory of thermo-mechanical coupling in finite visco-plasticity
https://resolver.caltech.edu/CaltechAUTHORS:20100225-094200302
Authors: {'items': [{'id': 'Stainier-Laurent', 'name': {'family': 'Stainier', 'given': 'L.'}, 'orcid': '0000-0001-6719-6616'}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'M.'}, 'orcid': '0000-0001-5877-4824'}]}
Year: 2010
DOI: 10.1016/j.ijsolstr.2009.11.012
We present an experimental validation of the variational theory of thermo-mechanical coupling of Yang et al. (2006) in the case of finite thermo-visco-plasticity. The variational theory results in precise predictions of the rate of heating due to dissipation and does not require an a priori definition or model of a fraction of plastic work converted to heat. We show that the predicted heat-to-plastic work ratios are in good agreement with experimental observations for 2024-T3 aluminum, α-titanium and pure polycrystalline tantalum, including their evolution with strain and their dependence on strain-rate. We also critically compare the variational theory to other theories and models in the literature.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/7rbkv-rwc89Measurement of the Depth of Maximum of Extensive Air Showers above 10^(18) eV
https://resolver.caltech.edu/CaltechAUTHORS:20100415-075729464
Authors: {'items': [{'id': 'Abraham-J', 'name': {'family': 'Abraham', 'given': 'J.'}}, {'id': 'Abreu-P', 'name': {'family': 'Abreu', 'given': 'P.'}}, {'id': 'Aglietta-M', 'name': {'family': 'Aglietta', 'given': 'M.'}}, {'id': 'Ahn-E-J', 'name': {'family': 'Ahn', 'given': 'E. J.'}}, {'id': 'Allard-D', 'name': {'family': 'Allard', 'given': 'D.'}}, {'id': 'Allekotte-I', 'name': {'family': 'Allekotte', 'given': 'I.'}}, {'id': 'Allen-J', 'name': {'family': 'Allen', 'given': 'J.'}}, {'id': 'Alvarez-Muñiz-J', 'name': {'family': 'Alvarez-Muñiz', 'given': 'J.'}}, {'id': 'Ambrosio-M', 'name': {'family': 'Ambrosio', 'given': 'M.'}}, {'id': 'Anchordoqui-L', 'name': {'family': 'Anchordoqui', 'given': 'L.'}}, {'id': 'Andringa-S', 'name': {'family': 'Andringa', 'given': 'S.'}}, {'id': 'Antičić-T', 'name': {'family': 'Antičić', 'given': 'T.'}}, {'id': 'Anzalone-A', 'name': {'family': 'Anzalone', 'given': 'A.'}}, {'id': 'Aramo-C', 'name': {'family': 'Aramo', 'given': 'C.'}}, {'id': 'Arganda-E', 'name': {'family': 'Arganda', 'given': 'E.'}}, {'id': 'Arisaka-K', 'name': {'family': 'Arisaka', 'given': 'K.'}}, {'id': 'Arqueros-F', 'name': {'family': 'Arqueros', 'given': 'F.'}}, {'id': 'Asorey-H', 'name': {'family': 'Asorey', 'given': 'H.'}}, {'id': 'Assis-P', 'name': {'family': 'Assis', 'given': 'P.'}}, {'id': 'Aublin-J', 'name': {'family': 'Aublin', 'given': 'J.'}}, {'id': 'Ave-M', 'name': {'family': 'Ave', 'given': 'M.'}}, {'id': 'Avila-G', 'name': {'family': 'Avila', 'given': 'G.'}}, {'id': 'Bäcker-T', 'name': {'family': 'Bäcker', 'given': 'T.'}}, {'id': 'Badagnani-D', 'name': {'family': 'Badagnani', 'given': 'D.'}}, {'id': 'Balzer-M', 'name': {'family': 'Balzer', 'given': 'M.'}}, {'id': 'Barber-K-B', 'name': {'family': 'Barber', 'given': 'K. B.'}}, {'id': 'Barbosa-A-F', 'name': {'family': 'Barbosa', 'given': 'A. F.'}}, {'id': 'Barroso-S-L-C', 'name': {'family': 'Barroso', 'given': 'S. L. C.'}}, {'id': 'Baughman-B', 'name': {'family': 'Baughman', 'given': 'B.'}}, {'id': 'Bauleo-P', 'name': {'family': 'Bauleo', 'given': 'P.'}}, {'id': 'Beatty-J-J', 'name': {'family': 'Beatty', 'given': 'J. J.'}}, {'id': 'Becker-B-R', 'name': {'family': 'Becker', 'given': 'B. R.'}}, {'id': 'Becker-K-H', 'name': {'family': 'Becker', 'given': 'K. H.'}}, {'id': 'Bellétoile-A', 'name': {'family': 'Bellétoile', 'given': 'A.'}}, {'id': 'Bellido-J-A', 'name': {'family': 'Bellido', 'given': 'J. A.'}}, {'id': 'BenZvi-S', 'name': {'family': 'BenZvi', 'given': 'S.'}}, {'id': 'Berat-C', 'name': {'family': 'Berat', 'given': 'C.'}}, {'id': 'Bergmann-T', 'name': {'family': 'Bergmann', 'given': 'T.'}}, {'id': 'Bertou-X', 'name': {'family': 'Bertou', 'given': 'X.'}}, {'id': 'Biermann-P-L', 'name': {'family': 'Biermann', 'given': 'P. L.'}}, {'id': 'Billoir-P', 'name': {'family': 'Billoir', 'given': 'P.'}}, {'id': 'Blanch-Bigas-O', 'name': {'family': 'Blanch-Bigas', 'given': 'O.'}}, {'id': 'Blanco-F', 'name': {'family': 'Blanco', 'given': 'F.'}}, {'id': 'Blanco-M-Astro', 'name': {'family': 'Blanco', 'given': 'M.'}}, {'id': 'Bleve-C', 'name': {'family': 'Bleve', 'given': 'C.'}}, {'id': 'Blümer-H', 'name': {'family': 'Blümer', 'given': 'H.'}}, {'id': 'Boháčová-M', 'name': {'family': 'Boháčová', 'given': 'M.'}}, {'id': 'Boncioli-D', 'name': {'family': 'Boncioli', 'given': 'D.'}}, {'id': 'Bonifazi-C', 'name': {'family': 'Bonifazi', 'given': 'C.'}}, {'id': 'Bonino-R', 'name': {'family': 'Bonino', 'given': 'R.'}}, {'id': 'Borodai-N', 'name': {'family': 'Borodai', 'given': 'N.'}}, {'id': 'Brack-J', 'name': {'family': 'Brack', 'given': 'J.'}}, {'id': 'Brogueira-P', 'name': {'family': 'Brogueira', 'given': 'P.'}}, {'id': 'Brown-William-C-Physics', 'name': {'family': 'Brown', 'given': 'W. C.'}}, {'id': 'Bruijn-R', 'name': {'family': 'Bruijn', 'given': 'R.'}}, {'id': 'Buchholz-D', 'name': {'family': 'Buchholz', 'given': 'D.'}}, {'id': 'Bueno-A', 'name': {'family': 'Bueno', 'given': 'A.'}}, {'id': 'Burton-R-E', 'name': {'family': 'Burton', 'given': 'R. E.'}}, {'id': 'Busca-N-G', 'name': {'family': 'Busca', 'given': 'N. G.'}}, {'id': 'Caballero-Mora-K-S', 'name': {'family': 'Caballero-Mora', 'given': 'K. 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M.'}}, {'id': 'Perrone-L', 'name': {'family': 'Perrone', 'given': 'L.'}}, {'id': 'Pesce-R', 'name': {'family': 'Pesce', 'given': 'R.'}}, {'id': 'Petermann-E', 'name': {'family': 'Petermann', 'given': 'E.'}}, {'id': 'Petrera-S', 'name': {'family': 'Petrera', 'given': 'S.'}}, {'id': 'Petrinca-P', 'name': {'family': 'Petrinca', 'given': 'P.'}}, {'id': 'Petrolini-A', 'name': {'family': 'Petrolini', 'given': 'A.'}}, {'id': 'Petrov-Y', 'name': {'family': 'Petrov', 'given': 'Y.'}}, {'id': 'Petrovic-J', 'name': {'family': 'Petrovic', 'given': 'J.'}}, {'id': 'Pfendner-C', 'name': {'family': 'Pfendner', 'given': 'C.'}}, {'id': 'Piegaia-R', 'name': {'family': 'Piegaia', 'given': 'R.'}}, {'id': 'Pierog-T', 'name': {'family': 'Pierog', 'given': 'T.'}}, {'id': 'Pimenta-M', 'name': {'family': 'Pimenta', 'given': 'M.'}}, {'id': 'Pirronello-V', 'name': {'family': 'Pirronello', 'given': 'V.'}}, {'id': 'Platino-M', 'name': {'family': 'Platino', 'given': 'M.'}}, {'id': 'Ponce-V-H', 'name': {'family': 'Ponce', 'given': 'V. H.'}}, {'id': 'Pontz-M', 'name': {'family': 'Pontz', 'given': 'M.'}}, {'id': 'Privitera-P', 'name': {'family': 'Privitera', 'given': 'P.'}}, {'id': 'Prouza-M', 'name': {'family': 'Prouza', 'given': 'M.'}}, {'id': 'Quel-E-J', 'name': {'family': 'Quel', 'given': 'E. J.'}}, {'id': 'Rautenberg-J', 'name': {'family': 'Rautenberg', 'given': 'J.'}}, {'id': 'Ravel-O', 'name': {'family': 'Ravel', 'given': 'O.'}}, {'id': 'Ravignani-D', 'name': {'family': 'Ravignani', 'given': 'D.'}}, {'id': 'Redondo-A', 'name': {'family': 'Redondo', 'given': 'A.'}}, {'id': 'Revenu-B', 'name': {'family': 'Revenu', 'given': 'B.'}}, {'id': 'Rezende-F-A-S', 'name': {'family': 'Rezende', 'given': 'F. A. S.'}}, {'id': 'Ridky-J', 'name': {'family': 'Ridky', 'given': 'J.'}}, {'id': 'Riggi-S', 'name': {'family': 'Riggi', 'given': 'S.'}}, {'id': 'Risse-M', 'name': {'family': 'Risse', 'given': 'M.'}}, {'id': 'Ristori-P', 'name': {'family': 'Ristori', 'given': 'P.'}}, {'id': 'Rivière-C', 'name': {'family': 'Rivière', 'given': 'C.'}}, {'id': 'Rizi-V', 'name': {'family': 'Rizi', 'given': 'V.'}}, {'id': 'Robledo-C', 'name': {'family': 'Robledo', 'given': 'C.'}}, {'id': 'Rodriguez-G', 'name': {'family': 'Rodriguez', 'given': 'G.'}}, {'id': 'Rodriguez-Martino-J', 'name': {'family': 'Rodriguez-Martino', 'given': 'J.'}}, {'id': 'Rodriguez-Rojo-J', 'name': {'family': 'Rodriguez-Rojo', 'given': 'J.'}}, {'id': 'Rodriguez-Cabo-I', 'name': {'family': 'Rodriguez-Cabo', 'given': 'I.'}}, {'id': 'Rodríguez-Frías-M-D', 'name': {'family': 'Rodríguez-Frías', 'given': 'M. D.'}}, {'id': 'Ros-G', 'name': {'family': 'Ros', 'given': 'G.'}}, {'id': 'Rosado-J', 'name': {'family': 'Rosado', 'given': 'J.'}}, {'id': 'Rossler-T', 'name': {'family': 'Rossler', 'given': 'T.'}}, {'id': 'Roth-M', 'name': {'family': 'Roth', 'given': 'M.'}}, {'id': "Rouillé-d'Orfeui-B", 'name': {'family': "Rouillé-d'Orfeui", 'given': 'B.'}}, {'id': 'Roulet-E', 'name': {'family': 'Roulet', 'given': 'E.'}}, {'id': 'Rovero-A-C', 'name': {'family': 'Rovero', 'given': 'A. C.'}}, {'id': 'Salamida-F', 'name': {'family': 'Salamida', 'given': 'F.'}}, {'id': 'Salazar-H', 'name': {'family': 'Salazar', 'given': 'H.'}}, {'id': 'Salina-G', 'name': {'family': 'Salina', 'given': 'G.'}}, {'id': 'Sánchez-F', 'name': {'family': 'Sánchez', 'given': 'F.'}}, {'id': 'Santander-M', 'name': {'family': 'Santander', 'given': 'M.'}}, {'id': 'Santo-C-E', 'name': {'family': 'Santo', 'given': 'C. E.'}}, {'id': 'Santos-E', 'name': {'family': 'Santos', 'given': 'E.'}}, {'id': 'Santos-E-M', 'name': {'family': 'Santos', 'given': 'E. M.'}}, {'id': 'Sarazin-F', 'name': {'family': 'Sarazin', 'given': 'F.'}}, {'id': 'Sarkar-S', 'name': {'family': 'Sarkar', 'given': 'S.'}}, {'id': 'Sato-R', 'name': {'family': 'Sato', 'given': 'R.'}}, {'id': 'Scharf-N', 'name': {'family': 'Scharf', 'given': 'N.'}}, {'id': 'Scherini-V', 'name': {'family': 'Scherini', 'given': 'V.'}}, {'id': 'Schieler-H', 'name': {'family': 'Schieler', 'given': 'H.'}}, {'id': 'Schiffer-P', 'name': {'family': 'Schiffer', 'given': 'P.'}}, {'id': 'Schmidt-A', 'name': {'family': 'Schmidt', 'given': 'A.'}, 'orcid': '0000-0001-8759-2843'}, {'id': 'Schmidt-F', 'name': {'family': 'Schmidt', 'given': 'F.'}}, {'id': 'Schmidt-T', 'name': {'family': 'Schmidt', 'given': 'T.'}}, {'id': 'Scholten-O', 'name': {'family': 'Scholten', 'given': 'O.'}}, {'id': 'Schoorlemmer-H', 'name': {'family': 'Schoorlemmer', 'given': 'H.'}}, {'id': 'Schovancova-J', 'name': {'family': 'Schovancova', 'given': 'J.'}}, {'id': 'Schovánek-P', 'name': {'family': 'Schovánek', 'given': 'P.'}}, {'id': 'Schroeder-F', 'name': {'family': 'Schroeder', 'given': 'F.'}}, {'id': 'Schulte-S', 'name': {'family': 'Schulte', 'given': 'S.'}}, {'id': 'Schüssler-F', 'name': {'family': 'Schüssler', 'given': 'F.'}}, {'id': 'Schuster-D', 'name': {'family': 'Schuster', 'given': 'D.'}}, {'id': 'Sciutto-S-J', 'name': {'family': 'Sciutto', 'given': 'S. J.'}}, {'id': 'Scuderi-M', 'name': {'family': 'Scuderi', 'given': 'M.'}}, {'id': 'Segreto-A', 'name': {'family': 'Segreto', 'given': 'A.'}}, {'id': 'Semikoz-D', 'name': {'family': 'Semikoz', 'given': 'D.'}}, {'id': 'Settimo-M', 'name': {'family': 'Settimo', 'given': 'M.'}}, {'id': 'Shadkam-A', 'name': {'family': 'Shadkam', 'given': 'A.'}}, {'id': 'Shellard-R-C', 'name': {'family': 'Shellard', 'given': 'R. C.'}}, {'id': 'Sidelnik-I', 'name': {'family': 'Sidelnik', 'given': 'I.'}}, {'id': 'Siffert-B-B', 'name': {'family': 'Siffert', 'given': 'B. B.'}}, {'id': 'Sigl-G', 'name': {'family': 'Sigl', 'given': 'G.'}}, {'id': 'Śmiałkowski-A', 'name': {'family': 'Śmiałkowski', 'given': 'A.'}}, {'id': 'Šmída-R', 'name': {'family': 'Šmída', 'given': 'R.'}}, {'id': 'Snow-G-R', 'name': {'family': 'Snow', 'given': 'G. R.'}}, {'id': 'Sommers-P', 'name': {'family': 'Sommers', 'given': 'P.'}}, {'id': 'Sorokin-J', 'name': {'family': 'Sorokin', 'given': 'J.'}}, {'id': 'Spinka-H-M', 'name': {'family': 'Spinka', 'given': 'H.'}}, {'id': 'Squartini-R', 'name': {'family': 'Squartini', 'given': 'R.'}}, {'id': 'Stasielak-J', 'name': {'family': 'Stasielak', 'given': 'J.'}}, {'id': 'Stephan-M', 'name': {'family': 'Stephan', 'given': 'M.'}}, {'id': 'Strazzeri-E', 'name': {'family': 'Strazzeri', 'given': 'E.'}}, {'id': 'Stutz-A-M', 'name': {'family': 'Stutz', 'given': 'A.'}, 'orcid': '0000-0003-2300-8200'}, {'id': 'Suarez-F', 'name': {'family': 'Suarez', 'given': 'F.'}}, {'id': 'Suomijärvi-T', 'name': {'family': 'Suomijärvi', 'given': 'T.'}}, {'id': 'Supanitsky-A-D', 'name': {'family': 'Supanitsky', 'given': 'A. D.'}}, {'id': 'Šuša-T', 'name': {'family': 'Šuša', 'given': 'T.'}}, {'id': 'Sutherland-M-S', 'name': {'family': 'Sutherland', 'given': 'M. S.'}}, {'id': 'Swain-J', 'name': {'family': 'Swain', 'given': 'J.'}}, {'id': 'Szadkowski-Z', 'name': {'family': 'Szadkowski', 'given': 'Z.'}}, {'id': 'Tamashiro-A', 'name': {'family': 'Tamashiro', 'given': 'A.'}}, {'id': 'Tamburro-A', 'name': {'family': 'Tamburro', 'given': 'A.'}}, {'id': 'Tapia-A', 'name': {'family': 'Tapia', 'given': 'A.'}}, {'id': 'Tarutina-T', 'name': {'family': 'Tarutina', 'given': 'T.'}}, {'id': 'Taşcău-O', 'name': {'family': 'Taşcău', 'given': 'O.'}}, {'id': 'Tcaciuc-R', 'name': {'family': 'Tcaciuc', 'given': 'R.'}}, {'id': 'Tcherniakhovski-D', 'name': {'family': 'Tcherniakhovski', 'given': 'D.'}}, {'id': 'Tegolo-D', 'name': {'family': 'Tegolo', 'given': 'D.'}}, {'id': 'Thao-N-T', 'name': {'family': 'Thao', 'given': 'N. T.'}}, {'id': 'Thomas-D', 'name': {'family': 'Thomas', 'given': 'D.'}}, {'id': 'Tiffenberg-J', 'name': {'family': 'Tiffenberg', 'given': 'J.'}}, {'id': 'Timmermans-C', 'name': {'family': 'Timmermans', 'given': 'C.'}}, {'id': 'Tkaczyk-W', 'name': {'family': 'Tkaczyk', 'given': 'W.'}}, {'id': 'Todero-Peixoto-C-J', 'name': {'family': 'Todero-Peixoto', 'given': 'C. J.'}}, {'id': 'Tomé-B', 'name': {'family': 'Tomé', 'given': 'B.'}}, {'id': 'Tonachini-A', 'name': {'family': 'Tonachini', 'given': 'A.'}}, {'id': 'Travnicek-P', 'name': {'family': 'Travnicek', 'given': 'P.'}}, {'id': 'Tridapalli-D-B', 'name': {'family': 'Tridapalli', 'given': 'D. B.'}}, {'id': 'Tristram-G', 'name': {'family': 'Tristram', 'given': 'G.'}}, {'id': 'Trovato-E', 'name': {'family': 'Trovato', 'given': 'E.'}}, {'id': 'Tueros-M', 'name': {'family': 'Tueros', 'given': 'M.'}}, {'id': 'Ulrich-R', 'name': {'family': 'Ulrich', 'given': 'R.'}}, {'id': 'Unger-M', 'name': {'family': 'Unger', 'given': 'M.'}}, {'id': 'Urban-M', 'name': {'family': 'Urban', 'given': 'M.'}}, {'id': 'Valdés-Galicia-J-F', 'name': {'family': 'Valdés-Galicia', 'given': 'J. F.'}}, {'id': 'Valiño-I', 'name': {'family': 'Valiño', 'given': 'I.'}}, {'id': 'Valore-L', 'name': {'family': 'Valore', 'given': 'L.'}}, {'id': 'van-den-Berg-A-M', 'name': {'family': 'van-den-Berg', 'given': 'A. M.'}}, {'id': 'Vázquez-J-R', 'name': {'family': 'Vázquez', 'given': 'J. R.'}}, {'id': 'Vázquez-R-A', 'name': {'family': 'Vázquez', 'given': 'R. A.'}}, {'id': 'Veberič-D', 'name': {'family': 'Veberič', 'given': 'D.'}}, {'id': 'Venters-T', 'name': {'family': 'Venters', 'given': 'T.'}}, {'id': 'Verzi-V', 'name': {'family': 'Verzi', 'given': 'V.'}}, {'id': 'Videla-M', 'name': {'family': 'Videla', 'given': 'M.'}}, {'id': 'Villaseñor-L', 'name': {'family': 'Villaseñor', 'given': 'L.'}}, {'id': 'Vorobiov-S', 'name': {'family': 'Vorobiov', 'given': 'S.'}}, {'id': 'Voyvodic-L', 'name': {'family': 'Voyvodic', 'given': 'L.'}}, {'id': 'Wahlberg-H', 'name': {'family': 'Wahlberg', 'given': 'H.'}}, {'id': 'Wahrlich-P', 'name': {'family': 'Wahrlich', 'given': 'P.'}}, {'id': 'Wainberg-O', 'name': {'family': 'Wainberg', 'given': 'O.'}}, {'id': 'Warner-D', 'name': {'family': 'Warner', 'given': 'D.'}}, {'id': 'Watson-A-A', 'name': {'family': 'Watson', 'given': 'A. A.'}}, {'id': 'Westerhoff-S', 'name': {'family': 'Westerhoff', 'given': 'S.'}}, {'id': 'Whelan-B-J', 'name': {'family': 'Whelan', 'given': 'B. J.'}}, {'id': 'Wieczorek-G', 'name': {'family': 'Wieczorek', 'given': 'G.'}}, {'id': 'Wiencke-L', 'name': {'family': 'Wiencke', 'given': 'L.'}}, {'id': 'Wilczyńska-B', 'name': {'family': 'Wilczyńska', 'given': 'B.'}}, {'id': 'Wilczyński-H', 'name': {'family': 'Wilczyński', 'given': 'H.'}}, {'id': 'Williamz-C', 'name': {'family': 'Williams', 'given': 'C.'}}, {'id': 'Winchen-T', 'name': {'family': 'Winchen', 'given': 'T.'}}, {'id': 'Winnick-M-G', 'name': {'family': 'Winnick', 'given': 'M. G.'}}, {'id': 'Wundheiler-B', 'name': {'family': 'Wundheiler', 'given': 'B.'}}, {'id': 'Yamamoto-T', 'name': {'family': 'Yamamoto', 'given': 'T.'}}, {'id': 'Younk-P', 'name': {'family': 'Younk', 'given': 'P.'}}, {'id': 'Yuan-G', 'name': {'family': 'Yuan', 'given': 'G.'}}, {'id': 'Yushkov-A', 'name': {'family': 'Yushkov', 'given': 'A.'}}, {'id': 'Zas-E', 'name': {'family': 'Zas', 'given': 'E.'}}, {'id': 'Zavrtanik-D', 'name': {'family': 'Zavrtanik', 'given': 'D.'}}, {'id': 'Zavrtanik-M', 'name': {'family': 'Zavrtanik', 'given': 'M.'}}, {'id': 'Zaw-I', 'name': {'family': 'Zaw', 'given': 'I.'}}, {'id': 'Zepeda-A', 'name': {'family': 'Zepeda', 'given': 'A.'}}, {'id': 'Ziolkowski-M', 'name': {'family': 'Ziolkowski', 'given': 'M.'}}]}
Year: 2010
DOI: 10.1103/PhysRevLett.104.091101
We describe the measurement of the depth of maximum, X_(max), of the longitudinal development of air
showers induced by cosmic rays. Almost 4000 events above 10^(18) eV observed by the fluorescence
detector of the Pierre Auger Observatory in coincidence with at least one surface detector station are selected for the analysis. The average shower maximum was found to evolve with energy at a rate of
(106_(-21)^(+35))
g/cm^2/decade below 10^(18:24±0.05) eV, and (24±3) g/cm^ 2=decade above this energy. The
measured shower-to-shower fluctuations decrease from about 55 to 26 g/cm^2. The interpretation of these
results in terms of the cosmic ray mass composition is briefly discussed.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/n0z3s-yws82Energy-stepping integrators in Lagrangian mechanics
https://resolver.caltech.edu/CaltechAUTHORS:20100513-140146860
Authors: {'items': [{'id': 'Gonzalez-M', 'name': {'family': 'Gonzalez', 'given': 'M.'}}, {'id': 'Schmidt-B', 'name': {'family': 'Schmidt', 'given': 'B.'}}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'M.'}, 'orcid': '0000-0001-5877-4824'}]}
Year: 2010
DOI: 10.1002/nme.2753
We present a class of integration schemes for Lagrangian mechanics, referred to as energy-stepping integrators, that are momentum and energy conserving, symplectic and convergent. In order to achieve these properties we replace the original potential energy by a piecewise constant, or terraced approximation at steps of uniform height. By taking steps of diminishing height, an approximating sequence of energies is generated. The trajectories of the resulting approximating Lagrangians can be characterized explicitly and consist of intervals of piecewise rectilinear motion. We show that the energy-stepping trajectories are symplectic, exactly conserve all the momentum maps of the original system and, subject to a transversality condition, converge to trajectories of the original system when the energy step is decreased to zero. These properties, the excellent long-term behavior of energy-stepping and its automatic time-step selection property, are born out by selected examples of application, including the dynamics of a frozen Argon cluster, the spinning of an elastic cube and the collision of two elastic spheres.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/yt08h-2gt66Dissipative Systems in Contact with a Heat Bath: Application to Andrade Creep
https://resolver.caltech.edu/CaltechAUTHORS:20200603-073605619
Authors: {'items': [{'id': 'Theil-F', 'name': {'family': 'Theil', 'given': 'Florian'}}, {'id': 'Sullivan-T', 'name': {'family': 'Sullivan', 'given': 'Tim'}}, {'id': 'Koslovski-M', 'name': {'family': 'Koslovski', 'given': 'Marisol'}}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'Michael'}, 'orcid': '0000-0001-5877-4824'}]}
Year: 2010
DOI: 10.1007/978-90-481-9195-6_20
We develop a theory of statistical mechanics for dissipative systems governed by equations of evolution that assigns probabilities to individual trajectories of the system. The theory is made mathematically rigorous and leads to precise predictions regarding the behavior of dissipative systems at finite temperature. Such predictions include the effect of temperature on yield phenomena and rheological time exponents. The particular case of an ensemble of dislocations moving in a slip plane through a random array of obstacles is studied numerically in detail. The numerical results bear out the analytical predictions regarding the mean response of the system, which exhibits Andrade creep.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/kbb2q-gk954Discrete dislocations in graphene
https://resolver.caltech.edu/CaltechAUTHORS:20171117-151152380
Authors: {'items': [{'id': 'Ariza-M-P', 'name': {'family': 'Ariza', 'given': 'M. P.'}, 'orcid': '0000-0003-0266-0216'}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'M.'}, 'orcid': '0000-0001-5877-4824'}]}
Year: 2010
DOI: 10.1016/j.jmps.2010.02.008
In this work, we present an application of the theory of discrete dislocations of Ariza and Ortiz (2005) to the analysis of dislocations in graphene. Specifically, we discuss the specialization of the theory to graphene and its further specialization to the force-constant model of Aizawa et al. (1990). The ability of the discrete-dislocation theory to predict dislocation core structures and energies is critically assessed for periodic arrangements of dislocation dipoles and quadrupoles. We show that, with the aid of the discrete Fourier transform, those problems are amenable to exact solution within the discrete-dislocation theory, which confers the theory a distinct advantage over conventional atomistic models. The discrete dislocations exhibit 5–7 ring core structures that are consistent with observation and result in dislocation energies that fall within the range of prediction of other models. The asymptotic behavior of dilute distributions of dislocations is characterized analytically in terms of a discrete prelogarithmic energy tensor. Explicit expressions for this discrete prelogarithmic energy tensor are provided up to quadratures.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/6783h-x5m30Optimal Control Strategies for Robust Certification
https://resolver.caltech.edu/CaltechAUTHORS:20100709-105908209
Authors: {'items': [{'id': 'Leyendecker-S', 'name': {'family': 'Leyendecker', 'given': 'Sigrid'}}, {'id': 'Lucas-L-J', 'name': {'family': 'Lucas', 'given': 'Leonard J.'}}, {'id': 'Owhadi-H', 'name': {'family': 'Owhadi', 'given': 'Houman'}, 'orcid': '0000-0002-5677-1600'}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'Michael'}, 'orcid': '0000-0001-5877-4824'}]}
Year: 2010
DOI: 10.1115/1.4001375
We present an optimal control methodology, which we refer to as concentration-of-measure optimal control (COMOC), that seeks to minimize a concentration-of-measure upper bound on the probability of failure of a system. The systems under consideration are characterized by a single performance measure that depends on random inputs through a known response function. For these systems, concentration-of-measure upper bound on the probability of failure of a system can be formulated in terms of the mean performance measure and a system diameter that measures the uncertainty in the operation of the system. COMOC then seeks to determine the optimal controls that maximize the confidence in the safe operation of the system, defined as the ratio of the design margin, which is measured by the difference between the mean performance and the design threshold, to the system uncertainty, which is measured by the system diameter. This strategy has been assessed in the case of a robot-arm maneuver for which the performance measure of interest is assumed to be the placement accuracy of the arm tip. The ability of COMOC to significantly increase the design confidence in that particular example of application is demonstrated.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/4q7s8-4z852Dislocation subgrain structures and modeling the plastic hardening of metallic single crystals
https://resolver.caltech.edu/CaltechAUTHORS:20100712-142922131
Authors: {'items': [{'id': 'Hansen-B-L', 'name': {'family': 'Hansen', 'given': 'B. L.'}}, {'id': 'Bronkhorst-C-A', 'name': {'family': 'Bronkhorst', 'given': 'C. A.'}}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'M.'}, 'orcid': '0000-0001-5877-4824'}]}
Year: 2010
DOI: 10.1088/0965-0393/18/5/055001
A single crystal plasticity theory for insertion into finite element simulation is formulated using sequential laminates to model subgrain dislocation structures. It is known that local models do not adequately account for latent hardening, as latent hardening is not only a material property, but a nonlocal property (e.g. grain size and shape). The addition of the nonlocal energy from the formation of subgrain structure dislocation walls and the boundary layer misfits provide both latent and self-hardening of a crystal slip. Latent hardening occurs as the formation of new dislocation walls limits motion of new mobile dislocations, thus hardening future slip systems. Self-hardening is accomplished by an evolution of the subgrain structure length scale. The substructure length scale is computed by minimizing the nonlocal energy. The minimization of the nonlocal energy is a competition between the dislocation wall energy and the boundary layer energies. The nonlocal terms are also directly minimized within the subgrain model as they affect deformation response. The geometrical relationship between the dislocation walls and slip planes affecting the dislocation mean free path is taken into account, giving a first-order approximation to shape effects. A coplanar slip model is developed due to requirements while modeling the subgrain structure. This subgrain structure plasticity model is noteworthy as all material parameters are experimentally determined rather than fit. The model also has an inherit path dependence due to the formation of the subgrain structures. Validation is accomplished by comparison with single crystal tension test results.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/zv8st-ndz42Optimal transportation meshfree approximation schemes for fluid and plastic flows
https://resolver.caltech.edu/CaltechAUTHORS:20101022-154521445
Authors: {'items': [{'id': 'Li-Bo', 'name': {'family': 'Li', 'given': 'B.'}, 'orcid': '0000-0002-8019-8891'}, {'id': 'Habbal-F', 'name': {'family': 'Habbal', 'given': 'F.'}}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'M.'}, 'orcid': '0000-0001-5877-4824'}]}
Year: 2010
DOI: 10.1002/nme.2869
We develop an optimal transportation meshfree (OTM) method for simulating general solid and fluid flows, including fluid–structure interaction. The method combines concepts from optimal transportation theory with material-point sampling and max-ent meshfree interpolation. The proposed OTM method generalizes the Benamou–Brenier differential formulation of optimal mass transportation problems to problems including arbitrary geometries and constitutive behavior. The OTM method enforces mass transport and essential boundary conditions exactly and is free from tension instabilities. The OTM method exactly conserves linear and angular momentum and its convergence characteristics are verified in standard benchmark problems. We illustrate the range and scope of the method by means of two examples of application: the bouncing of a gas-filled balloon off a rigid wall; and the classical Taylor-anvil benchmark test extended to the hypervelocity range.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/4zdyd-0ns63Evolution of anodic stress corrosion cracking in a coated material
https://resolver.caltech.edu/CaltechAUTHORS:20101004-105129323
Authors: {'items': [{'id': 'Bjerkén-C', 'name': {'family': 'Bjerkén', 'given': 'C.'}}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'M.'}, 'orcid': '0000-0001-5877-4824'}]}
Year: 2010
DOI: 10.1007/s10704-010-9514-5
In the present paper, we investigate the influence of corrosion driving forces and interfacial toughness for a coated material subjected to mechanical loading. If the protective coating is cracked, the substrate material may become exposed to a corrosive media. For a stress corrosion sensitive substrate material, this may lead to detrimental crack growth. A crack is assumed to grow by anodic dissolution, inherently leading to a blunt crack tip. The evolution of the crack surface is modelled as a moving boundary problem using an adaptive finite element method. The rate of dissolution along the crack surface in the substrate is assumed to be proportional to the chemical potential, which is function of the local surface energy density and elastic strain energy density. The surface energy tends to flatten the surface, whereas the strain energy due to stress concentration promotes material dissolution. The influence of the interface energy density parameter for the solid–fluid combination, interface corrosion resistance and stiffness ratios between coating and substrate is investigated. Three characteristic crack shapes are obtained; deepening and narrowing single cracks, branched cracks and sharp interface cracks. The crack shapes obtained by our simulations are similar to real sub-coating cracks reported in the literature.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/rqafd-x8041On the convergence of 3D free discontinuity models in variational fracture
https://resolver.caltech.edu/CaltechAUTHORS:20101011-101117330
Authors: {'items': [{'id': 'Fraternali-F', 'name': {'family': 'Fraternali', 'given': 'Fernando'}, 'orcid': '0000-0002-7549-6405'}, {'id': 'Negri-M', 'name': {'family': 'Negri', 'given': 'Matteo'}}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'Michael'}, 'orcid': '0000-0001-5877-4824'}]}
Year: 2010
DOI: 10.1007/s10704-010-9462-0
Free discontinuity problems arising in the variational theory for fracture mechanics are considered. A Γ -convergence proof for an r-adaptive 3D finite element discretization is given in the case of a brittle material. The optimal displacement field, crack pattern and mesh geometry are obtained through a variational procedure that encompasses both mechanical and configurational forces. Possible extensions to cohesive fracture and quasi-static evolutions are discussed.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/23kpe-p2e35Long-term dynamic stability of discrete dislocations in graphene at finite temperature
https://resolver.caltech.edu/CaltechAUTHORS:20101012-093620068
Authors: {'items': [{'id': 'Ariza-M-P', 'name': {'family': 'Ariza', 'given': 'M. P.'}, 'orcid': '0000-0003-0266-0216'}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'M.'}, 'orcid': '0000-0001-5877-4824'}, {'id': 'Serrano-R', 'name': {'family': 'Serrano', 'given': 'R.'}}]}
Year: 2010
DOI: 10.1007/s10704-010-9527-0
We present an assessment of the finite-temperature dynamical stability of discrete dislocations in graphene. In order to ascertain stability, we insert discrete dislocation quadrupole configurations into molecular dynamics calculations as initial conditions. In calculations we use Sandia National Laboratories Large-scale Atomic/Molecular Massively Parallel Simulator (LAMMPS) and the Adaptive Intermolecular Reactive Empirical Bond-Order (AIREBO) potential. The analysis shows that the core structures predicted by discrete dislocation theory are dynamically stable up to temperatures of 2,500 K, though they tend to relax somewhat in the course of molecular dynamics. In addition, we find that discrete dislocation theory accurately predicts energies, though it exhibits a slight overly-stiff bias.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/dvrt5-d3r87Discrete mechanics and optimal control for constrained systems
https://resolver.caltech.edu/CaltechAUTHORS:20110310-100105962
Authors: {'items': [{'id': 'Leyendecker-S', 'name': {'family': 'Leyendecker', 'given': 'S.'}}, {'id': 'Ober-Bloebaum-S', 'name': {'family': 'Ober-Bloebaum', 'given': 'S.'}}, {'id': 'Marsden-J-E', 'name': {'family': 'Marsden', 'given': 'J. E.'}}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'M.'}, 'orcid': '0000-0001-5877-4824'}]}
Year: 2010
DOI: 10.1002/oca.912
The equations of motion of a controlled mechanical system subject to holonomic constraints may be formulated in terms
of the states and controls by applying a constrained version of the Lagrange-d'Alembert principle. This paper derives a structure-preserving scheme for the optimal control of such systems using, as one of the key ingredients, a discrete analogue of that principle. This property is inherited when the system is reduced to its minimal dimension by the discrete null space method. Together with initial and final conditions on the configuration and conjugate momentum, the reduced discrete
equations serve as nonlinear equality constraints for the minimization of a given objective functional. The algorithm yields a sequence of discrete configurations together with a sequence of actuating forces, optimally guiding the system from the initial to the desired final state. In particular, for the optimal control of multibody systems, a force formulation consistent with the joint constraints is introduced. This enables one to prove the consistency of the evolution of momentum maps. Using a two-link pendulum, the method is compared with existing methods. Further, it is applied to a satellite reorientation maneuver and a biomotion problem.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/037by-rg788An Eulerian hybrid WENO centered-difference solver for elastic-plastic solids
https://resolver.caltech.edu/CaltechAUTHORS:20110302-102610242
Authors: {'items': [{'id': 'Hill-D-J', 'name': {'family': 'Hill', 'given': 'D. J.'}}, {'id': 'Pullin-D-I', 'name': {'family': 'Pullin', 'given': 'D.'}}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'M.'}, 'orcid': '0000-0001-5877-4824'}, {'id': 'Meiron-D-I', 'name': {'family': 'Meiron', 'given': 'D.'}, 'orcid': '0000-0003-0397-3775'}]}
Year: 2010
DOI: 10.1016/j.jcp.2010.08.020
We present a finite-difference based solver for hyper-elastic and viscoplastic systems using a hybrid of the weighted essentially non-oscillatory (WENO) schemes combined with explicit centered difference to solve the equations of motion expressed in an Eulerian formulation. By construction our approach minimizes both numerical dissipation errors and the creation of curl-constraint violating errors away from discontinuities while avoiding
the calculation of hyperbolic characteristics often needed in general finite-volume schemes. As a result of the latter feature, the formulation allows for a wide range of
constitutive relations and only an upper-bound on the speed of sound at each time is required to ensure a stable timestep is chosen. Several one- and two-dimensional examples are presented using a range of constitutive laws with and without additional plastic modeling. In addition we extend the reflection technique combined with ghost-cells to enforce fixed boundaries with a zero tangential stress condition (i.e. free-slip).https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/4tha9-8x095Force-stepping integrators in Lagrangian mechanics
https://resolver.caltech.edu/CaltechAUTHORS:20110119-101735770
Authors: {'items': [{'id': 'Gonzalez-M', 'name': {'family': 'Gonzalez', 'given': 'M.'}}, {'id': 'Schmidt-B', 'name': {'family': 'Schmidt', 'given': 'B.'}}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'M.'}, 'orcid': '0000-0001-5877-4824'}]}
Year: 2010
DOI: 10.1002/nme.2942
We formulate an integration scheme for Lagrangian mechanics, referred to as the force-stepping scheme,
which is symplectic, energy conserving, time-reversible, and convergent with automatic selection of the
time-step size. The scheme also conserves approximately all the momentum maps associated with the
symmetries of the system. The exact conservation of momentum maps may additionally be achieved by
recourse to the Lagrangian reduction. The force-stepping scheme is obtained by replacing the potential
energy by a piecewise affine approximation over a simplicial grid or regular triangulation. By taking
triangulations of diminishing size, an approximating sequence of energies is generated. The trajectories of
the resulting approximate Lagrangians can be characterized explicitly and consist of piecewise parabolic
motion, or free fall. Selected numerical tests demonstrate the excellent long-term behavior of force-stepping,
its automatic time-step selection property, and the ease with which it deals with constraints,
including contact problems.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/cw0ks-e2829Modelo de fuerzas interatómicas para el grafeno a partir del potencial AIREBO
https://resolver.caltech.edu/CaltechAUTHORS:20120113-102143268
Authors: {'items': [{'id': 'Ariza-M-P', 'name': {'family': 'Ariza', 'given': 'M. P.'}, 'orcid': '0000-0003-0266-0216'}, {'id': 'Ventura-C', 'name': {'family': 'Ventura', 'given': 'C.'}}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'M.'}, 'orcid': '0000-0001-5877-4824'}]}
Year: 2011
Dado que las propiedades eléctricas y térmicas del grafeno están influenciadas por la presencia de defectos topológicos en el material y que éstos condicionan así las futuras aplicaciones del grafeno como material base de componentes nanoelectrónicos, es necesario disponer de un modelo de comportamiento del grafeno que permita incluir dichos defectos. En este trabajo se ha obtenido un modelo de fuerzas interatómicas a partir del potencial AIREBO (Adaptive Intermolecular Reactive Empirical Bond-Order), desarrollado por Stuart et al. [1], que incluye interacciones atómicas hasta vecinos de orden cuarto. Se presentan, tanto expresiones explícitas de las derivadas del potencial, como los valores de las constantes de fuerza. Hemos verificado que el modelo de fuerzas cumple con las simetrías del cristal y las curvas de dispersión de fonones del correspondiente modelo dinámico presentan un buen acuerdo con las obtenidas por otros autores. Además, hemos verificado que las interacciones con vecinos terceros y cuartos no modifican, ni la estructura del campo de desplazamientos alrededor de los núcleos de dislcocación, ni sus correspondientes energías de formación que se predicen a partir de la teoría discreta de dislocaciones de Ariza y Ortiz [2]. Summary In view of the influence that topological defects have on the thermal and electrical properties of graphene, and given the pivotal role that such properties play in potential applications of graphene as a building block for nano-electronic components, models of graphene behavior that allow for the consideration of such defects are of the essence. In the present work, we have obtained an atomic force-constant model from the AIREBO potential (Adaptive Intermolecular Reactive Empirical Bond-Order), of Stuart et al. [1], that accounts for interatomic interactions up to fourth neighbors. We present explicit expressions of the potential derivatives as well as the force-constant values. We have verified that the force-constant model is invariant under the crystal symmetries and that the phonondispersion curves of the corresponding dynamic model are in good agreement with those obtained by other authors. In addition, we have verified that the thirdand fourth-neighbor interactions affect neither the displacement field in the vicinity of dislocation cores nor the corresponding formation energies predicted by the theory of discrete dislocations of Ariza and Ortiz [2].https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/s3nhn-18e26A discrete mechanics approach to the Cosserat rod theory-Part 1: static equilibria
https://resolver.caltech.edu/CaltechAUTHORS:20110222-151826704
Authors: {'items': [{'id': 'Jung-P', 'name': {'family': 'Jung', 'given': 'Pascal'}}, {'id': 'Leyendecker-S', 'name': {'family': 'Leyendecker', 'given': 'Sigrid'}}, {'id': 'Linn-J', 'name': {'family': 'Linn', 'given': 'Joachim'}}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'Michael'}, 'orcid': '0000-0001-5877-4824'}]}
Year: 2011
DOI: 10.1002/nme.2950
A theory of discrete Cosserat rods is formulated in the language of discrete Lagrangian mechanics. By exploiting Kirchhoff's kinetic analogy, the potential energy density of a rod is a function on the tangent bundle of the configuration manifold and thus formally corresponds to the Lagrangian function of a dynamical system. The equilibrium equations are derived from a variational principle using a
formulation that involves null-space matrices. In this formulation, no Lagrange multipliers are necessary to enforce orthonormality of the directors. Noether's theorem relates first integrals of the equilibrium equations to Lie group actions on the configuration bundle, so-called
symmetries. The symmetries relevant for rod mechanics are
frame-indifference, isotropy, and uniformity. We show that a completely analogous and self-contained theory of discrete rods can be formulated in which the arc-length is a discrete variable ab initio. In this formulation, the potential energy density is defined directly on pairs
of points along the arc-length of the rod, in analogy to Veselov's discrete reformulation of Lagrangian mechanics. A discrete version of Noether's theorem then identifies exact first integrals of the discrete equilibrium equations. These exact conservation properties confer the discrete solutions accuracy and robustness, as demonstrated by selected examples of application.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/k8tg5-4dr43A duality-based method for generating geometric representations of polycrystals
https://resolver.caltech.edu/CaltechAUTHORS:20110510-105826693
Authors: {'items': [{'id': 'Rimoli-J-J', 'name': {'family': 'Rimoli', 'given': 'J. J.'}, 'orcid': '0000-0002-8707-2968'}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'M.'}, 'orcid': '0000-0001-5877-4824'}]}
Year: 2011
DOI: 10.1002/nme.3090
We present a method, which we have termed Relaxed Dual Complex (RDC), for generating geometric representations and computational models of polycrystals of arbitrary shape. The RDC method combines a first topological step, which defines an initial unrelaxed polycrystal geometry as the barycentric dual of an input triangulation of the solid, and a second relaxation step, in which the grain boundaries are relaxed by means of a gradient flow driven by grain boundary energy. The RDC method applies to arbitrary solids defined by means of a triangulation and, in this manner, it couples seamlessly to standard solid modelling engines. An additional appealing feature of the RDC method is that it generates a conforming tetrahedral mesh of the polycrystal that can be used as a basis for subsequent simulations. The RDC method also affords some control over the statistical properties of the polycrystal, including grain size, which provides a convenient device for matching experimental statistical data. The range, versatility, and performance of the RDC method have been demonstrated by means of selected examples.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/nmrj1-dv583A mesh-free convex approximation scheme for Kohn–Sham density functional theory
https://resolver.caltech.edu/CaltechAUTHORS:20110623-074123014
Authors: {'items': [{'id': 'Suryanarayana-P', 'name': {'family': 'Suryanarayana', 'given': 'Phanish'}, 'orcid': '0000-0001-5172-0049'}, {'id': 'Bhattacharya-K', 'name': {'family': 'Bhattacharya', 'given': 'Kaushik'}, 'orcid': '0000-0003-2908-5469'}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'Michael'}, 'orcid': '0000-0001-5877-4824'}]}
Year: 2011
DOI: 10.1016/j.jcp.2011.03.018
Density functional theory developed by Hohenberg, Kohn and Sham is a widely accepted, reliable ab initio method. We present a non-periodic, real space, mesh-free convex approximation scheme for Kohn–Sham density functional theory. We rewrite the original variational problem as a saddle point problem and discretize it using basis functions which form the Pareto optimum between competing objectives of maximizing entropy and minimizing the total width of the approximation scheme. We show the utility of the approximation scheme in performing both all-electron and pseudopotential calculations, the results of which are in good agreement with literature.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/4s1kv-0ma31Rigorous uncertainty quantification without integral testing
https://resolver.caltech.edu/CaltechAUTHORS:20110822-140452319
Authors: {'items': [{'id': 'Topcu-U', 'name': {'family': 'Topcu', 'given': 'U.'}}, {'id': 'Lucas-L-J', 'name': {'family': 'Lucas', 'given': 'L. J.'}}, {'id': 'Owhadi-H', 'name': {'family': 'Owhadi', 'given': 'H.'}, 'orcid': '0000-0002-5677-1600'}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'M.'}, 'orcid': '0000-0001-5877-4824'}]}
Year: 2011
DOI: 10.1016/j.ress.2010.07.013
We describe a rigorous approach for certifying the safe operation of complex systems that bypasses the need for integral testing. We specifically consider systems that have a modular structure. These systems are composed of subsystems, or components, that interact through unidirectional interfaces. We show that, for systems that have the structure of an acyclic graph, it is possible to obtain rigorous upper bounds on the probability of failure of the entire system from an uncertainty analysis of the individual components and their interfaces and without the need for integral testing. Certification is then achieved if the probability of failure upper bound is below an acceptable failure tolerance. We demonstrate the approach by means of an example concerned with the performance of a fractal electric circuit.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/y3r8e-40v42Nanovoid nucleation by vacancy aggregation and vacancy-cluster coarsening in high-purity metallic single crystals
https://resolver.caltech.edu/CaltechAUTHORS:20111011-115920039
Authors: {'items': [{'id': 'Reina-C', 'name': {'family': 'Reina', 'given': 'C.'}}, {'id': 'Marian-J', 'name': {'family': 'Marian', 'given': 'J.'}}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'M.'}, 'orcid': '0000-0001-5877-4824'}]}
Year: 2011
DOI: 10.1103/PhysRevB.84.104117
A numerical model to estimate critical times required for nanovoid nucleation in high-purity aluminum single crystals subjected to shock loading is presented. We regard a nanovoid to be nucleated when it attains a size sufficient for subsequent growth by dislocation-mediated plasticity. Nucleation is assumed to proceed by means of diffusion-mediated vacancy aggregation and subsequent vacancy cluster coarsening. Nucleation times are computed by a combination of lattice kinetic Monte Carlo simulations and simple estimates of nanovoid cavitation pressures and vacancy concentrations. The domain of validity of the model is established by considering rate-limiting physical processes and theoretical strength limits. The computed nucleation times are compared to experiments suggesting that vacancy aggregation and cluster coarsening are feasible mechanisms of nanovoid nucleation in a specific subdomain of the pressure-strain rate-temperature space.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/cvz8g-btc39Optimal Uncertainty Quantification
https://resolver.caltech.edu/CaltechAUTHORS:20111012-113158874
Authors: {'items': [{'id': 'Owhadi-H', 'name': {'family': 'Owhadi', 'given': 'H.'}, 'orcid': '0000-0002-5677-1600'}, {'id': 'Scovel-C', 'name': {'family': 'Scovel', 'given': 'C.'}, 'orcid': '0000-0001-7757-3411'}, {'id': 'Sullivan-T-J', 'name': {'family': 'Sullivan', 'given': 'T. J.'}}, {'id': 'McKerns-M', 'name': {'family': 'McKerns', 'given': 'M.'}}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'M.'}, 'orcid': '0000-0001-5877-4824'}]}
Year: 2011
DOI: 10.7907/TTW6-QD19
We propose a rigorous framework for Uncertainty Quantification (UQ) in which
the UQ objectives and the assumptions/information set are brought to the forefront.
This framework, which we call Optimal Uncertainty Quantification (OUQ), is based
on the observation that, given a set of assumptions and information about the problem,
there exist optimal bounds on uncertainties: these are obtained as extreme
values of well-defined optimization problems corresponding to extremizing probabilities
of failure, or of deviations, subject to the constraints imposed by the scenarios
compatible with the assumptions and information. In particular, this framework
does not implicitly impose inappropriate assumptions, nor does it repudiate relevant
information.
Although OUQ optimization problems are extremely large, we show that under
general conditions, they have finite-dimensional reductions. As an application,
we develop Optimal Concentration Inequalities (OCI) of Hoeffding and McDiarmid
type. Surprisingly, contrary to the classical sensitivity analysis paradigm, these results
show that uncertainties in input parameters do not necessarily propagate to
output uncertainties.
In addition, a general algorithmic framework is developed for OUQ and is tested
on the Caltech surrogate model for hypervelocity impact, suggesting the feasibility
of the framework for important complex systems.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/5j8b4-b5n05Replica time integrators
https://resolver.caltech.edu/CaltechAUTHORS:20111114-145609664
Authors: {'items': [{'id': 'Venturini-Gabriela-N', 'name': {'family': 'Venturini', 'given': 'G.'}}, {'id': 'Yang-J', 'name': {'family': 'Yang', 'given': 'J. Z.'}}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'M.'}, 'orcid': '0000-0001-5877-4824'}, {'id': 'Marsden-J-E', 'name': {'family': 'Marsden', 'given': 'J. E.'}}]}
Year: 2011
DOI: 10.1002/nme.3202
This paper is concerned with the classical problem of wave propagation in discrete models of nonuniform spatial resolution. We develop a new class of Replica Time Integrators (RTIs) that permit the two-way transmission of thermal phonons across mesh interfaces. This two-way transmissibility is accomplished by representing the state of the coarse regions by means of replica ensembles, consisting of collections of identical copies of the coarse regions. In dimension d, RTIs afford an O(n^d) speed-up factor in sequential mode, and O(n^(d + 1)) in parallel, over regions that are coarsened n-fold. In this work, we restrict ourselves to the solution of the 3d continuous wave equation, for both linear and non-linear materials. By a combination of phase-error analysis and numerical testing, we show that RTIs are convergent and result in exact two-way transmissibility at the Courant–Friedrichs–Lewy limit for any angle of incidence. In this limit, RTIs allow step waves and high-frequency harmonics to cross mesh interfaces in both directions without internal reflections or appreciable loss or addition of energy. The possible connections of RTIs with discrete-to-continuum approaches and, in particular, with the transition between molecular dynamics and continuum thermodynamics are also pointed to by way of future outlook.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/7t69n-emm44From atomistics to the continuum: a mesh-free quasicontinuum formulation based on local max-ent approximation schemes
https://resolver.caltech.edu/CaltechAUTHORS:20180223-110852480
Authors: {'items': [{'id': 'Kochmann-D-M', 'name': {'family': 'Kochmann', 'given': 'Dennis M.'}, 'orcid': '0000-0002-9112-6615'}, {'id': 'Amelang-J-S', 'name': {'family': 'Amelang', 'given': 'Jeffrey S.'}}, {'id': 'Español-M-I', 'name': {'family': 'Español', 'given': 'Malena I.'}}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'Michael'}, 'orcid': '0000-0001-5877-4824'}]}
Year: 2011
DOI: 10.1002/pamm.201110188
A novel quasicontinuum formulation based on mesh-free local maximum-entropy approximation schemes is presented, whose accuracy (compared to full atomistic simulations) is tunable and, in particular, can be designed superior to conventional affine approximation schemes.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/9amaf-hvv63Thermal Expansion Behavior of AL and TA Using a Finite-Temperature Extension of the Quasicontinuum Method
https://resolver.caltech.edu/CaltechAUTHORS:20120517-081016822
Authors: {'items': [{'id': 'Venturini-Gabriela-N', 'name': {'family': 'Venturini', 'given': 'G.'}}, {'id': 'Marian-J', 'name': {'family': 'Marian', 'given': 'J.'}}, {'id': 'Knap-J', 'name': {'family': 'Knap', 'given': 'J.'}}, {'id': 'Campbell-G', 'name': {'family': 'Campbell', 'given': 'G.'}}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'M.'}, 'orcid': '0000-0001-5877-4824'}]}
Year: 2012
Numerical methods that bridge the atomistic andcontinuum scales concurrently have been applied successfully to anumber of materials science problems involving both nonlinear andlong-range deformation fields. However, extension of thesemethods to finite temperature, nonequilibrium dynamics isdifficult due to the intrinsic incoherency between moleculardynamics and continuum thermodynamics, which possess differentcrystal vibrational spectra and therefore result in unphysicalwave reflections across domain boundaries. Here we review ourrecent finite temperature extension of the three-dimensional,non-local quasicontinuum (QC) method based on Langevin dynamicsand carry out an analysis of the systematic errors associated withthe entropic depletion that results from the QC reduction. Weapply the method to Al and Ta structured meshes ranging fromatomistic resolution to minimum-node representations using thethermal expansion coefficient as the standard metric. We findthat, while Al errors scale linearly with the number of meshnodes, Ta displays a very erratic behavior that degrades rapidlywith mesh coarsening.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/ke9jf-fwt18Mesoscopic approach to granular crystal dynamics
https://resolver.caltech.edu/CaltechAUTHORS:20111128-085742465
Authors: {'items': [{'id': 'Gonzalez-M', 'name': {'family': 'Gonzalez', 'given': 'Marcial'}}, {'id': 'Yang-Jinkyu', 'name': {'family': 'Yang', 'given': 'Jinkyu'}}, {'id': 'Daraio-C', 'name': {'family': 'Daraio', 'given': 'Chiara'}, 'orcid': '0000-0001-5296-4440'}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'Michael'}, 'orcid': '0000-0001-5877-4824'}]}
Year: 2012
DOI: 10.1103/PhysRevE.85.016604
We present a mesoscopic approach to granular crystal dynamics, which comprises a three-dimensional finite-element model and a one-dimensional regularized contact model. The approach investigates the role of vibrational-energy trapping effects in the dynamic behavior of one-dimensional chains of particles in contact (i.e., granular crystals), under small to moderate impact velocities. The only inputs of the models are the geometry and the elastic material properties of the individual particles that form the system. We present detailed verification results and validate the model comparing its predictions with experimental data. This approach provides a physically sound, first-principle description of dissipative losses in granular systems.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/j0rz4-a2y47HotQC simulation of nanovoid growth under tension
in copper
https://resolver.caltech.edu/CaltechAUTHORS:20120430-074243222
Authors: {'items': [{'id': 'Ariza-M-P', 'name': {'family': 'Ariza', 'given': 'M. P.'}, 'orcid': '0000-0003-0266-0216'}, {'id': 'Romero-I', 'name': {'family': 'Romero', 'given': 'I.'}, 'orcid': '0000-0003-0364-6969'}, {'id': 'Ponga-M', 'name': {'family': 'Ponga', 'given': 'M.'}, 'orcid': '0000-0001-5058-1454'}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'M.'}, 'orcid': '0000-0001-5877-4824'}]}
Year: 2012
DOI: 10.1007/s10704-011-9660-4
We apply the HotQC method of Kulkarni
et al. (J Mech Phys Solids 56:1417–1449, 2008)
to the study of quasistatic void growth in copper
single crystals at finite temperature under triaxial
expansion. The void is strained to 30% deformation
at initial temperatures and nominal strain rates ranging
from 150 to 600Kand from 2.5×10^5 to 2.5×10^(11) s^(−1),
respectively. The interatomic potential used in the calculations
is Johnson's Embedded-Atom Method potential
Johnson (Phys Rev B 37:3924–3931, 1988). The
computed pressure versus volumetric strain is in close
agreement with that obtained using molecular dynamics,
which suggests that inertia effects are not dominant
for the void size and conditions considered. Upon the
attainment of a critical or cavitation strain of the order
of 20%, dislocations are abruptly and profusely emitted
from the void and the rate of growth of the void increases precipitously. Prior to cavitation, the crystal
cools down due to the thermoelastic effect. Following
cavitation dislocation emission causes rapid local heating
in the vicinity of the void, which in turn sets up a
temperature gradient and results in the conduction of
heat away from the void. The cavitation pressure is
found to be relatively temperature-insensitive at low
temperatures and decreases markedly beyond a transition
temperature of the order of 250 K.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/txvnt-5w819Double kink mechanisms for discrete dislocations in BCC
crystals
https://resolver.caltech.edu/CaltechAUTHORS:20120430-084558611
Authors: {'items': [{'id': 'Ariza-M-P', 'name': {'family': 'Ariza', 'given': 'M. P.'}, 'orcid': '0000-0003-0266-0216'}, {'id': 'Tellechea-E', 'name': {'family': 'Tellechea', 'given': 'E.'}}, {'id': 'Menguiano-A-S', 'name': {'family': 'Menguiano', 'given': 'A. S.'}}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'M.'}, 'orcid': '0000-0001-5877-4824'}]}
Year: 2012
DOI: 10.1007/s10704-012-9681-7
We present an application of the discrete dislocation theory to the characterization of the energetics of kinks in Mo, Ta and W body-centered cubic (BCC) crystals. The discrete dislocation calculations supply detailed predictions of formation and interaction energies for various double-kink formation and spreading mechanisms as a function of the geometry of the double kinks, including: the dependence of the formation energy of a double kink on its width; the energy of formation of a double kink on a screw dislocation containing a pre-existing double kink; and energy of formation of a double kink on a screw dislocation containing a pre-existing single kink. The computed interaction energies are expected to facilitates the nucleation of double kinks in close proximity to each other and to pre-existing kinks, thus promoting clustering of double kinks on screw segments and of 'daughter' double kinks ahead of 'mother' kinks. The predictions of the discrete dislocation theory are found to be in good agreement with the full atomistic calculations based on empirical interatomic potentials available in the literature.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/k07h4-bxv07Verification and validation of the Optimal Transportation Meshfree (OTM) simulation of terminal ballistics
https://resolver.caltech.edu/CaltechAUTHORS:20120403-094946212
Authors: {'items': [{'id': 'Li-B', 'name': {'family': 'Li', 'given': 'B.'}}, {'id': 'Kidane-A', 'name': {'family': 'Kidane', 'given': 'A.'}}, {'id': 'Ravichandran-G', 'name': {'family': 'Ravichandran', 'given': 'G.'}, 'orcid': '0000-0002-2912-0001'}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'M.'}, 'orcid': '0000-0001-5877-4824'}]}
Year: 2012
DOI: 10.1016/j.ijimpeng.2011.11.003
We evaluate the performance of the OptimalTransportationMeshfree (OTM) method of Li et al. [21], suitably extended to account for seizing contact and fracture, in applications involving terminalballistics. The evaluation takes the form of a conventional Verification and Validation (V&V) analysis. In support of the validation analysis, we have conducted tests concerned with the normal impact of Aluminum alloy 6061-T6 thin plates by S2 tool steel spherical projectile over a range of plate thicknesses of [0.8 mm, 1.6 mm] and a range of impact velocities of [100, 400]m/s. The tests were conducted at Caltech's GALCIT gas-gun Plate-Impact Facility. We find excellent agreement between measured and computed perforation areas and a ballistic limits over the thickness and velocity ranges considered. Our verification analysis consists of model-on-model comparisons and an assessment of the convergence of the OTM method. Specifically, we find excellent agreement between the incident vs. residual velocities predicted by the OTM method and by the power-law relation of Recht and Ipson [36]. We also find robust linear convergence of the OTM method as measured in terms of residual velocity error vs. number of nodes.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/m5t76-chh94Rigorous model-based uncertainty quantification with application to terminal ballistics—Part II. Systems with uncontrollable inputs and large scatter
https://resolver.caltech.edu/CaltechAUTHORS:20120430-133945935
Authors: {'items': [{'id': 'Adams-M', 'name': {'family': 'Adams', 'given': 'M.'}}, {'id': 'Lashgari-A', 'name': {'family': 'Lashgari', 'given': 'A.'}}, {'id': 'Li-B', 'name': {'family': 'Li', 'given': 'B.'}}, {'id': 'McKerns-M', 'name': {'family': 'McKerns', 'given': 'M.'}}, {'id': 'Mihaly-J', 'name': {'family': 'Mihaly', 'given': 'J.'}}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'M.'}, 'orcid': '0000-0001-5877-4824'}, {'id': 'Owhadi-H', 'name': {'family': 'Owhadi', 'given': 'H.'}, 'orcid': '0000-0002-5677-1600'}, {'id': 'Rosakis-A-J', 'name': {'family': 'Rosakis', 'given': 'A. J.'}, 'orcid': '0000-0003-0559-0794'}, {'id': 'Stalzer-M', 'name': {'family': 'Stalzer', 'given': 'M.'}}, {'id': 'Sullivan-T-J', 'name': {'family': 'Sullivan', 'given': 'T. J.'}}]}
Year: 2012
DOI: 10.1016/j.jmps.2011.12.002
This Part II of this series is concerned with establishing the feasibility of an extended data-on-demand (XDoD) uncertainty quantification (UQ) protocol based on concentration-of-measure inequalities and martingale theory. Specific aims are to establish the feasibility of the protocol and its basic properties, including the tightness of the predictions afforded by the protocol. The assessment is based on an application to terminal ballistics and a specific system configuration consisting of 6061-T6 aluminum plates struck by spherical 440c stainless steel projectiles at ballistic impact speeds in the range of 2.4–2.8 km/s. The system's inputs are the plate thickness, plate obliquity and impact velocity. The perforation area is chosen as the sole performance measure of the system. The objective of the UQ analysis is to certify the lethality of the projectile, i.e., that the projectile perforates the plate with high probability over a prespecified range of impact velocities, plate thicknesses and plate obliquities. All tests were conducted at Caltech's Small Particle Hypervelocity Range (SPHIR), which houses a two-stage gas gun. A feature of this facility is that the impact velocity, while amenable to precise measurement, cannot be controlled precisely but varies randomly according to a known probability density function. In addition, due to a competition between petalling and plugging mechanisms for the material system under consideration, the measured perforation area exhibits considerable scatter. The analysis establishes the feasibility of the XDoD UQ protocol as a rigorous yet practical approach for model-based certification of complex systems characterized by uncontrollable inputs and noisy experimental data.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/at0kp-sq105Rigorous model-based uncertainty quantification with application to terminal ballistics, part I: Systems with controllable inputs and small scatter
https://resolver.caltech.edu/CaltechAUTHORS:20120502-091106236
Authors: {'items': [{'id': 'Kidane-A', 'name': {'family': 'Kidane', 'given': 'A.'}}, {'id': 'Lashgari-A', 'name': {'family': 'Lashgari', 'given': 'A.'}}, {'id': 'Li-B', 'name': {'family': 'Li', 'given': 'B.'}}, {'id': 'McKerns-M', 'name': {'family': 'McKerns', 'given': 'M.'}}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'M.'}, 'orcid': '0000-0001-5877-4824'}, {'id': 'Owhadi-H', 'name': {'family': 'Owhadi', 'given': 'H.'}, 'orcid': '0000-0002-5677-1600'}, {'id': 'Ravichandran-G', 'name': {'family': 'Ravichandran', 'given': 'G.'}, 'orcid': '0000-0002-2912-0001'}, {'id': 'Stalzer-M', 'name': {'family': 'Stalzer', 'given': 'M.'}}, {'id': 'Sullivan-T-J', 'name': {'family': 'Sullivan', 'given': 'T. J.'}}]}
Year: 2012
DOI: 10.1016/j.jmps.2011.12.001
This work is concerned with establishing the feasibility of a data-on-demand (DoD) uncertainty quantification (UQ) protocol based on concentration-of-measure inequalities. Specific aims are to establish the feasibility of the protocol and its basic properties, including the tightness of the predictions afforded by the protocol. The assessment is based on an application to terminal ballistics and a specific system configuration consisting of 6061-T6 aluminum plates struck by spherical S-2 tool steel projectiles at ballistic impact speeds. The system's inputs are the plate thickness and impact velocity and the perforation area is chosen as the sole performance measure of the system. The objective of the UQ analysis is to certify the lethality of the projectile, i.e., that the projectile perforates the plate with high probability over a prespecified range of impact velocities and plate thicknesses. The net outcome of the UQ analysis is an M/U ratio, or confidence factor, of 2.93, indicative of a small probability of no perforation of the plate over its entire operating range. The high-confidence (>99.9%) in the successful operation of the system afforded the analysis and the small number of tests (40) required for the determination of the modeling-error diameter, establishes the feasibility of the DoD UQ protocol as a rigorous yet practical approach for model-based certification of complex systems.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/1cv45-zxs55Convergent meshfree approximation schemes of arbitrary order and smoothness
https://resolver.caltech.edu/CaltechAUTHORS:20120525-095216954
Authors: {'items': [{'id': 'Bompadre-A', 'name': {'family': 'Bompadre', 'given': 'A.'}}, {'id': 'Perotti-L-E', 'name': {'family': 'Perotti', 'given': 'L. E.'}}, {'id': 'Cyron-C-J', 'name': {'family': 'Cyron', 'given': 'C. J.'}}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'M.'}, 'orcid': '0000-0001-5877-4824'}]}
Year: 2012
DOI: 10.1016/j.cma.2012.01.020
Local Maximum-Entropy (LME) approximation schemes are meshfree approximation schemes that satisfy consistency conditions of order one, i.e., they approximate affine functions exactly. In addition, LME approximation schemes converge in the Sobolev space W^(1,p), i.e., they are C^0-continuous in the conventional terminology of finite-element interpolation. Here we present a generalization of the Local Max-Ent approximation schemes that are consistent to arbitrary order, i.e., interpolate polynomials of arbitrary degree exactly, and which converge in W^(k,p), i.e., they are C^k-continuous to arbitrary order k. We refer to these approximation schemes as High Order Local Maximum-Entropy Approximation Schemes (HOLMES). We prove uniform error bounds for the HOLMES approximates and their derivatives up to order k. Moreover, we show that the HOLMES of order k is dense in the Sobolev space W^(k,p), for any 1⩽p<∞. The good performance of HOLMES relative to other meshfree schemes in selected test cases is also critically appraised.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/zyn6v-dk256Convergence Analysis of Meshfree Approximation Schemes
https://resolver.caltech.edu/CaltechAUTHORS:20121203-131119602
Authors: {'items': [{'id': 'Bompadre-A', 'name': {'family': 'Bompadre', 'given': 'A.'}}, {'id': 'Schmidt-B', 'name': {'family': 'Schmidt', 'given': 'B.'}}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'M.'}, 'orcid': '0000-0001-5877-4824'}]}
Year: 2012
DOI: 10.1137/110828745
This work is concerned with the formulation of a general framework for the analysis of meshfree approximation schemes and with the convergence analysis of the local maximum-entropy (LME) scheme as a particular example. We provide conditions for the convergence in Sobolev spaces
of schemes that are n-consistent in the sense of exactly reproducing polynomials of degree less than or equal to n ≥ 1 and whose basis functions are of rapid decay. The convergence of the LME in W^(1,p)_(loc) (Ω) follows as a direct application of the general theory. The analysis shows that the convergence order is linear in h, a measure of the density of the point set. The analysis also shows how to parameterize the LME scheme for optimal convergence. Because of the convex approximation property of LME, its behavior near the boundary is singular and requires additional analysis. For the particular case of polyhedral domains we show that, away from a small singular part of the boundary, any Sobolev function can be approximated by means of the LME scheme. With the aid of a capacity argument, we further obtain approximation results with truncated LME basis functions in H^1(Ω) and for spatial
dimension d > 2.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/8nxmm-k9d46Stacking faults and partial dislocations in graphene
https://resolver.caltech.edu/CaltechAUTHORS:20120625-113231865
Authors: {'items': [{'id': 'Ariza-M-P', 'name': {'family': 'Ariza', 'given': 'M. P.'}, 'orcid': '0000-0003-0266-0216'}, {'id': 'Serrano-R', 'name': {'family': 'Serrano', 'given': 'R.'}}, {'id': 'Mendez-Granado-J-P', 'name': {'family': 'Mendez', 'given': 'J. P.'}, 'orcid': '0000-0002-9493-0879'}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'M.'}, 'orcid': '0000-0001-5877-4824'}]}
Year: 2012
DOI: 10.1080/14786435.2012.657254
We investigate two mechanisms of crystallographic slip in graphene, corresponding to glide and shuffle generalized stacking faults (GSF), and compute their γ-curves using Sandia National Laboratories Large-scale Atomic/Molecular Massively Parallel Simulator (LAMMPS). We find evidence of metastable partial dislocations for the glide GSF only.
The computed values of the stable and unstable stacking-fault energies are suggestive of a high stability of full dislocations against dissociation and of dislocation dipoles against annihilation.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/rntkk-qgr40Surface effects and the size-dependent hardening and strengthening of nickel micropillars
https://resolver.caltech.edu/CaltechAUTHORS:20120720-152701866
Authors: {'items': [{'id': 'Hurtado-D-E', 'name': {'family': 'Hurtado', 'given': 'Daniel E.'}}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'Michael'}, 'orcid': '0000-0001-5877-4824'}]}
Year: 2012
DOI: 10.1016/j.jmps.2012.04.009
We evaluate the extent to which two mechanisms contribute to the observed size effect of the ultimate yield strength of micropillars of diameters in the range of 1-30 µm: dislocation pile-ups, modeled by means of a physically based non-local single-crystal plasticity model; and the short-range interaction of dislocations with the free surface of the micropillars, e.g., through the formation of surface steps. To this end, we formulate a crystal-plasticity model that accounts for the self-energy of geometrically necessary dislocations and the formation energy of dislocation steps at the boundary of the solid. These two additional sources of energy have the effect of rendering the internal energy of the solid non-local, thereby introducing the possibility of size effects. By way of validation of the model, we simulate the uniaxial compression tests on [269] nickel micropillars of Dimiduk et al. (2005). The calculated dependence of the ultimate strength of the micropillars exhibits strong power-law behavior, and is in good agreement with observation. Our analysis suggests that non-local hardening due to the self-energy of geometrically necessary dislocations does not suffice to account for the observed size effect of the ultimate yield strength of micropillars, and that surface effects, such as resulting from the formation energy of dislocation steps, contribute significantly to that size effect.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/gn8d2-6a417A linear programming-based algorithm for the signed separation of (non-smooth) convex bodies
https://resolver.caltech.edu/CaltechAUTHORS:20121107-081815613
Authors: {'items': [{'id': 'Johnson-G', 'name': {'family': 'Johnson', 'given': 'G.'}}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'M.'}, 'orcid': '0000-0001-5877-4824'}, {'id': 'Leyendecker-S', 'name': {'family': 'Leyendecker', 'given': 'S.'}}]}
Year: 2012
DOI: 10.1016/j.cma.2012.04.006
A subdifferentiable global contact detection algorithm, the Supporting Separating Hyperplane (SSH) algorithm, based on the signed distance between supporting hyperplanes of two convex sets is developed. It is shown that for polyhedral sets, the SSH algorithm may be evaluated as a linear program, and that this linear program is always feasible and always subdifferentiable with respect to the configuration variables, which define the constraint matrix. This is true regardless of whether the program is primal degenerate, dual degenerate, or both. The subgradient of the SSH linear program always lies in the normal cone of the closest admissible configuration to an inadmissible contact configuration. In particular if a contact surface exists, the subgradient of the SSH linear program is orthogonal to the contact surface, as required of contact reactions. This property of the algorithm is particularly important in modeling stiff systems, rigid bodies, and tightly packed or jammed systems.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/brxn1-wjq41HOLMES: Convergent Meshfree Approximation Schemes of Arbitrary Order and Smoothness
https://resolver.caltech.edu/CaltechAUTHORS:20200519-145536180
Authors: {'items': [{'id': 'Bompadre-A', 'name': {'family': 'Bompadre', 'given': 'Agustín'}}, {'id': 'Perotti-L-E', 'name': {'family': 'Perotti', 'given': 'Luigi E.'}}, {'id': 'Cyron-C-J', 'name': {'family': 'Cyron', 'given': 'Christian J.'}}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'Michael'}, 'orcid': '0000-0001-5877-4824'}]}
Year: 2012
DOI: 10.1007/978-3-642-32979-1_7
Local Maximum-Entropy (LME) approximation schemes are meshfree approximation schemes that satisfy consistency conditions of order 1, i.e., they approximate affine functions exactly. In addition, LME approximation schemes converge in the Sobolev space W^(1,p), i.e., they are C⁰-continuous in the conventional terminology of finite-element interpolation. Here we present a generalization of the Local Max-Ent approximation schemes that are consistent to arbitrary order, i.e., interpolate polynomials of arbitrary degree exactly, and which converge in W^(k,p), i.e., they are C^k -continuous to arbitrary order k. We refer to these approximation schemes as High Order Local Maximum-Entropy Approximation Schemes (HOLMES). We prove uniform error bounds for the HOLMES approximates and their derivatives up to order k. Moreover, we show that the HOLMES of order k is dense in the Sobolev Space W^(k,p), for any 1 ≤ p < ∞. The good performance of HOLMES relative to other meshfree schemes in selected test cases is also critically appraised.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/jqfxj-8t304Relaxed incremental variational formulation for damage at large strains with application to fiber-reinforced materials and materials with truss-like microstructures
https://resolver.caltech.edu/CaltechAUTHORS:20121129-084222336
Authors: {'items': [{'id': 'Balzani-D', 'name': {'family': 'Balzani', 'given': 'Daniel'}}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'Michael'}, 'orcid': '0000-0001-5877-4824'}]}
Year: 2012
DOI: 10.1002/nme.4351
In this paper, an incremental variational formulation for damage at finite strains is presented. The classical continuum damage mechanics serves as a basis where a stress-softening term depending on a scalar-valued damage function is prepended an effective hyperelastic strain energy function, which describes the virtually undamaged material. Because loss of convexity is obtained at some critical deformations, a relaxed incremental stress potential is constructed, which convexifies the original nonconvex problem. The resulting model can be interpreted as the homogenization of a microheterogeneous material bifurcated into a strongly and weakly damaged phase at the microscale. A one-dimensional relaxed formulation is derived, and a model for fiber-reinforced materials based thereon is given. Finally, numerical examples illustrate the performance of the model by showing mesh independency of the model in an extended truss, analyzing a numerically homogenized microtruss material and investigating a fiber-reinforced cantilever beam subject to bending and an overstretched arterial wall.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/x6m2n-w7y67An eigenerosion approach to brittle fracture
https://resolver.caltech.edu/CaltechAUTHORS:20121129-135118318
Authors: {'items': [{'id': 'Pandolfi-A', 'name': {'family': 'Pandolfi', 'given': 'A.'}, 'orcid': '0000-0002-7084-7456'}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'M.'}, 'orcid': '0000-0001-5877-4824'}]}
Year: 2012
DOI: 10.1002/nme.4352
The present work is concerned with the verification and validation of a variant of the eigenfracture scheme of Schmidt et al. (2009) based on element erosion, which we refer to as eigenerosion. Eigenerosion is derived from the general eigenfracture scheme by restricting the eigendeformations in a binary sense: they can be either zero, in which case the local behavior is elastic, or they can be equal to the local displacement gradient, in which case the corresponding material neighborhood is failed or eroded. When combined with a finite-element approximation, this scheme gives rise to element erosion, i.e., the elements can be either intact, in which case their behavior is elastic, or be completly failed, or eroded, and have no load bearing capacity. We verify the eigenerosion scheme through comparisons with analytical solutions and through convergence studies for mode I fracture propagation, both in two and three dimensions and for structured and random meshes. Finally, by way of validation, we apply the eigenerosion scheme to the simulation of mixed modes I–III experiments in poly-methyl methacrylate plates.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/dpm7v-24645Large scale Optimal Transportation Meshfree (OTM) Simulations of
Hypervelocity Impact
https://resolver.caltech.edu/CaltechAUTHORS:20130619-145739093
Authors: {'items': [{'id': 'Li-Bo', 'name': {'family': 'Li', 'given': 'B.'}, 'orcid': '0000-0002-8019-8891'}, {'id': 'Perotti-L-E', 'name': {'family': 'Perotti', 'given': 'L.'}}, {'id': 'Adams-M', 'name': {'family': 'Adams', 'given': 'M.'}}, {'id': 'Mihaly-J', 'name': {'family': 'Mihaly', 'given': 'J.'}}, {'id': 'Rosakis-A-J', 'name': {'family': 'Rosakis', 'given': 'A. J.'}, 'orcid': '0000-0003-0559-0794'}, {'id': 'Stalzer-M', 'name': {'family': 'Stalzer', 'given': 'M.'}}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'Michael'}, 'orcid': '0000-0001-5877-4824'}]}
Year: 2013
DOI: 10.1016/j.proeng.2013.05.036
Large scale three-dimensional numerical simulations of hypervelocity impact of Aluminum alloy 6061-T6 plates by Nylon 6/6 cylindrical
projectile have been performed using the Optimal Transportation Meshfree (OTM) method of Li et al. [7] along with the seizing contact
and variational material point failure algorithm [17, 18]. The dynamic response of the Al6061-T6 plate including phase transition in the
high strain rate, high pressure and high temperature regime expected in our numerical analysis is described by the use of a variational
thermomechanical coupling constitutive model with SESAME equation of state, rate-dependent J2 plasticity with power law hardening
and thermal softening and temperature dependent Newtonian viscosity. A polytropic type of equation of state fit to in-house ReaxFF
calculations is employed to model the Nylon 6/6 projectile under extreme conditions. The evaluation of the performance of the numerical
model takes the form of a conventional validation analysis. In support of the analysis, we have conducted experiments over a range of
plate thicknesses of [0.5, 3.0] mm, a range of impact velocities of [5.0, 7.0]km/s and a range of obliquities of [0, 70]° at Caltech's Small
Particle Hypervelocity Range (SPHIR) Facility. Large scale three-dimensional OTM simulations of hypervelocity impact are performed
on departmental class systems using a dynamic load balancing MPI/PThreads parallel implementation of the OTM method. We find
excellent full field agreement between measured and computed perforation areas, debris cloud and temperature field.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/qwsjr-r6q09Coupled thermoelastic simulation of nanovoid cavitation by dislocation emission at finite temperature
https://resolver.caltech.edu/CaltechAUTHORS:20141218-102818033
Authors: {'items': [{'id': 'Ponga-M', 'name': {'family': 'Ponga', 'given': 'M.'}, 'orcid': '0000-0001-5058-1454'}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'M.'}, 'orcid': '0000-0001-5877-4824'}, {'id': 'Ariza-M-P', 'name': {'family': 'Ariza', 'given': 'M. P.'}, 'orcid': '0000-0003-0266-0216'}]}
Year: 2013
In this work we study the early onset of void growth by dislocation emission at finite temperature in single crystal of copper under uniaxial loading conditions using
the HotQC method. The results provide a detailed characterization of the cavitation mechanism, including the geometry of the emitted dislocations, the dislocation reaction paths and attendant macroscopic quantities of interest such as the cavitation pressure. In addition, this work shows that as prismatic dislocation loops grow and move away from the void, the material surrounded by these loops is pushed away from the void surface, giving rise to a flux of material together with a heat flux through the crystal.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/29tac-6zx33Coarse-graining Kohn–Sham Density Functional Theory
https://resolver.caltech.edu/CaltechAUTHORS:20121204-074348348
Authors: {'items': [{'id': 'Suryanarayana-P', 'name': {'family': 'Suryanarayana', 'given': 'Phanish'}, 'orcid': '0000-0001-5172-0049'}, {'id': 'Bhattacharya-K', 'name': {'family': 'Bhattacharya', 'given': 'Kaushik'}, 'orcid': '0000-0003-2908-5469'}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'Michael'}, 'orcid': '0000-0001-5877-4824'}]}
Year: 2013
DOI: 10.1016/j.jmps.2012.09.002
We present a real-space formulation for coarse-graining Kohn–Sham Density Functional Theory that significantly speeds up the analysis of material defects without appreciable loss of accuracy. The approximation scheme consists of two steps. First, we develop a linear-scaling method that enables the direct evaluation of the electron density without the need to evaluate individual orbitals. We achieve this by performing Gauss quadrature over the spectrum of the linearized Hamiltonian operator appearing in each iteration of the self-consistent field method. Building on the linear-scaling method, we introduce a spatial approximation scheme resulting in a coarse-grained Density Functional Theory. The spatial approximation is adapted so as to furnish fine resolution where necessary and to coarsen elsewhere. This coarse-graining step enables the analysis of defects at a fraction of the original computational cost, without any significant loss of accuracy. Furthermore, we show that the coarse-grained solutions are convergent with respect to the spatial approximation. We illustrate the scope, versatility, efficiency and accuracy of the scheme by means of selected examples.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/745vs-5kc97Coarse-graining Kohn-Sham Density Functional Theory
https://resolver.caltech.edu/CaltechAUTHORS:20160316-132823605
Authors: {'items': [{'id': 'Suryanarayana-P', 'name': {'family': 'Suryanarayana', 'given': 'Phanish'}, 'orcid': '0000-0001-5172-0049'}, {'id': 'Bhattacharya-K', 'name': {'family': 'Bhattacharya', 'given': 'Kaushik'}, 'orcid': '0000-0003-2908-5469'}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'Michael'}, 'orcid': '0000-0001-5877-4824'}]}
Year: 2013
DOI: 10.1016/j.jmps.2012.09.002
We present a real-space formulation for coarse-graining Kohn–Sham Density Functional Theory that significantly speeds up the analysis of material defects without appreciable loss of accuracy. The approximation scheme consists of two steps. First, we develop a linear-scaling method that enables the direct evaluation of the electron density without the need to evaluate individual orbitals. We achieve this by performing Gauss quadrature over the spectrum of the linearized Hamiltonian operator appearing in each iteration of the self-consistent field method. Building on the linear-scaling method, we introduce a spatial approximation scheme resulting in a coarse-grained Density Functional Theory. The spatial approximation is adapted so as to furnish fine resolution where necessary and to coarsen elsewhere. This coarse-graining step enables the analysis of defects at a fraction of the original computational cost, without any significant loss of accuracy. Furthermore, we show that the coarse-grained solutions are convergent with respect to the spatial approximation. We illustrate the scope, versatility, efficiency and accuracy of the scheme by means of selected examples.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/wxqcb-3s146Finite element analysis of geometrically necessary dislocations in crystal plasticity
https://resolver.caltech.edu/CaltechAUTHORS:20130115-101157040
Authors: {'items': [{'id': 'Hurtado-D-E', 'name': {'family': 'Hurtado', 'given': 'Daniel E.'}}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'Michael'}, 'orcid': '0000-0001-5877-4824'}]}
Year: 2013
DOI: 10.1002/nme.4376
We present a finite element method for the analysis of ductile crystals whose energy depends on the density of geometrically necessary dislocations (GNDs). We specifically focus on models in which the energy of the GNDs is assumed to be proportional to the total variation of the slip strains. In particular, the GND energy is homogeneous of degree one in the slip strains. Such models indeed arise from rigorous multiscale analysis as the macroscopic limit of discrete dislocation models or from phenomenological considerations such as a line-tension approximation for the dislocation self-energy. The incorporation of internal variable gradients into the free energy of the system renders the constitutive model non-local. We show that an equivalent free-energy functional, which does not depend on internal variable gradients, can be obtained by exploiting the variational definition of the total variation. The reformulation of the free energy comes at the expense of auxiliary variational problems, which can be efficiently solved using finite element approximations. The addition of surface terms in the formulation of the free energy results in additional boundary conditions for the internal variables. The proposed framework is verified by way of numerical convergence tests, and simulations of three-dimensional problems are presented to showcase its applicability. A performance analysis shows that the proposed framework solves strain-gradient plasticity problems in computing times of the order of local plasticity simulations, making it a promising tool for non-local crystal plasticity three-dimensional large-scale simulations.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/w4n0s-1dn47Thermalization of rate-independent processes by entropic regularization
https://resolver.caltech.edu/CaltechAUTHORS:20171117-150903971
Authors: {'items': [{'id': 'Sullivan-T-J', 'name': {'family': 'Sullivan', 'given': 'T. J.'}}, {'id': 'Koslowski-Marisol', 'name': {'family': 'Koslowski', 'given': 'M.'}}, {'id': 'Theil-Florian', 'name': {'family': 'Theil', 'given': 'F.'}}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'Michael'}, 'orcid': '0000-0001-5877-4824'}]}
Year: 2013
DOI: 10.3934/dcdss.2013.6.215
We consider the effective behaviour of a rate-independent process when it is placed in contact with a heat bath. The method used to ``thermalize'' the process is an interior-point entropic regularization of the Moreau--Yosida incremental formulation of the unperturbed process. It is shown that the heat bath destroys the rate independence in a controlled and deterministic way, and that the effective dynamics are those of a non-linear gradient descent in the original energetic potential with respect to a different and non-trivial effective dissipation potential.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/21ykn-a9q36Elastic response of water-filled fiber composite tubes under shock wave loading
https://resolver.caltech.edu/CaltechAUTHORS:20130301-090507891
Authors: {'items': [{'id': 'Perotti-L-E', 'name': {'family': 'Perotti', 'given': 'L. E.'}}, {'id': 'Deiterding-R', 'name': {'family': 'Deiterding', 'given': 'R.'}}, {'id': 'Inaba-K', 'name': {'family': 'Inaba', 'given': 'K.'}}, {'id': 'Shepherd-J-E', 'name': {'family': 'Shepherd', 'given': 'J.'}, 'orcid': '0000-0003-3181-9310'}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'M.'}, 'orcid': '0000-0001-5877-4824'}]}
Year: 2013
DOI: 10.1016/j.ijsolstr.2012.10.015
We experimentally and numerically investigate the response of fluid-filled filament-wound composite tubes subjected to axial shock wave loading in water. Our study focuses on the fluid–structure interaction occurring when the shock wave in the fluid propagates parallel to the axis of the tube, creating pressure waves in the fluid coupled to flexural waves in the shell. The in-house-developed computational scheme couples an Eulerian fluid solver with a Lagrangian shell solver, which includes a new and simple material model to capture the response of fiber composites in finite kinematics. In the experiments and simulations we examine tubes with fiber winding angles equal to 45° and 60°, and we measure the precursor and primary wave speeds, hoop and longitudinal strains, and pressure. The experimental and computational results are in agreement, showing the validity of the computational scheme in complex fluid–structure interaction problems involving fiber composite materials subjected to shock waves. The analyses of the measured quantities show the strong coupling of axial and hoop deformations and the significant effect of fiber winding angle on the composite tube response, which differs substantially from that of a metal tube in the same configuration.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/exen9-4tj18A micromechanical model of distributed damage due to void growth in general materials and under general deformation histories
https://resolver.caltech.edu/CaltechAUTHORS:20130221-133820482
Authors: {'items': [{'id': 'Reina-C', 'name': {'family': 'Reina', 'given': 'Celia'}}, {'id': 'Li-Bo', 'name': {'family': 'Li', 'given': 'Bo'}, 'orcid': '0000-0002-8019-8891'}, {'id': 'Weinberg-K', 'name': {'family': 'Weinberg', 'given': 'Kerstin'}}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'Michael'}, 'orcid': '0000-0001-5877-4824'}]}
Year: 2013
DOI: 10.1002/nme.4397
We develop a multiscale model of ductile damage by void growth in general materials undergoing arbitrary deformations. The model is formulated in the spirit of multiscale finite element methods (FE 2), that is, the macroscopic behavior of the material is obtained by a simultaneous numerical evaluation of the response of a representative volume element. The representative microscopic model considered in this work consists of a space-filling assemblage of hollow spheres. Accordingly, we refer to the present model as the packed hollow sphere (PHS) model. A Ritz–Galerkin method based on spherical harmonics, specialized quadrature rules, and exact boundary conditions is employed to discretize individual voids at the microscale. This discretization results in material frame indifference, and it exactly preserves all material symmetries. The effective macroscopic behavior is then obtained by recourse to Hill's averaging theorems. The deformation and stress fields of the hollow spheres are globally kinematically and statically admissible regardless of material constitution and deformation history, which leads to exact solutions over the entire representative volume under static conditions. Excellent convergence and scalability properties of the PHS model are demonstrated through convergence analyses and examples of application. We also illustrate the broad range of material behaviors that are captured by the PHS model, including elastic and plastic cavitation and the formation of a vertex in the yield stress of porous metals at low triaxiality. This vertex allows ductile damage to occur under shear-dominated conditions, thus overcoming a well-known deficiency of Gurson's model.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/da27n-6bc45Optimal Uncertainty Quantification
https://resolver.caltech.edu/CaltechAUTHORS:20130618-075057070
Authors: {'items': [{'id': 'Owhadi-H', 'name': {'family': 'Owhadi', 'given': 'H.'}, 'orcid': '0000-0002-5677-1600'}, {'id': 'Scovel-C', 'name': {'family': 'Scovel', 'given': 'C.'}, 'orcid': '0000-0001-7757-3411'}, {'id': 'Sullivan-T-J', 'name': {'family': 'Sullivan', 'given': 'T. J.'}}, {'id': 'McKerns-M', 'name': {'family': 'McKerns', 'given': 'M.'}}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'M.'}, 'orcid': '0000-0001-5877-4824'}]}
Year: 2013
DOI: 10.1137/10080782X
We propose a rigorous framework for uncertainty quantification (UQ) in which the UQ objectives and its assumptions/information set are brought to the forefront. This framework, which we call optimal uncertainty quantification (OUQ), is based on the observation that, given a set of assumptions and information about the problem, there exist optimal bounds on uncertainties: these are obtained as values of well-defined optimization problems corresponding to extremizing probabilities of failure, or of deviations, subject to the constraints imposed by the scenarios compatible with the assumptions and information. In particular, this framework does not implicitly impose inappropriate assumptions, nor does it repudiate relevant information. Although OUQ optimization problems are extremely large, we show that under general conditions they have finite-dimensional reductions. As an application, we develop optimal concentration inequalities (OCI) of Hoeffding and McDiarmid type. Surprisingly, these results show that uncertainties in input parameters, which propagate to output uncertainties in the classical sensitivity analysis paradigm, may fail to do so if the transfer functions (or probability distributions) are imperfectly known. We show how, for hierarchical structures, this phenomenon may lead to the nonpropagation of uncertainties or information across scales. In addition, a general algorithmic framework is developed for OUQ and is tested on the Caltech surrogate model for hypervelocity impact and on the seismic safety assessment of truss structures, suggesting the feasibility of the framework for important complex systems. The introduction of this paper provides both an overview of the paper and a self-contained minitutorial on the basic concepts and issues of UQ.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/n4qe1-qtp61A Γ-Convergence Analysis of the Quasicontinuum Method
https://resolver.caltech.edu/CaltechAUTHORS:20131104-155146267
Authors: {'items': [{'id': 'Español-M-I', 'name': {'family': 'Español', 'given': 'Malena I.'}}, {'id': 'Kochmann-D-M', 'name': {'family': 'Kochmann', 'given': 'Dennis M.'}, 'orcid': '0000-0002-9112-6615'}, {'id': 'Conti-S', 'name': {'family': 'Conti', 'given': 'Sergio'}, 'orcid': '0000-0001-7987-9174'}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'Michael'}, 'orcid': '0000-0001-5877-4824'}]}
Year: 2013
DOI: 10.1137/120895354
We present a Γ-convergence analysis of the quasicontinuum method focused on the behavior of the approximate energy functionals in the continuum limit of a harmonic and defect-free crystal. The analysis shows that, under general conditions of stability and boundedness of the energy, the continuum limit is attained provided that the continuum---e.g., finite-element---approximation spaces are strongly dense in an appropriate topology and provided that the lattice size converges to zero more rapidly than the mesh size. The equicoercivity of the quasicontinuum energy functionals is likewise established with broad generality, which, in conjunction with Γ-convergence, ensures the convergence of the minimizers. We also show under rather general conditions that, for interatomic energies having a clusterwise additive structure, summation or quadrature rules that suitably approximate the local element energies do not affect the continuum limit. Finally, we propose a discrete patch test that provides a practical means of assessing the convergence of quasicontinuum approximations. We demonstrate the utility of the discrete patch test by means of selected examples of application.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/fdqeb-pty38Optimal Uncertainty Quantification for Legacy Data Observations of Lipschitz Functions
https://resolver.caltech.edu/CaltechAUTHORS:20131119-093417975
Authors: {'items': [{'id': 'Sullivan-T-J', 'name': {'family': 'Sullivan', 'given': 'T. J.'}}, {'id': 'McKerns-M', 'name': {'family': 'McKerns', 'given': 'M.'}}, {'id': 'Meyer-D', 'name': {'family': 'Meyer', 'given': 'D.'}}, {'id': 'Theil-F', 'name': {'family': 'Theil', 'given': 'F.'}}, {'id': 'Owhadi-H', 'name': {'family': 'Owhadi', 'given': 'H.'}, 'orcid': '0000-0002-5677-1600'}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'M.'}, 'orcid': '0000-0001-5877-4824'}]}
Year: 2013
DOI: 10.1051/m2an/2013083
We consider the problem of providing optimal uncertainty quantification (UQ) – and hence rigorous certification – for partially-observed functions. We present a UQ framework within which the observations may be small or large in number, and need not carry information about the probability distribution of the system in operation. The UQ objectives are posed as optimization problems, the solutions of which are optimal bounds on the quantities of interest; we consider two typical settings, namely parameter sensitivities (McDiarmid diameters) and output deviation (or failure) probabilities. The solutions of these optimization problems depend non-trivially (even non-monotonically and discontinuously) upon the specified legacy data. Furthermore, the extreme values are often determined by only a few members of the data set; in our principal physically-motivated example, the bounds are determined by just 2 out of 32 data points, and the remainder carry no information and could be neglected without changing the final answer. We propose an analogue of the simplex algorithm from linear programming that uses these observations to offer efficient and rigorous UQ for high-dimensional systems with high-cardinality legacy data. These findings suggest natural methods for selecting optimal (maximally informative) next experiments.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/egntf-h9y04Modeling fracture by material-point erosion
https://resolver.caltech.edu/CaltechAUTHORS:20140109-090108326
Authors: {'items': [{'id': 'Pandolfi-A', 'name': {'family': 'Pandolfi', 'given': 'A.'}, 'orcid': '0000-0002-7084-7456'}, {'id': 'Li-B', 'name': {'family': 'Li', 'given': 'B.'}}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'M.'}, 'orcid': '0000-0001-5877-4824'}]}
Year: 2013
DOI: 10.1007/s10704-012-9788-x
The present work is concerned with the verification and validation of an implementation of the eigenfracture scheme of Schmidt et al. (SIAM J Multiscale Model Simul 7:1237–1266, 2009) based on material-point erosion, which we refer to as eigenerosion. Eigenerosion is derived from the general eigenfracture scheme by restricting the eigendeformations in a binary sense: they can be either zero, in which case the local behavior is elastic; or they can be equal to the local displacement gradient, in which case the corresponding material neighborhood is failed, or eroded. When combined with a material-point spatial discretization, this scheme gives rise to material-point erosion, i. e., each material point can be either intact, in which case its behavior is elastic, or be completely failed—or eroded—and has no load bearing capacity. We verify the eigenerosion scheme through convergence studies for mode I fracture propagation in three-dimensional problems. By way of validation we apply the eigenerosion scheme to the simulation of combined torsion-traction experiments in aluminum-oxide bars.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/vwp2e-pp377Automatically inf-sup compliant diamond-mixed finite elements for Kirchhoff plates
https://resolver.caltech.edu/CaltechAUTHORS:20131108-093716091
Authors: {'items': [{'id': 'Perotti-L-E', 'name': {'family': 'Perotti', 'given': 'L. E.'}}, {'id': 'Bompadre-A', 'name': {'family': 'Bompadre', 'given': 'A.'}}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'M.'}, 'orcid': '0000-0001-5877-4824'}]}
Year: 2013
DOI: 10.1002/nme.4555
We develop a mixed finite-element approximation scheme for Kirchhoff plate theory based on the reformulation of Kirchhoff plate theory of Ortiz and Morris [1]. In this reformulation the moment-equilibrium problem for the rotations is in direct analogy to the problem of incompressible two-dimensional elasticity. This analogy in turn opens the way for the application of diamond approximation schemes (Hauret et al. [2]) to Kirchhoff plate theory. We show that a special class of meshes derived from an arbitrary triangulation of the domain, the diamond meshes, results in the automatic satisfaction of the corresponding inf − sup condition for Kirchhoff plate theory. The attendant optimal convergence properties of the diamond approximation scheme are demonstrated by means of the several standard benchmark tests. We also provide a reinterpretation of the diamond approximation scheme for Kirchhoff plate theory within the framework of discrete mechanics. In this interpretation, the discrete moment-equilibrium problem is formally identical to the classical continuous problem, and the two differ only in the choice of differential structures. It also follows that the satisfaction of the inf − sup condition is a property of the cohomology of a certain discrete transverse differential complex. This close connection between the classical inf − sup condition and cohomology evinces the important role that the topology of the discretization plays in determining convergence in mixed problems.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/m2g0h-e5t09Optimal scaling laws for ductile fracture derived from strain-gradient microplasticity
https://resolver.caltech.edu/CaltechAUTHORS:20140130-134426507
Authors: {'items': [{'id': 'Fokoua-L', 'name': {'family': 'Fokoua', 'given': 'Landry'}}, {'id': 'Conti-S', 'name': {'family': 'Conti', 'given': 'Sergio'}, 'orcid': '0000-0001-7987-9174'}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'Michael'}, 'orcid': '0000-0001-5877-4824'}]}
Year: 2014
DOI: 10.1016/j.jmps.2013.11.002
We perform an optimal-scaling analysis of ductile fracture in metals. We specifically consider the deformation up to failure of a slab of finite thickness subject to monotonically increasing normal opening displacements on its surfaces. We show that ductile fracture emerges as the net outcome of two competing effects: the sublinear growth characteristic of the hardening of metals and strain-gradient plasticity. We also put forth physical arguments that identify the intrinsic length of strain-gradient plasticity and the critical opening displacement for fracture. We show that, when J_c is renormalized in a manner suggested by the optimal scaling laws, the experimental data tends to cluster—with allowances made for experimental scatter—within bounds dependent on the hardening exponent but otherwise material independent.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/0kce6-9tb97Linear Scaling DFT for defects in metals
https://resolver.caltech.edu/CaltechAUTHORS:20141124-095544294
Authors: {'items': [{'id': 'Ponga-Mauricio', 'name': {'family': 'Ponga', 'given': 'Mauricio'}, 'orcid': '0000-0001-5058-1454'}, {'id': 'Ariza-Pilar', 'name': {'family': 'Ariza', 'given': 'Pilar'}, 'orcid': '0000-0003-0266-0216'}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'Michael'}, 'orcid': '0000-0001-5877-4824'}, {'id': 'Bhattacharya-K', 'name': {'family': 'Bhattacharya', 'given': 'Kaushik'}, 'orcid': '0000-0003-2908-5469'}]}
Year: 2014
DOI: 10.1002/9781118889879.ch35
This work presents a study of defects in solid using Density Functional Theory (DFT) as the only input to predict its information energies. The method used, called the Linnear Scaling Spectral Gauss Quadrature (LSSGQ), has linear scaling with the number of atoms for insulators as well as for metals. This behaviour allows us to stimulate relatively large systems in a fraction of the time demanded by other traditional DFT methods. We demostrate the effectiveness of the method, the linear scaling of large problems and also the size dependence in the formation energy of defects through the simulation of (001) surface relaxation and single vacancy in Body Centered Cubic (BCC) Sodium crystals.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/kv9tb-zp895The special-linear update: An application of differential manifold theory to the update of isochoric plasticity flow rules
https://resolver.caltech.edu/CaltechAUTHORS:20140116-143601176
Authors: {'items': [{'id': 'Hurtado-D-E', 'name': {'family': 'Hurtado', 'given': 'D. E.'}}, {'id': 'Stainier-Laurent', 'name': {'family': 'Stainier', 'given': 'L.'}, 'orcid': '0000-0001-6719-6616'}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'M.'}, 'orcid': '0000-0001-5877-4824'}]}
Year: 2014
DOI: 10.1002/nme.4600
The evolution of plastic deformations in metals, governed by incompressible flow rules, has been traditionally solved using the exponential mapping. However, the accurate calculation of the exponential mapping and its tangents may result in computationally demanding schemes in some cases, while common low-order approximations may lead to poor behavior of the constitutive update because of violation of the incompressibility condition. Here, we introduce the special-linear (SL) update for isochoric plasticity, a flow-rule integration scheme based on differential manifolds concepts. The proposed update exactly enforces the plastic incompressibility condition while being first-order accurate and consistent with the flow rule, thus bearing all the desirable properties of the now standard exponential mapping update. In contrast to the exponential-mapping update, we demonstrate that the SL update can drastically reduce the computing time, reaching one order of magnitude speed-ups in the calculation of the update tangents. We demonstrate the applicability of the update by way of simulation of single-crystal plasticity uniaxial loading tests. We anticipate that the SL update will open the way to efficient constitutive updates for the solution of complex multiscale material models, thus making it a very promising tool for large-scale simulations.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/9mpbb-etj42Optimal Scaling in Solids Undergoing Ductile Fracture by Void Sheet Formation
https://resolver.caltech.edu/CaltechAUTHORS:20140327-112854588
Authors: {'items': [{'id': 'Fokoua-L', 'name': {'family': 'Fokoua', 'given': 'Landry'}}, {'id': 'Conti-S', 'name': {'family': 'Conti', 'given': 'Sergio'}, 'orcid': '0000-0001-7987-9174'}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'Michael'}, 'orcid': '0000-0001-5877-4824'}]}
Year: 2014
DOI: 10.1007/s00205-013-0687-8
This work is concerned with the derivation of optimal scaling laws, in the sense of matching lower and upper bounds on the energy, for a solid undergoing ductile fracture. The specific problem considered concerns a material sample in the form of an infinite slab of finite thickness subjected to prescribed opening displacements on its two surfaces. The solid is assumed to obey deformation-theory of plasticity and, in order to further simplify the analysis, we assume isotropic rigid-plastic deformations with zero plastic spin. When hardening exponents are given values consistent with observation, the energy is found to exhibit sublinear growth. We regularize the energy through the addition of nonlocal energy terms of the strain-gradient plasticity type. This nonlocal regularization has the effect of introducing an intrinsic length scale into the energy. Under these assumptions, ductile fracture emerges as the net result of two competing effects: whereas the sublinear growth of the local energy promotes localization of deformation to failure planes, the nonlocal regularization stabilizes this process, thus resulting in an orderly progression towards failure and a well-defined specific fracture energy. The optimal scaling laws derived here show that ductile fracture results from localization of deformations to void sheets, and that it requires a well-defined energy per unit fracture area. In particular, fractal modes of fracture are ruled out under the assumptions of the analysis. The optimal scaling laws additionally show that ductile fracture is cohesive in nature, that is, it obeys a well-defined relation between tractions and opening displacements. Finally, the scaling laws supply a link between micromechanical properties and macroscopic fracture properties. In particular, they reveal the relative roles that surface energy and microplasticity play as contributors to the specific fracture energy of the material.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/ndj7p-pjc02Metaconcrete: designed aggregates to enhance dynamic performance
https://resolver.caltech.edu/CaltechAUTHORS:20140508-084344238
Authors: {'items': [{'id': 'Mitchell-S-J', 'name': {'family': 'Mitchell', 'given': 'Stephanie J.'}}, {'id': 'Pandolfi-A', 'name': {'family': 'Pandolfi', 'given': 'Anna'}, 'orcid': '0000-0002-7084-7456'}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'Michael'}, 'orcid': '0000-0001-5877-4824'}]}
Year: 2014
DOI: 10.1016/j.jmps.2014.01.003
We propose a new type of concrete for the attenuation of elastic waves induced by dynamic excitation. In this metamaterial, which we call metaconcrete, the stone, sand, and gravel aggregates of standard concrete are replaced with spherical inclusions consisting of a heavy metal core coated with a soft outer layer. These engineered aggregates can be tuned so that particular frequencies of a propagating blast wave will activate resonant oscillations of the heavy mass within the inclusions. The resonant behavior causes the system to exhibit negative effective mass, and this interaction between the wave motion and the resonant aggregates results in the attenuation of the applied dynamic loading. We introduce the concept of negative mass by deriving the effective momentum mass for the system and we define the geometrical and material parameters for the design of resonant aggregates. We develop finite element models for the analysis of metaconcrete behavior, defining a section of slab containing a periodic arrangement of inclusions. By computing the energy histories for the system when subject to a blast load, we show that there is a transfer of energy between the inclusions and the surrounding mortar. The inclusions are able to absorb a significant portion of the applied energy, resulting in a reduction in the amount of stress carried by the mortar phase and greatly improving the ability of the material to resist damage under explosive dynamic loading.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/571zk-xxc92Modeling fracture by material-point erosion
https://resolver.caltech.edu/CaltechAUTHORS:20170719-112646074
Authors: {'items': [{'id': 'Pandolfi-A', 'name': {'family': 'Pandolfi', 'given': 'A.'}, 'orcid': '0000-0002-7084-7456'}, {'id': 'Li-B', 'name': {'family': 'Li', 'given': 'B.'}}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'M.'}, 'orcid': '0000-0001-5877-4824'}]}
Year: 2014
DOI: 10.1007/978-3-319-04397-5_2
The present work is concerned with the verification and validation of an implementation of the eigenfracture scheme of Schmidt et al. (SIAM J Multi-scale Model Simul 7:1237–1266, 2009) based on material-point erosion, which we refer to as eigenerosion. Eigenerosion is derived from the general eigenfracture scheme by restricting the eigendeformations in a binary sense: they can be either zero, in which case the local behavior is elastic; or they can be equal to the local displacement gradient, in which case the corresponding material neighborhood is failed, or eroded. When combined with a material-point spatial discretization, this scheme gives rise to material-point erosion, i. e., each material point can be either intact, in which case its behavior is elastic, or be completely failed—or eroded—and has no load bearing capacity. We verify the eigenerosion scheme through convergence studies for mode I fracture propagation in three-dimensional problems. By way of validation we apply the eigene-rosion scheme to the simulation of combined torsion- traction experiments in aluminum-oxide bars.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/mr74c-7qt42A massively parallel implementation of the Optimal Transportation Meshfree method for explicit solid dynamics
https://resolver.caltech.edu/CaltechAUTHORS:20141002-101310343
Authors: {'items': [{'id': 'Li-B', 'name': {'family': 'Li', 'given': 'B.'}}, {'id': 'Stalzer-M', 'name': {'family': 'Stalzer', 'given': 'M.'}}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'M.'}, 'orcid': '0000-0001-5877-4824'}]}
Year: 2014
DOI: 10.1002/nme.4710
Presented is a massively parallel implementation of the Optimal Transportation Meshfree (pOTM) method Li et al., 2010 for explicit solid dynamics. Its implementation is based on a two-level scheme using Message Passing Interface between compute servers and threaded parallelism on the multi-core processors within each server. Both layers dynamically subdivide the problem to provide excellent parallel scalability. pOTM is used on three problems and compared to experiments to demonstrate accuracy and performance. For both a Taylor-anvil and a hypervelocity impact problem, the pOTM implementation scales nearly perfectly to about 8000 cores.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/acv5r-bkt28Atomistic Models of Long-Term Hydrogen Diffusion in Metals
https://resolver.caltech.edu/CaltechAUTHORS:20171117-150624065
Authors: {'items': [{'id': 'Ariza-M-P', 'name': {'family': 'Ariza', 'given': 'M. P.'}, 'orcid': '0000-0003-0266-0216'}, {'id': 'Wang-Kevin-G', 'name': {'family': 'Wang', 'given': 'K. G.'}}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'M.'}, 'orcid': '0000-0001-5877-4824'}]}
Year: 2014
DOI: 10.4028/www.scientific.net/AST.93.118
The effective and efficient storage of hydrogen is one of the key challenges in developing a hydrogen economy. Recently, intensive research has been focused on developing and optimizing metal-based nanomaterials for high-speed, high-capacity, reversible hydrogen storage applications. Notably, the absorption and desorption of hydrogen in nanomaterials is characterized by an atomic, deformation-diffusion coupled process with a time scale of the order of seconds to hours--far beyond the time windows of existing simulation technologies such as Molecular Dynamics (MD) and Monte Carlo (MC) methods. In this work, we present a novel deformation-diffusion coupled computational framework, which allows the long-term simulation of such slow processes and at the same time maintains a strictly atomistic description of the material. Specifically, we first propose a theory of non-equilibrium statistical thermodynamics for multi-species particulate solids based on Jayne's maximum entropy principle and the meanfield approximation approach. This non-equilibrium statistical thermodynamics model is then coupled with novel discrete kinetics laws, which governs the diffusion of mass--and possibly also conduction of heat--at atomic scale. Finally, this thermo-chemo-mechanical coupled system is solved numerically using a staggered procedure. The salient features of this computational framework are demonstrated in the simulation of a specific hydrogen diffusion problem using palladium nanofilms, which comes with a simulation time of one second. More generally, the proposed computational framework can be considered as an ideal tool for the study of many deformation-diffusion coupled phenomena in hydrogen-storage-related applications including, but not limited to, hydrogen embrittlement, grain boundary diffusion, and various cyclic behaviors.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/x7142-n7w29Optimal uncertainty quantification with model uncertainty and legacy data
https://resolver.caltech.edu/CaltechAUTHORS:20141201-081327318
Authors: {'items': [{'id': 'Kamga-P-H-T', 'name': {'family': 'Kamga', 'given': 'P.-H. T.'}}, {'id': 'Li-B', 'name': {'family': 'Li', 'given': 'B.'}}, {'id': 'McKerns-M', 'name': {'family': 'McKerns', 'given': 'M.'}}, {'id': 'Nguyen-L-H', 'name': {'family': 'Nguyen', 'given': 'L. H.'}}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'M.'}, 'orcid': '0000-0001-5877-4824'}, {'id': 'Owhadi-H', 'name': {'family': 'Owhadi', 'given': 'H.'}, 'orcid': '0000-0002-5677-1600'}, {'id': 'Sullivan-T-J', 'name': {'family': 'Sullivan', 'given': 'T. J.'}}]}
Year: 2014
DOI: 10.1016/j.jmps.2014.07.007
We present an optimal uncertainty quantification (OUQ) protocol for systems that are characterized by an existing physics-based model and for which only legacy data is available, i.e., no additional experimental testing of the system is possible. Specifically, the OUQ strategy developed in this work consists of using the legacy data to establish, in a probabilistic sense, the level of error of the model, or modeling error, and to subsequently use the validated model as a basis for the determination of probabilities of outcomes. The quantification of modeling uncertainty specifically establishes, to a specified confidence, the probability that the actual response of the system lies within a certain distance of the model. Once the extent of model uncertainty has been established in this manner, the model can be conveniently used to stand in for the actual or empirical response of the system in order to compute probabilities of outcomes. To this end, we resort to the OUQ reduction theorem of Owhadi et al. (2013) in order to reduce the computation of optimal upper and lower bounds on probabilities of outcomes to a finite-dimensional optimization problem. We illustrate the resulting UQ protocol by means of an application concerned with the response to hypervelocity impact of 6061-T6 Aluminum plates by Nylon 6/6 impactors at impact velocities in the range of 5–7 km/s. The ability of the legacy OUQ protocol to process diverse information on the system and its ability to supply rigorous bounds on system performance under realistic—and less than ideal—scenarios demonstrated by the hypervelocity impact application is remarkable.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/rjkpc-sq491Calculation of Optimal Bounds on the Probability of Failure of Soft Biological Tissues
https://resolver.caltech.edu/CaltechAUTHORS:20170330-072907176
Authors: {'items': [{'id': 'Balzani-D', 'name': {'family': 'Balzani', 'given': 'Daniel'}}, {'id': 'Schmidt-T', 'name': {'family': 'Schmidt', 'given': 'Thomas'}}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'Michael'}, 'orcid': '0000-0001-5877-4824'}]}
Year: 2014
DOI: 10.1002/pamm.201410034
In this contribution, a methodology for the calculation of optimal bounds on the probability of failure of soft biological tissues is presented. Two potential rupture criteria are considered and an uncertainty quantification method [1] is applied to a virtual experimental data set. The results for both criteria are compared in a finite element example.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/2jr2s-9x642Atomistic long-term simulation of heat and mass transport
https://resolver.caltech.edu/CaltechAUTHORS:20141015-093205200
Authors: {'items': [{'id': 'Venturini-Gabriela-N', 'name': {'family': 'Venturini', 'given': 'G.'}}, {'id': 'Wang-K', 'name': {'family': 'Wang', 'given': 'K.'}}, {'id': 'Romero-I', 'name': {'family': 'Romero', 'given': 'I.'}, 'orcid': '0000-0003-0364-6969'}, {'id': 'Ariza-M-P', 'name': {'family': 'Ariza', 'given': 'M. P.'}, 'orcid': '0000-0003-0266-0216'}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'M.'}, 'orcid': '0000-0001-5877-4824'}]}
Year: 2014
DOI: 10.1016/j.jmps.2014.09.008
We formulate a theory of non-equilibrium statistical thermodynamics for ensembles of atoms or molecules. The theory is an application of Jayne's maximum entropy principle, which allows the statistical treatment of systems away from equilibrium. In particular, neither temperature nor atomic fractions are required to be uniform but instead are allowed to take different values from particle to particle. In addition, following the Coleman-Noll method of continuum thermodynamics we derive a dissipation inequality expressed in terms of discrete thermodynamic fluxes and forces. This discrete dissipation inequality effectively sets the structure for discrete kinetic potentials that couple the microscopic field rates to the corresponding driving forces, thus resulting in a closed set of equations governing the evolution of the system. We complement the general theory with a variational meanfield theory that provides a basis for the formulation of computationally tractable approximations. We present several validation cases, concerned with equilibrium properties of alloys, heat conduction in silicon nanowires and hydrogen desorption from palladium thin films, that demonstrate the range and scope of the method and assess its fidelity and predictiveness. These validation cases are characterized by the need or desirability to account for atomic-level properties while simultaneously entailing time scales much longer than those accessible to direct molecular dynamics. The ability of simple meanfield models and discrete kinetic laws to reproduce equilibrium properties and long-term behavior of complex systems is remarkable.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/tkqe7-ywn70Discontinuous variational time integrators for complex multibody collisions
https://resolver.caltech.edu/CaltechAUTHORS:20141219-081601928
Authors: {'items': [{'id': 'Johnson-G', 'name': {'family': 'Johnson', 'given': 'G.'}}, {'id': 'Leyendecker-S', 'name': {'family': 'Leyendecker', 'given': 'S.'}}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'M.'}, 'orcid': '0000-0001-5877-4824'}]}
Year: 2014
DOI: 10.1002/nme.4764
The objective of the present work is to formulate a new class of discontinuous variational time integrators that allow the system to adopt two possibly different configurations at each sampling time tk, representing predictor and corrector configurations of the system. The resulting sequence of configuration pairs then represents a discontinuous—or non-classical—trajectory. Continuous or classical trajectories are recovered simply by enforcing a continuity constraint at all times. In particular, in systems subject to one-sided contact constraints simulated via discontinuous variational time integrators, the predictor configuration is not required to satisfy the one-sided constraints, whereas the corrector configuration is obtained by a closest-point projection (CPP) onto the admissible set. The resulting trajectories are generally discontinuous, or non-classical, but are expected to converge to classical or continuous solutions for decreasing time steps. We account for dissipation, including friction, by means of a discrete Lagrange–d'Alembert principle, and make extensive use of the spacetime formalism in order to ensure exact energy conservation in conservative systems, and the right rate of energy decay in dissipative systems. The structure, range and scope of the discontinuous variational time integrators, and their accuracy characteristics are illustrated by means of examples of application concerned with rigid multibody dynamics.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/sqxh8-cq905Atomistic Modeling and Simulation of Long-Term Transport Phenomena in Nanomaterials
https://resolver.caltech.edu/CaltechAUTHORS:20160930-132814884
Authors: {'items': [{'id': 'Ariza-M-P', 'name': {'family': 'Ariza', 'given': 'M. P.'}, 'orcid': '0000-0003-0266-0216'}, {'id': 'Martin-C-S', 'name': {'family': 'Martin', 'given': 'C. S.'}}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'M.'}, 'orcid': '0000-0001-5877-4824'}]}
Year: 2015
In the past two decades, extensive research has been conducted towards developing nanomaterials with superior transport properties, such as heat conductivity and mass diffusivity, for applications in various industries including, but not limited to, energy storage and microelectronics. In terms of modeling and simulation, a long-standing difficulty lies in the separation of temporal and spatial scales. Indeed, many transport phenomena in nanomaterials are characterized by slow kinetic processes with time scale of the order of seconds, hours, or even years, far beyond the time windows of existing simulation technologies such as molecular dynamics (MD) and Monte Carlo (MC) methods. We have developed a novel deformation-diffusion coupled computational framework that allows long-term simulation of such slow processes, while at the same time maintains a strictly atomistic description of the material. Our non-equilibrium statistical thermodynamics model includes discrete kinetic laws, which govern mass diffusion and heat conduction at atomic scale. In this work, we explore the capabilities and performance of this computational framework through its application to heat conduction problems.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/2zsfw-g6848Material-point erosion simulation of dynamic fragmentation of metals
https://resolver.caltech.edu/CaltechAUTHORS:20150205-083744373
Authors: {'items': [{'id': 'Li-B', 'name': {'family': 'Li', 'given': 'B.'}}, {'id': 'Pandolfi-A', 'name': {'family': 'Pandolfi', 'given': 'A.'}, 'orcid': '0000-0002-7084-7456'}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'M.'}, 'orcid': '0000-0001-5877-4824'}]}
Year: 2015
DOI: 10.1016/j.mechmat.2014.03.008
We present a validation assessment of the eigenerosion scheme applied in conjunction with the Optimal Transportation Meshfree (OTM) method. The assessment is based on the detonation-driven 304L steel spherical-cap fragmentation experiments of Campbell et al. (2007). Metrics used for purposes of validation include the velocity history of a witness point of the shell and the histogram of recovered fragment sizes. The results of the simulations are found to be in overall good agreement with the experimental measurements, especially when allowances are made for uncertainties in the characterization of the drive and material properties. The ability of the approach to predictively simulate exceedingly complex patterns of fracture and fragmentation under severe conditions of loading and material behavior is remarkable, especially in consideration of the simplicity of the fracture model and its implementation.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/hyzhq-v1h13A micromechanical damage and fracture model for polymers based on fractional strain-gradient elasticity
https://resolver.caltech.edu/CaltechAUTHORS:20141117-084849745
Authors: {'items': [{'id': 'Heyden-S', 'name': {'family': 'Heyden', 'given': 'S.'}, 'orcid': '0000-0002-7035-7975'}, {'id': 'Li-B', 'name': {'family': 'Li', 'given': 'B.'}}, {'id': 'Weinberg-K', 'name': {'family': 'Weinberg', 'given': 'K.'}}, {'id': 'Conti-S', 'name': {'family': 'Conti', 'given': 'S.'}, 'orcid': '0000-0001-7987-9174'}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'M.'}, 'orcid': '0000-0001-5877-4824'}]}
Year: 2015
DOI: 10.1016/j.jmps.2014.08.005
We formulate a simple one-parameter macroscopic model of distributed damage and fracture of polymers that is amenable to a straightforward and efficient numerical implementation. We show that the macroscopic model can be rigorously derived, in the sense of optimal scaling, from a micromechanical model of chain elasticity and failure regularized by means of fractional strain-gradient elasticity. In particular, we derive optimal scaling laws that supply a link between the single parameter of the macroscopic model, namely, the critical energy-release rate of the material, and micromechanical parameters pertaining to the elasticity and strength of the polymer chains and to the strain-gradient elasticity regularization. We show how the critical energy-release rate of specific materials can be determined from test data. Finally, we demonstrate the scope and fidelity of the model by means of an example of application, namely, Taylor-impact experiments of polyurea 1000 rods.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/9qaw0-eqp19Long-term atomistic simulation of hydrogen diffusion in metals
https://resolver.caltech.edu/CaltechAUTHORS:20150515-073520397
Authors: {'items': [{'id': 'Wang-K-G', 'name': {'family': 'Wang', 'given': 'K. G.'}}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'M.'}, 'orcid': '0000-0001-5877-4824'}, {'id': 'Ariza-M-P', 'name': {'family': 'Ariza', 'given': 'M. P.'}, 'orcid': '0000-0003-0266-0216'}]}
Year: 2015
DOI: 10.1016/j.ijhydene.2015.01.110
Whereas great strides have been taken towards the characterization of metal-based nanomaterials for high-speed, high capacity, reversible hydrogen storage applications, most mesoscopic approaches to date have relied on molecular dynamics (MD) as their chief representational and computational paradigm. However, the absorption and desorption of hydrogen in nanomaterials is characterized by an atomic, deformation-diffusion coupled process with a time scale of the order of seconds to hours–far beyond the characteristic time windows of MD-based simulations. In this work, we present an application of a novel deformation-diffusion coupled computational framework, which allows the long-term simulation of such slow processes and at the same time maintains a strictly atomistic description of the material. Specifically, we have studied the diffusion of hydrogen in palladium nanofilms and compared our predictions with previous hydrogen desorption results obtained by electrochemical cycling experiments.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/b0h8t-35x91Scaling Laws in the Ductile Fracture of Metallic Crystals
https://resolver.caltech.edu/CaltechAUTHORS:20150625-135311281
Authors: {'items': [{'id': 'Baskes-M-I', 'name': {'family': 'Baskes', 'given': 'M. I.'}}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'M.'}, 'orcid': '0000-0001-5877-4824'}]}
Year: 2015
DOI: 10.1115/1.4030329
We explore whether the continuum scaling behavior of the fracture energy of metals extends down to the atomistic level. We use an embedded atom method (EAM) model of Ni, thus bypassing the need to model strain-gradient plasticity at the continuum level. The calculations are performed with a number of different 3D periodic size cells using standard molecular dynamics (MD) techniques. A void nucleus of a single vacancy is placed in each cell and the cell is then expanded through repeated NVT MD increments. For each displacement, we then determine which cell size has the lowest energy. The optimal cell size and energy bear a power-law relation to the opening displacement that is consistent with continuum estimates based on strain-gradient plasticity (Fokoua et al., 2014, "Optimal Scaling in Solids Undergoing Ductile Fracture by Void Sheet Formation," Arch. Ration. Mech. Anal. (in press); Fokoua et al., 2014, "Optimal Scaling Laws for Ductile Fracture Derived From Strain-Gradient Microplasticity," J. Mech. Phys. Solids, 62, pp. 295–311). The persistence of power-law scaling of the fracture energy down to the atomistic level is remarkable.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/brbhb-65c55Acceleration of material-dominated calculations via phase-space simplicial subdivision and interpolation
https://resolver.caltech.edu/CaltechAUTHORS:20150724-105805749
Authors: {'items': [{'id': 'Klusemann-B', 'name': {'family': 'Klusemann', 'given': 'B.'}}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'M.'}, 'orcid': '0000-0001-5877-4824'}]}
Year: 2015
DOI: 10.1002/nme.4887
We develop an acceleration method for material-dominated calculations based on phase-space simplicial interpolation of the relevant material-response functions. This process of interpolation constitutes an approximation scheme by which an exact material-response function is replaced by a sequence of approximating response functions. The terms in the sequence are increasingly accurate, thus ensuring the convergence of the overall solution. The acceleration ratio depends on the dimensionality, the complexity of the deformation, the time-step size, and the fineness of the phase-space interpolation. We ascertain these trade-offs analytically and by recourse to selected numerical tests. The numerical examples with piecewise-quadratic interpolation in phase space confirm the analytical estimates.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/vhrvc-9x026Modeling thermal conductivity in silicon nanowires
https://resolver.caltech.edu/CaltechAUTHORS:20171117-150333066
Authors: {'items': [{'id': 'Martin-C-S', 'name': {'family': 'Martin', 'given': 'C. S.'}}, {'id': 'Ariza-M-P', 'name': {'family': 'Ariza', 'given': 'M. P.'}, 'orcid': '0000-0003-0266-0216'}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'M.'}, 'orcid': '0000-0001-5877-4824'}]}
Year: 2015
DOI: 10.1002/gamm.201510011
The complexity of heat transport in silicon nanowires (SiNWs) and, specifically, its dependence on temperature and the nanowire diameter, is beyond continuum models of heat conduction and necessitate consideration of atomic-level heat-conduction models. In this work, we specifically aim to ascertain the ability of models based on non-equilibrium statistical mechanics to reproduce the observed anisotropy, temperature and size dependence of the thermal conductivity of SiNWs. In this approach, the atomic-level kinetic relations are regarded as empirical and subject to modeling. Within this framework, we find that a simple model, based on the introduction of a thin amorphous layer at the surface of the SiNWs, yields effective thermal conductivities that are in excellent agreement with the experimental data over a range of temperatures and diameters.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/8nxv0-s1712The Line-Tension Approximation as the Dilute Limit of Linear-Elastic Dislocations
https://resolver.caltech.edu/CaltechAUTHORS:20150820-094455406
Authors: {'items': [{'id': 'Conti-S', 'name': {'family': 'Conti', 'given': 'Sergio'}, 'orcid': '0000-0001-7987-9174'}, {'id': 'Garroni-A', 'name': {'family': 'Garroni', 'given': 'Adriana'}}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'Michael'}, 'orcid': '0000-0001-5877-4824'}]}
Year: 2015
DOI: 10.1007/s00205-015-0869-7
We prove that the classical line-tension approximation for dislocations in crystals, that is, the approximation that neglects interactions at a distance between dislocation segments and accords dislocations energy in proportion to their length, follows as the Γ-limit of regularized linear-elasticity as the lattice parameter becomes increasingly small or, equivalently, as the dislocation measure becomes increasingly dilute. We consider two regularizations of the theory of linear-elastic dislocations: a core-cutoff and a mollification of the dislocation measure. We show that both regularizations give the same energy in the limit, namely, an energy defined on matrix-valued divergence-free measures concentrated on lines. The corresponding self-energy per unit length ψ(b,t), which depends on the local Burgers vector and orientation of the dislocation, does not, however, necessarily coincide with the self-energy per unit length ψ0(b,t) obtained from the classical theory of the prelogarithmic factor of linear-elastic straight dislocations. Indeed, microstructure can occur at small scales resulting in a further relaxation of the classical energy down to its H1-elliptic envelope.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/jx4ae-h9s63Finite-temperature non-equilibrium quasi-continuum analysis of nanovoid growth in copper at low and high strain rates
https://resolver.caltech.edu/CaltechAUTHORS:20151016-125346179
Authors: {'items': [{'id': 'Ponga-M', 'name': {'family': 'Ponga', 'given': 'M.'}, 'orcid': '0000-0001-5058-1454'}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'M.'}, 'orcid': '0000-0001-5877-4824'}, {'id': 'Ariza-M-P', 'name': {'family': 'Ariza', 'given': 'M. P.'}, 'orcid': '0000-0003-0266-0216'}]}
Year: 2015
DOI: 10.1016/j.mechmat.2015.02.007
We study dynamic nanovoid growth in copper single crystals under prescribed volumetric strain rates ranging from moderate (∊̇=10^5 s^(-1)) to high (∊̇=10^(10)s^(-1)). We gain access to lower strain rates by accounting for thermal vibrations in an entropic sense within the framework of maximum-entropy non-equilibrium statistical mechanics. We additionally account for heat conduction by means of empirical atomic-level kinetic laws. The resulting mean trajectories of the atoms are smooth and can be integrated implicitly using large time steps, greatly in excess of those required by molecular dynamics. We also gain access to large computational cells by means of spatial coarse-graining using the quasicontinuum method. On this basis, we identify a transition, somewhere between 10^7 and 10^8 s^(−1), between two regimes: a quasistatic regime characterized by nearly isothermal behavior and low dislocation velocities; and a dynamic regime characterized by nearly adiabatic conditions and high dislocation velocities. We also elucidate the precise mechanisms underlying dislocation emission from the nanovoids during cavitation. We additionally investigate the sensitivity of the results of the analysis to the choice of interatomic potential by comparing two EAM-type potentials.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/4cmbz-ydp90A nonlocal model of fracture by crazing in polymers
https://resolver.caltech.edu/CaltechAUTHORS:20151016-131555916
Authors: {'items': [{'id': 'Heyden-S', 'name': {'family': 'Heyden', 'given': 'S.'}, 'orcid': '0000-0002-7035-7975'}, {'id': 'Conti-S', 'name': {'family': 'Conti', 'given': 'S.'}, 'orcid': '0000-0001-7987-9174'}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'M.'}, 'orcid': '0000-0001-5877-4824'}]}
Year: 2015
DOI: 10.1016/j.mechmat.2015.02.006
We derive and numerically verify scaling laws for the macroscopic fracture energy of polymers undergoing crazing from a micromechanical model of damage. The model posits a local energy density that generalizes the classical network theory of polymers so as to account for chain failure and a nonlocal regularization based on strain-gradient elasticity. We specifically consider periodic deformations of a slab subject to prescribed opening displacements on its surfaces. Based on the growth properties of the energy densities, scaling relations for the local and nonlocal energies and for the specific fracture energy are derived. We present finite-element calculations that bear out the heuristic scaling relations.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/xfzmp-dvx67Investigation of elastic wave transmission in a metaconcrete slab
https://resolver.caltech.edu/CaltechAUTHORS:20160107-133701732
Authors: {'items': [{'id': 'Mitchell-S-J', 'name': {'family': 'Mitchell', 'given': 'Stephanie J.'}}, {'id': 'Pandolfi-A', 'name': {'family': 'Pandolfi', 'given': 'Anna'}, 'orcid': '0000-0002-7084-7456'}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'Michael'}, 'orcid': '0000-0001-5877-4824'}]}
Year: 2015
DOI: 10.1016/j.mechmat.2015.08.004
A new type of modified concrete, termed metaconcrete, has been shown to exhibit trapping of wave energy and a reduction in mortar stress when subjected to dynamic loading. Metaconcrete replaces the standard stone and gravel aggregates of regular concrete with spherical inclusions consisting of a heavy core coated with a compliant outer layer. These new layered aggregates resonate at designed frequencies by allowing for relative motion between the heavy core and the mortar matrix, which causes the aggregate to absorb energy and therefore reduce stress within the mortar phase of the composite material. The transmission of wave energy through a metaconcrete slab can be used to visualize the effect of resonant behavior within the metaconcrete aggregates. To quantify this behavior we compute a transmission coefficient, which is a method of measuring the absorption of wave energy as an applied forcing of known frequency travels through the material. The transmission coefficient is plotted against forcing frequency for four different aggregate material and geometry configurations. A reduction in transmission ratio is observed at or near the computed natural modes of the aggregate, indicating the activation of resonance within the inclusions. This behavior is consistent with observations from studies on sonic metamaterials containing resonant inclusions with a similar layered structure. The frequency location and width of the dip in transmission coefficient will aid in the design of metaconcrete aggregates for specific forcing applications.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/rjwaf-a5619Material modeling of cardiac valve tissue: Experiments, constitutive analysis and numerical investigation
https://resolver.caltech.edu/CaltechAUTHORS:20151130-103341973
Authors: {'items': [{'id': 'Heyden-S', 'name': {'family': 'Heyden', 'given': 'Stefanie'}, 'orcid': '0000-0002-7035-7975'}, {'id': 'Nagler-A', 'name': {'family': 'Nagler', 'given': 'Andreas'}}, {'id': 'Bertoglio-C', 'name': {'family': 'Bertoglio', 'given': 'Cristóbal'}}, {'id': 'Biehler-J', 'name': {'family': 'Biehler', 'given': 'Jonas'}}, {'id': 'Gee-M-W', 'name': {'family': 'Gee', 'given': 'Michael W.'}}, {'id': 'Wall-W-A', 'name': {'family': 'Wall', 'given': 'Wolfgang A.'}}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'Michael'}, 'orcid': '0000-0001-5877-4824'}]}
Year: 2015
DOI: 10.1016/j.jbiomech.2015.10.043
A key element of the cardiac cycle of the human heart is the opening and closing of the four valves. However, the material properties of the leaflet tissues, which fundamentally contribute to determine the mechanical response of the valves, are still an open field of research. The main contribution of the present study is to provide a complete experimental data set for porcine heart valve samples spanning all valve and leaflet types under tensile loading. The tests show a fair degree of reproducibility and are clearly indicative of a number of fundamental tissue properties, including a progressively stiffening response with increasing elongation. We then propose a simple anisotropic constitutive model, which is fitted to the experimental data set, showing a reasonable interspecimen variability. Furthermore, we present a dynamic finite element analysis of the aortic valve to show the direct usability of the obtained material parameters in computational simulations.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/73ex5-zx788Optimal Scaling in Solids Undergoing Ductile Fracture by Crazing
https://resolver.caltech.edu/CaltechAUTHORS:20160128-110737717
Authors: {'items': [{'id': 'Conti-S', 'name': {'family': 'Conti', 'given': 'Sergio'}, 'orcid': '0000-0001-7987-9174'}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'Michael'}, 'orcid': '0000-0001-5877-4824'}]}
Year: 2016
DOI: 10.1007/s00205-015-0901-y
We derive optimal scaling laws for the macroscopic fracture energy of polymers failing by crazing. We assume that the effective deformation-theoretical free-energy density is additive in the first and fractional deformation-gradients, with zero growth in the former and linear growth in the latter. The specific problem considered concerns a material sample in the form of an infinite slab of finite thickness subjected to prescribed opening displacements on its two surfaces. For this particular geometry, we derive optimal scaling laws for the dependence of the specific fracture energy on cross-sectional area, micromechanical parameters, opening displacement and intrinsic length of the material. In particular, the upper bound is obtained by means of a construction of the crazing type.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/1bdxm-any26The optimal uncertainty algorithm in the mystic framework
https://resolver.caltech.edu/CaltechAUTHORS:20160224-080348129
Authors: {'items': [{'id': 'McKerns-M', 'name': {'family': 'McKerns', 'given': 'M.'}}, {'id': 'Owhadi-H', 'name': {'family': 'Owhadi', 'given': 'H.'}, 'orcid': '0000-0002-5677-1600'}, {'id': 'Scovel-C', 'name': {'family': 'Scovel', 'given': 'C.'}, 'orcid': '0000-0001-7757-3411'}, {'id': 'Sullivan-T-J', 'name': {'family': 'Sullivan', 'given': 'T. J.'}}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'M.'}, 'orcid': '0000-0001-5877-4824'}]}
Year: 2016
DOI: 10.48550/arXiv.1202.1055
We have recently proposed a rigorous framework for Uncertainty Quantification (UQ) in which UQ objectives and assumption/information set are brought into
the forefront, providing a framework for the communication and comparison of UQ
results. In particular, this framework does not implicitly impose inappropriate assumptions nor does it repudiate relevant information.
This framework, which we call Optimal Uncertainty Quantification (OUQ), is
based on the observation that given a set of assumptions and information, there
exist bounds on uncertainties obtained as values of optimization problems and that
these bounds are optimal. It provides a uniform environment for the optimal solution of the problems of validation, certification, experimental design, reduced order
modeling, prediction, extrapolation, all under aleatoric and epistemic uncertainties.
OUQ optimization problems are extremely large, and even though under general
conditions they have finite-dimensional reductions, they must often be solved numerically. This general algorithmic framework for OUQ has been implemented in the
mystic optimization framework. We describe this implementation, and demonstrate
its use in the context of the Caltech surrogate model for hypervelocity impact.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/qffgv-kme54Effect of Brittle Fracture in a Metaconcrete Slab under Shock Loading
https://resolver.caltech.edu/CaltechAUTHORS:20160425-142101643
Authors: {'items': [{'id': 'Mitchell-S-J', 'name': {'family': 'Mitchell', 'given': 'Stephanie J.'}}, {'id': 'Pandolfi-A', 'name': {'family': 'Pandolfi', 'given': 'Anna'}, 'orcid': '0000-0002-7084-7456'}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'Michael'}, 'orcid': '0000-0001-5877-4824'}]}
Year: 2016
DOI: 10.1061/(ASCE)EM.1943-7889.0001034
A new type of concrete, named metaconcrete, has been developed for the attenuation of shock waves induced by dynamic excitation. Inspired by the metamaterials used for the manipulation of electromagnetic and acoustic waves, this new metamaterial for the mitigation of shock waves utilizes the activation of resonance within engineered inclusions. Metaconcrete replaces the standard stone and gravel aggregates of regular concrete with spherical inclusions consisting of a heavy core coated in a compliant outer layer. Finite-element analyses of metaconcrete slabs for the case of purely elastic constituents reveal trapping of the supplied energy within the inclusions and a reduction in mortar stress, indicating the presence of resonance behavior within the aggregates. Mortar is, however, a brittle material and the fracture properties under dynamic loading should also be considered. Thus, the models used in the elastic analyses are extended by incorporating brittle fracture through the use of an eigenerosion scheme, which erodes elements satisfying an energy-based fracture criterion. The effect of different fracture parameters on the performance of the slab is investigated through parametric studies, looking at the change in slab behavior caused by various aggregate geometry and material configurations. These studies indicate that mechanical energy is captured by the aggregates, reducing the transmission of energy through the slab, the extension of the zone damaged by fracture, and the longitudinal stress within the mortar matrix. The understanding gained from these analyses incorporating fracture characteristics will enable more informed design of metaconcrete aggregates for dynamic loading applications, such as blast shielding and impact protection.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/bahq0-1s089An analytical model of interfacial energy based on a lattice-matching interatomic energy
https://resolver.caltech.edu/CaltechAUTHORS:20160301-092051608
Authors: {'items': [{'id': 'Runnels-B', 'name': {'family': 'Runnels', 'given': 'Brandon'}}, {'id': 'Beyerlein-I-J', 'name': {'family': 'Beyerlein', 'given': 'Irene J.'}}, {'id': 'Conti-S', 'name': {'family': 'Conti', 'given': 'Sergio'}, 'orcid': '0000-0001-7987-9174'}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'Michael'}, 'orcid': '0000-0001-5877-4824'}]}
Year: 2016
DOI: 10.1016/j.jmps.2016.01.008
We develop an explicit model for the interfacial energy in crystals that emphasizes the geometric origin of the cusps in the energy profile. We start by formulating a general class of interatomic energies that are reference-configuration-free but explicitly incorporate the lattice geometry of the ground state. In particular, away from the interface the energy is minimized by a perfect lattice. We build these attributes into the energy by locally matching, as best as possible, a perfect lattice to the atomic positions and then quantifying the local energy in terms of the inevitable remaining mismatch, hence the term lattice-matching used to describe the resulting interatomic energy. Based on this general energy, we formulate a simpler rigid-lattice model in which the atomic positions on both sides of the interface coincide with perfect, but misoriented, lattices. In addition, we restrict the lattice-matching operation to a binary choice between the perfect lattices on both sides of the interface. Finally, we prove an L^2-bound on the interatomic energy and use that bound as a basis for comparison with experiment. We specifically consider symmetric tilt grain boundaries (STGB), symmetric twist grain boundaries (STwGB) and asymmetric twist grain boundaries (ATwGB) in face-centered cubic (FCC) and body-centered cubic (BCC) crystals. Two or more materials are considered for each choice of crystal structure and boundary class, with the choice of materials conditioned by the availability of molecular dynamics data. Despite the approximations made, we find very good overall agreement between the predicted interfacial energy structure and that calculated by molecular dynamics. In particular, the positions of the cusps are predicted well, and therefore, although surface reconstruction and faceting are not included in the model, the dominant orientations of the facets are correctly predicted by our geometrical model.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/e0zmw-w8668A numerical method for the time coarsening of transport processes at the atomistic scale
https://resolver.caltech.edu/CaltechAUTHORS:20160602-154054144
Authors: {'items': [{'id': 'Gonzalez-Ferreiro-B', 'name': {'family': 'Gonzalez-Ferreiro', 'given': 'B.'}}, {'id': 'Romero-I', 'name': {'family': 'Romero', 'given': 'I.'}, 'orcid': '0000-0003-0364-6969'}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'M.'}, 'orcid': '0000-0001-5877-4824'}]}
Year: 2016
DOI: 10.1088/0965-0393/24/4/045011
We propose a novel numerical scheme for the simulation of slow transport processes at the atomistic scale. The scheme is based on a model for non-equilibrium statistical thermodynamics recently proposed by the authors, and extends it by formulating a variational integrator, i.e. a discrete functional whose optimality conditions provide all the governing equations of the problem. The method is employed to study surface segregation of AuAg alloys and its convergence is confirmed numerically.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/b24sn-bdr03Morphing surfaces for the control of boundary layer transition
https://resolver.caltech.edu/CaltechAUTHORS:20200224-133536093
Authors: {'items': [{'id': 'McKeon-B-J', 'name': {'family': 'McKeon', 'given': 'Beverley'}, 'orcid': '0000-0003-4220-1583'}, {'id': 'Bhattacharya-K', 'name': {'family': 'Bhattacharya', 'given': 'Kaushik'}, 'orcid': '0000-0003-2908-5469'}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'Michael'}, 'orcid': '0000-0001-5877-4824'}]}
Year: 2016
A structure configured to modify its surface morphology between a smooth state and a rough state in response to an applied stress. In demonstrated examples, a soft (PDMS) substrate is produced, and is pre-strained. A relatively stiff overlayer of a metal, such as chromium and gold, is applied to the substrate. When the pre-strained substrate is allowed to relax, the free surface of the stiff overlayer is forced to become distorted, yielding a free surface having a roughness of less than 1 millimeter. Repeated application and removal of the applied stress has been shown to yield reproducible changes in the morphology of the free surface. An application of such morphing free surface is to control a boundary layer transition of an aerodynamic fluid flowing over the surface.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/91ahb-x7g76Data-driven computational mechanics
https://resolver.caltech.edu/CaltechAUTHORS:20160316-133550600
Authors: {'items': [{'id': 'Kirchdoerfer-T', 'name': {'family': 'Kirchdoerfer', 'given': 'T.'}}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'M.'}, 'orcid': '0000-0001-5877-4824'}]}
Year: 2016
DOI: 10.1016/j.cma.2016.02.001
We develop a new computing paradigm, which we refer to as data-driven computing, according to which calculations are carried out directly from experimental material data and pertinent constraints and conservation laws, such as compatibility and equilibrium, thus bypassing the empirical material modeling step of conventional computing altogether. Data-driven solvers seek to assign to each material point the state from a prespecified data set that is closest to satisfying the conservation laws. Equivalently, data-driven solvers aim to find the state satisfying the conservation laws that is closest to the data set. The resulting data-driven problem thus consists of the minimization of a distance function to the data set in phase space subject to constraints introduced by the conservation laws. We motivate the data-driven paradigm and investigate the performance of data-driven solvers by means of two examples of application, namely, the static equilibrium of nonlinear three-dimensional trusses and linear elasticity. In these tests, the data-driven solvers exhibit good convergence properties both with respect to the number of data points and with regard to local data assignment. The variational structure of the data-driven problem also renders it amenable to analysis. We show that, as the data set approximates increasingly closely a classical material law in phase space, the data-driven solutions converge to the classical solution. We also illustrate the robustness of data-driven solvers with respect to spatial discretization. In particular, we show that the data-driven solutions of finite-element discretizations of linear elasticity converge jointly with respect to mesh size and approximation by the data set.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/55gep-p9r83Oncotripsy: Targeting cancer cells selectively via resonant harmonic excitation
https://resolver.caltech.edu/CaltechAUTHORS:20160502-083438790
Authors: {'items': [{'id': 'Heyden-S', 'name': {'family': 'Heyden', 'given': 'S.'}, 'orcid': '0000-0002-7035-7975'}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'M.'}, 'orcid': '0000-0001-5877-4824'}]}
Year: 2016
DOI: 10.1016/j.jmps.2016.04.016
We investigate a method of selectively targeting cancer cells by means of ultrasound harmonic excitation at their resonance frequency, which we refer to as oncotripsy. The geometric model of the cells takes into account the cytoplasm, nucleus and nucleolus, as well as the plasma membrane and nuclear envelope. Material properties are varied within a pathophysiologically-relevant range. A first modal analysis reveals the existence of a spectral gap between the natural frequencies and, most importantly, resonant growth rates of healthy and cancerous cells. The results of the modal analysis are verified by simulating the fully-nonlinear transient response of healthy and cancerous cells at resonance. The fully nonlinear analysis confirms that cancerous cells can be selectively taken to lysis by the application of carefully tuned ultrasound harmonic excitation while simultaneously leaving healthy cells intact.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/zyaez-qmt20Dynamic behavior of nano-voids in magnesium under hydrostatic tensile stress
https://resolver.caltech.edu/CaltechAUTHORS:20160729-162325302
Authors: {'items': [{'id': 'Ponga-M', 'name': {'family': 'Ponga', 'given': 'Mauricio'}, 'orcid': '0000-0001-5058-1454'}, {'id': 'Ramabathiran-A-A', 'name': {'family': 'Ramabathiran', 'given': 'Amuthan A.'}}, {'id': 'Bhattacharya-K', 'name': {'family': 'Bhattacharya', 'given': 'Kaushik'}, 'orcid': '0000-0003-2908-5469'}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'Michael'}, 'orcid': '0000-0001-5877-4824'}]}
Year: 2016
DOI: 10.1088/0965-0393/24/6/065003
We investigate the mechanisms responsible for nano-void growth in single crystal magnesium under dynamic hydrostatic tensile stress. A key conclusion derived from our study is that there is no secondary strain hardening near the nano-void. This behavior, which is in remarkable contrast to face-centered cubic and body-centered cubic materials, greatly limits the peak stress and explains the relatively lower spall strength of magnesium. The lack of secondary strain hardening is due to the fact that pyramidal dislocations do not interact with basal or prismatic dislocations. Our analysis also shows that for loads applied at moderate strain rates (ϵ ⩽ 10^6 s^(−1)) the peak stress, dislocation velocity and temperature distribution converge asymptotically. However at very high strain rates (ϵ ⩾ 10^8 s^(−1)), there is a sharp transition in these quantities.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/8wm9s-5n146A Variational Framework for Spectral Approximations of Kohn–Sham Density Functional Theory
https://resolver.caltech.edu/CaltechAUTHORS:20160523-075651915
Authors: {'items': [{'id': 'Wang-Xin-Cindy', 'name': {'family': 'Wang', 'given': 'Xin-Cindy'}, 'orcid': '0000-0003-3854-4831'}, {'id': 'Blesgen-T', 'name': {'family': 'Blesgen', 'given': 'Thomas'}}, {'id': 'Bhattacharya-K', 'name': {'family': 'Bhattacharya', 'given': 'Kaushik'}, 'orcid': '0000-0003-2908-5469'}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'Michael'}, 'orcid': '0000-0001-5877-4824'}]}
Year: 2016
DOI: 10.1007/s00205-016-0978-y
We reformulate the Kohn–Sham density functional theory (KSDFT) as a nested variational problem in the one-particle density operator, the electrostatic potential and a field dual to the electron density. The corresponding functional is linear in the density operator and thus amenable to spectral representation. Based on this reformulation, we introduce a new approximation scheme, termed spectral binning, which does not require smoothing of the occupancy function and thus applies at arbitrarily low temperatures. We prove convergence of the approximate solutions with respect to spectral binning and with respect to an additional spatial discretization of the domain.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/1qh75-bs514A relaxation method for the energy and morphology of grain boundaries and interfaces
https://resolver.caltech.edu/CaltechAUTHORS:20160930-092102044
Authors: {'items': [{'id': 'Runnels-B', 'name': {'family': 'Runnels', 'given': 'Brandon'}}, {'id': 'Beyerlein-I-J', 'name': {'family': 'Beyerlein', 'given': 'Irene J.'}}, {'id': 'Conti-S', 'name': {'family': 'Conti', 'given': 'Sergio'}, 'orcid': '0000-0001-7987-9174'}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'Michael'}, 'orcid': '0000-0001-5877-4824'}]}
Year: 2016
DOI: 10.1016/j.jmps.2015.11.007
The energy density of crystal interfaces exhibits a characteristic "cusp" structure that renders it non-convex. Furthermore, crystal interfaces are often observed to be faceted, i.e., to be composed of flat facets in alternating directions. In this work, we forge a connection between these two observations by positing that the faceted morphology of crystal interfaces results from energy minimization. Specifically, we posit that the lack of convexity of the interfacial energy density drives the development of finely faceted microstructures and accounts for their geometry and morphology. We formulate the problem as a generalized minimal surface problem couched in a geometric measure-theoretical framework. We then show that the effective, or relaxed, interfacial energy density, with all possible interfacial morphologies accounted for, corresponds to the convexification of the bare or unrelaxed interfacial energy density, and that the requisite convexification can be attained by means of a faceting construction. We validate the approach by means of comparisons with experiment and atomistic simulations including symmetric and asymmetric tilt boundaries in face-centered cubic (FCC) and body-centered cubic (BCC) crystals. By comparison with simulated and experimental data, we show that this simple model of interfacial energy combined with a general microstructure construction based on convexification is able to replicate complex interfacial morphologies, including thermally induced morphological transitions.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/ngg7g-ewn66Computational multiobjective topology optimization of silicon anode structures for lithium-ion batteries
https://resolver.caltech.edu/CaltechAUTHORS:20160718-102711891
Authors: {'items': [{'id': 'Mitchell-S-L', 'name': {'family': 'Mitchell', 'given': 'Sarah L.'}}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'Michael'}, 'orcid': '0000-0001-5877-4824'}]}
Year: 2016
DOI: 10.1016/j.jpowsour.2016.06.136
This study utilizes computational topology optimization methods for the systematic design of optimal multifunctional silicon anode structures for lithium-ion batteries. In order to develop next generation high performance lithium-ion batteries, key design challenges relating to the silicon anode structure must be addressed, namely the lithiation-induced mechanical degradation and the low intrinsic electrical conductivity of silicon. As such this work considers two design objectives, the first being minimum compliance under design dependent volume expansion, and the second maximum electrical conduction through the structure, both of which are subject to a constraint on material volume. Density-based topology optimization methods are employed in conjunction with regularization techniques, a continuation scheme, and mathematical programming methods. The objectives are first considered individually, during which the influence of the minimum structural feature size and prescribed volume fraction are investigated. The methodology is subsequently extended to a bi-objective formulation to simultaneously address both the structural and conduction design criteria. The weighted sum method is used to derive the Pareto fronts, which demonstrate a clear trade-off between the competing design objectives. A rigid frame structure was found to be an excellent compromise between the structural and conduction design criteria, providing both the required structural rigidity and direct conduction pathways. The developments and results presented in this work provide a foundation for the informed design and development of silicon anode structures for high performance lithium-ion batteries.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/fp2zy-dcb78Effect of prestress on the stability of electrode–electrolyte interfaces during charging in lithium batteries
https://resolver.caltech.edu/CaltechAUTHORS:20160620-075212141
Authors: {'items': [{'id': 'Natsiavas-P-P', 'name': {'family': 'Natsiavas', 'given': 'P. P.'}}, {'id': 'Weinberg-K', 'name': {'family': 'Weinberg', 'given': 'K.'}}, {'id': 'Rosato-D', 'name': {'family': 'Rosato', 'given': 'D.'}}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'M.'}, 'orcid': '0000-0001-5877-4824'}]}
Year: 2016
DOI: 10.1016/j.jmps.2016.05.007
We formulate a model of the growth of electrode–electrolyte interfaces in lithium batteries in the presence of an elastic prestress. The model accounts for the kinetics of Li+ transport through a solid electrolyte and, within the interface, for the kinetics of Li^+ adsorption by the anode, electrostatics, and the elastic field. We specifically account for the effect of the elastic field through an asymptotic analysis of a nearly flat interface between two semi-infinite elastic bodies. We use the model as a basis for assessing the effect of prestress on the stability of planar growth and the potential of prestress as a means of suppressing the formation of deleterious dendrites. We present a linear stability analysis that results in explicit analytical expressions for the dependence of growth rates, and of the critical unstable wavelength for the interfacial roughening, on the state of prestress and on fundamental parameters such as surface diffusivities, surface energy, deposition kinetics, and elastic moduli. Finally, we examine the model in the light of experimental observations concerned with the effect of applied pressure on a lithium/dioxolane-dimethoxy ethane electrolyte systems. With reasonable choices of parameters and some calibration, the model accounts for the observation that a modest applied pressure indeed results in a substantial reduction in the roughening of the lithium surface during cycling.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/ky8ty-n5a87A sublinear-scaling approach to density-functional-theory analysis of crystal defects
https://resolver.caltech.edu/CaltechAUTHORS:20161006-104337036
Authors: {'items': [{'id': 'Ponga-M', 'name': {'family': 'Ponga', 'given': 'M.'}, 'orcid': '0000-0001-5058-1454'}, {'id': 'Bhattacharya-K', 'name': {'family': 'Bhattacharya', 'given': 'K.'}, 'orcid': '0000-0003-2908-5469'}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'M.'}, 'orcid': '0000-0001-5877-4824'}]}
Year: 2016
DOI: 10.1016/j.jmps.2016.05.029
We develop a sublinear-scaling method, referred to as MacroDFT, for the study of crystal defects using ab-initio Density Functional Theory (DFT). The sublinear scaling is achieved using a combination of the Linear Scaling Spectral Gauss Quadrature method (LSSGQ) and a Coarse-Graining approach (CG) based on the quasi-continuum method. LSSGQ reformulates DFT and evaluates the electron density without computing individual orbitals. This direct evaluation is possible by recourse to Gaussian quadrature over the spectrum of the linearized Hamiltonian operator. Furthermore, the nodes and weights of the quadrature can be computed independently for each point in the domain. This property is exploited in CG, where fields of interest are computed at selected nodes and interpolated elsewhere. In this paper, we present the MacroDFT method, its parallel implementation and an assessment of convergence and performance by means of test cases concerned with point defects in magnesium.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/gnfy7-ppc38All-atom molecular dynamics simulations of multiphase segregated polyurea under quasistatic, adiabatic, uniaxial compression
https://resolver.caltech.edu/CaltechAUTHORS:20161121-081314774
Authors: {'items': [{'id': 'Heyden-S', 'name': {'family': 'Heyden', 'given': 'S.'}, 'orcid': '0000-0002-7035-7975'}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'M.'}, 'orcid': '0000-0001-5877-4824'}, {'id': 'Fortunelli-A', 'name': {'family': 'Fortunelli', 'given': 'A.'}, 'orcid': '0000-0001-5337-4450'}]}
Year: 2016
DOI: 10.1016/j.polymer.2016.10.053
We present an approach to model the mechanical response of multiphase segregated polyurea under large quasistatic uniaxial compression. The approach is based on a two-step procedure. We first conduct all-atom NVE molecular dynamics simulations of the fully-mixed and hard phases of polyurea. We then put forth a model of hard-phase activation based on Taylor, or meanfield, averaging and compute the composite response. The predictions of the present approach, with or without Taylor averaging, show remarkable agreement with data from plate-impact experiments.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/bkdpq-bjb35A linearized porous brittle damage material model with distributed frictional-cohesive faults
https://resolver.caltech.edu/CaltechAUTHORS:20170119-123323401
Authors: {'items': [{'id': 'De-Bellis-M-L', 'name': {'family': 'De Bellis', 'given': 'M. L.'}}, {'id': 'Della-Vecchia-G', 'name': {'family': 'Della Vecchia', 'given': 'G.'}}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'M.'}, 'orcid': '0000-0001-5877-4824'}, {'id': 'Pandolfi-A', 'name': {'family': 'Pandolfi', 'given': 'A.'}, 'orcid': '0000-0002-7084-7456'}]}
Year: 2016
DOI: 10.1016/j.enggeo.2016.10.010
We present a simplified model of damaging porous material, obtained through consistent linearization from a recursive-faulting material model described in (Pandolfi et al. 2016). The brittle damage material model is characterized by special planar micro-structures, consisting of nested families of equi-spaced frictional-cohesive faults in an otherwise elastic matrix material. The linear kinematics model preserves the main microstructural features of the finite kinematics one but offers a far better computational performance. Unlike models commonly employed in geo-mechanical applications, the proposed model contains a small number of parameters, to wit, two elastic moduli, three frictional-cohesive parameters, and three hydraulic response parameters, all of which having clear physical meanings and amenable to direct experimental measurement through standard material tests. The model is validated by comparison to triaxial hydro-mechanical experimental data. Despite the paucity of material constants, the salient aspects of the observed behavior are well captured by the model, qualitatively and quantitatively. As an example of application of the model, we simulate the excavation of a borehole in a rocky embankment.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/d6mqy-an048Method for the quantification of rupture probability in soft collagenous tissues
https://resolver.caltech.edu/CaltechAUTHORS:20160307-085012921
Authors: {'items': [{'id': 'Balzani-D', 'name': {'family': 'Balzani', 'given': 'D.'}}, {'id': 'Schmidt-B', 'name': {'family': 'Schmidt', 'given': 'T.'}}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'M.'}, 'orcid': '0000-0001-5877-4824'}]}
Year: 2017
DOI: 10.1002/cnm.2781
A computational method is presented for the assessment of rupture probabilities in soft collagenous tissues. This may in particular be important for the quantitative analysis of medical diseases such as atherosclerotic arteries or abdominal aortic aneurysms, where an unidentified rupture has in most cases fatal consequences. The method is based on the numerical minimization and maximization of probabilities of failure, which arise from random input quantities, for example, tissue properties. Instead of assuming probability distributions for these quantities, which are typically unknown especially for soft collagenous tissues, only restricted knowledge of these distributions is taken into account. Given this limited statistical input data, the minimized/maximized probabilities represent optimal bounds on the rupture probability, which enable a quantitative estimation of potential risks of performing or not performing medical treatment. Although easily extendable to all kinds of mechanical rupture criteria, the approach presented here incorporates stretch-based and damage-based criteria. These are evaluated based on numerical simulations of loaded tissues, where continuum mechanical material formulations are considered, which capture the supra-physiological behavior of soft collagenous tissues. Numerical examples are provided demonstrating the applicability of the method in an overstretched atherosclerotic artery.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/nhs3m-1kb11Spectrum-splitting approach for Fermi-operator expansion in all-electron Kohn-Sham DFT calculations
https://resolver.caltech.edu/CaltechAUTHORS:20161012-162032480
Authors: {'items': [{'id': 'Motamarri-P', 'name': {'family': 'Motamarri', 'given': 'Phani'}}, {'id': 'Gavini-V', 'name': {'family': 'Gavini', 'given': 'Vikram'}}, {'id': 'Bhattacharya-K', 'name': {'family': 'Bhattacharya', 'given': 'Kaushik'}, 'orcid': '0000-0003-2908-5469'}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'Michael'}, 'orcid': '0000-0001-5877-4824'}]}
Year: 2017
DOI: 10.1103/PhysRevB.95.035111
We present a spectrum-splitting approach to conduct all-electron Kohn-Sham density functional theory (DFT) calculations by employing Fermi-operator expansion of the Kohn-Sham Hamiltonian. The proposed approach splits the subspace containing the occupied eigenspace into a core subspace, spanned by the core eigenfunctions, and its complement, the valence subspace, and thereby enables an efficient computation of the Fermi-operator expansion by reducing the expansion to the valence-subspace projected Kohn-Sham Hamiltonian. The key ideas used in our approach are as follows: (i) employ Chebyshev filtering to compute a subspace containing the occupied states followed by a localization procedure to generate nonorthogonal localized functions spanning the Chebyshev-filtered subspace; (ii) compute the Kohn-Sham Hamiltonian projected onto the valence subspace; (iii) employ Fermi-operator expansion in terms of the valence-subspace projected Hamiltonian to compute the density matrix, electron density, and band energy. We demonstrate the accuracy and performance of the method on benchmark materials systems involving silicon nanoclusters up to 1330 electrons, a single gold atom, and a six-atom gold nanocluster. The benchmark studies on silicon nanoclusters revealed a staggering fivefold reduction in the Fermi-operator expansion polynomial degree by using the spectrum-splitting approach for accuracies in the ground-state energies of ∼10^(−4) Ha/atom with respect to reference calculations. Further, numerical investigations on gold suggest that spectrum splitting is indispensable to achieve meaningful accuracies, while employing Fermi-operator expansion.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/tqz39-kaw25Investigation of the influence of viscoelasticity on oncotripsy
https://resolver.caltech.edu/CaltechAUTHORS:20170302-082150368
Authors: {'items': [{'id': 'Heyden-S', 'name': {'family': 'Heyden', 'given': 'S.'}, 'orcid': '0000-0002-7035-7975'}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'M.'}, 'orcid': '0000-0001-5877-4824'}]}
Year: 2017
DOI: 10.1016/j.cma.2016.08.026
Oncotripsy has recently been proposed as a means of selectively targeting cancer cells via resonant harmonic excitation (Heyden and Ortiz, 2016). The method makes use of aberrations in material properties of cancerous cells which allow to induce local resonance up to membrane lysis in cancerous cells while leaving healthy cells intact. Here, we explore the influence of viscoelasticity on the oncotripsy effect. Based on Rayleigh damping, we derive viscoelastic target frequencies and simulate the fully nonlinear transient response of healthy and cancerous cells at resonance. Results confirm the viability of oncotripsy with viscoelastic material behavior of cell constituents accounted for.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/dv9yc-pfs18Experimental Validation of Metaconcrete Blast Mitigation Properties
https://resolver.caltech.edu/CaltechAUTHORS:20170331-074653697
Authors: {'items': [{'id': 'Briccola-D', 'name': {'family': 'Briccola', 'given': 'Deborah'}}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'Michael'}, 'orcid': '0000-0001-5877-4824'}, {'id': 'Pandolfi-A', 'name': {'family': 'Pandolfi', 'given': 'Anna'}, 'orcid': '0000-0002-7084-7456'}]}
Year: 2017
DOI: 10.1115/1.4035259
We provide experimental evidence of the mitigation properties of metaconcrete under blast loading. Mitigation is achieved through resonance of engineered aggregates consisting of a heavy and stiff core coated by a light and compliant outer layer. These engineered aggregates replace the standard gravel in conventional concrete. To assess experimentally the attenuation properties of metaconcrete, we have cast two batches of cylindrical specimens. The mortar matrix of the first batch consists of cement combined with a regular sand mix, while the mortar matrix of the second batch consists of cement combined with sand mix, fine gravel, and polymeric fibers. One of the specimens of each batch was cast with no aggregates, while the other two contained 40 and 60, respectively, randomly arranged 22 mm diameter commercially available computer mouse balls. We performed nondestructive dynamic tests by applying a 10 V amplitude periodic signal to one end of the specimens and measuring the amplitude of the transmitted signal received at the other end. We observed a remarkable 2 order of magnitude reduction in the amplitude of the transmitted signal in metaconcrete relative to conventional concrete.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/deyvw-ee421A multiscale model of distributed fracture and permeability in solids in all-round compression
https://resolver.caltech.edu/CaltechAUTHORS:20160316-140142435
Authors: {'items': [{'id': 'De-Bellis-M-L', 'name': {'family': 'De Bellis', 'given': 'Maria Laura'}}, {'id': 'Della-Vecchia-G', 'name': {'family': 'Della Vecchia', 'given': 'Gabriele'}}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'Michael'}, 'orcid': '0000-0001-5877-4824'}, {'id': 'Pandolfi-A', 'name': {'family': 'Pandolfi', 'given': 'Anna'}, 'orcid': '0000-0002-7084-7456'}]}
Year: 2017
DOI: 10.1016/j.jmps.2017.03.017
We present a microstructural model of permeability in fractured solids, where the fractures are described in terms of recursive families of parallel, equidistant cohesive faults. Faults originate upon the attainment of tensile or shear strength in the undamaged material. Secondary faults may form in a hierarchical organization, creating a complex network of connected fractures that modify the permeability of the solid. The undamaged solid may possess initial porosity and permeability. The particular geometry of the superposed micro-faults lends itself to an explicit analytical quantification of the porosity and permeability of the damaged material. The model is the finite kinematics version of a recently proposed porous material model, applied with success to the simulation of laboratory tests and excavation problems [De Bellis, M. L., Della Vecchia, G., Ortiz, M., Pandolfi, A., 2016. A linearized porous brittle damage material model with distributed frictional-cohesive faults. Engineering Geology 215, 10–24. Cited By 0. 10.1016/j.enggeo.2016.10.010]. The extension adds over and above the linearized kinematics version for problems characterized by large deformations localized in narrow zones, while the remainder of the solid undergoes small deformations, as typically observed in soil and rock mechanics problems. The approach is particularly appealing as a means of modeling a wide scope of engineering problems, ranging from the prevention of water or gas outburst into underground mines, to the prediction of the integrity of reservoirs for CO_2 sequestration or hazardous waste storage, to hydraulic fracturing processes.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/maqst-zk804A comparative study of nanovoid growth in FCC metals
https://resolver.caltech.edu/CaltechAUTHORS:20171117-145404249
Authors: {'items': [{'id': 'Ponga-M', 'name': {'family': 'Ponga', 'given': 'M.'}, 'orcid': '0000-0001-5058-1454'}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'M.'}, 'orcid': '0000-0001-5877-4824'}, {'id': 'Ariza-M-P', 'name': {'family': 'Ariza', 'given': 'M. P.'}, 'orcid': '0000-0003-0266-0216'}]}
Year: 2017
DOI: 10.1080/14786435.2017.1364437
Previous HotQC studies of Cu nanovoids undergoing volumetric expansion conducted by the authors have uncovered a quasistatic-to-dynamic transition at a critical strain rate of the order of 10^8 s^(-1). At low strain rates nanovoid expansion takes place under essentially isothermal conditions, whereas at high strain rates it happens under essential adiabatic conditions. In this paper, we present a comparative study concerned with two different scenarios, each representing a variation on the reference case presented in [1]: (i) aluminium (Al) nanovoids undergoing volumetric expansion; and (ii) copper (Cu) nanovoids undergoing uniaxial deformation. Scenario (i) addresses material specificity by replacing Cu by Al in the reference case, whereas scenario (ii) addresses the effect of triaxiality by replacing volumetric expansion by uniaxial expansion in the reference case. We find a distinct quasistatic-to-dynamic transition in both scenarios, which suggests that the transition is indeed universal, i.e. material and strain-triaxiality independent. By contrast, the fine structure of the dislocation mechanisms that mediate void growth are strongly material and loading specific.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/h3jpz-51q94Data-Driven Computing
https://resolver.caltech.edu/CaltechAUTHORS:20170912-142917371
Authors: {'items': [{'id': 'Kirchdoerfer-T', 'name': {'family': 'Kirchdoerfer', 'given': 'Trenton'}}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'Michael'}, 'orcid': '0000-0001-5877-4824'}]}
Year: 2017
DOI: 10.1007/978-3-319-60885-3_8
Data-Driven Computing is a new field of computational analysis which uses provided data to directly produce predictive outcomes. Recent works in this developing field have established important properties of Data-Driven solvers, accommodated noisy data sets and demonstrated both quasi-static and dynamic solutions within mechanics. This work reviews this initial progress and advances some of the many possible improvements and applications that might best advance the field. Possible method improvements discuss incorporation of data quality metrics, and adaptive data additions while new applications focus on multi-scale analysis and the need for public databases to support constitutive data collaboration.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/qe0da-6nc51Atomistic Simulation of Hydrogen Diffusion in Palladium Nanoparticles Using a Diffusive Molecular Dynamics Method
https://resolver.caltech.edu/CaltechAUTHORS:20180418-093213482
Authors: {'items': [{'id': 'Sun-Xingsheng', 'name': {'family': 'Sun', 'given': 'Xingsheng'}}, {'id': 'Ariza-P', 'name': {'family': 'Ariza', 'given': 'Pilar'}, 'orcid': '0000-0003-0266-0216'}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'Michael'}, 'orcid': '0000-0001-5877-4824'}, {'id': 'Wang-Kevin-G', 'name': {'family': 'Wang', 'given': 'Kevin G.'}}]}
Year: 2017
DOI: 10.1115/IMECE2017-71400
Understanding the transport of hydrogen within metals is crucial for the advancement of energy storage and the mitigation of hydrogen embrittlement. Using nanosized palladium particles as a model, recent experimental studies have revealed several highly nonlinear phenomena that occur over a long period of time. The time scale of these phenomena is beyond the capability of established atomistic models. In this work, we present the application of a new model, referred to as diffusive molecular dynamics (DMD), to simulating long-term diffusive mass transport at atomistic length scale. Specifically, we validate the model for the long-term dynamics of a single hydrogen atom on palladium lattice. We show that the DMD result is in satisfactory agreement with the result of the classical random walk model. Then, we apply the DMD model to simulate the absorption of hydrogen by a palladium nanocube with an edge length of 16 nm. We show that the absorption process is dominated by the propagation of a sharp, coherent α/β hydride phase boundary. We also characterize the local lattice deformation near the dynamic phase boundary using the mean positions of the palladium and hydrogen atoms.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/k0ms6-ffs72Data Driven Computing with Noisy Material Data Sets
https://resolver.caltech.edu/CaltechAUTHORS:20170612-102809775
Authors: {'items': [{'id': 'Kirchdoerfer-T', 'name': {'family': 'Kirchdoerfer', 'given': 'T.'}}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'M.'}, 'orcid': '0000-0001-5877-4824'}]}
Year: 2017
DOI: 10.1016/j.cma.2017.07.039
We formulate a Data Driven Computing paradigm, termed max-ent Data Driven Computing, that generalizes distance-minimizing Data Driven Computing and is robust with respect to outliers. Robustness is achieved by means of clustering analysis. Specifically, we assign data points a variable relevance depending on distance to the solution and on maximum-entropy estimation. The resulting scheme consists of the minimization of a suitably-defined free energy over phase space subject to compatibility and equilibrium constraints. Distance-minimizing Data Driven schemes are recovered in the limit of zero temperature. We present selected numerical tests that establish the convergence properties of the max-ent Data Driven solvers and solutions.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/wreft-4ra83Geometrically exact time-integration mesh-free schemes for advection-diffusion problems derived from optimal transportation theory and their connection with particle methods
https://resolver.caltech.edu/CaltechAUTHORS:20171106-141823774
Authors: {'items': [{'id': 'Fedeli-L', 'name': {'family': 'Fedeli', 'given': 'L.'}}, {'id': 'Pandolfi-A', 'name': {'family': 'Pandolfi', 'given': 'A.'}, 'orcid': '0000-0002-7084-7456'}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'M.'}, 'orcid': '0000-0001-5877-4824'}]}
Year: 2017
DOI: 10.1002/nme.5552
We develop an optimal transportation mesh-free particle method for advection-diffusion in which the concentration or density of the diffusive species is approximated by Dirac measures. We resort to an incremental variational principle for purposes of time discretization of the diffusive step. This principle characterizes the evolution of the density as a competition between the Wasserstein distance between two consecutive densities and entropy. Exploiting the structure of the Euler–Lagrange equations, we approximate the density as a collection of Diracs. The interpolation of the incremental transport map is effected through mesh-free max-ent interpolation. Remarkably, the resulting update is geometrically exact with respect to advection and volume. We present three-dimensional examples of application that illustrate the scope and robustness of the method.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/5snfz-xxa51Acceleration of diffusive molecular dynamics simulations through mean field approximation and subcycling time integration
https://resolver.caltech.edu/CaltechAUTHORS:20170912-141252063
Authors: {'items': [{'id': 'Sun-X', 'name': {'family': 'Sun', 'given': 'X.'}}, {'id': 'Ariza-M-P', 'name': {'family': 'Ariza', 'given': 'M. P.'}, 'orcid': '0000-0003-0266-0216'}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'M.'}, 'orcid': '0000-0001-5877-4824'}, {'id': 'Wang-K-G', 'name': {'family': 'Wang', 'given': 'K. G.'}}]}
Year: 2017
DOI: 10.1016/j.jcp.2017.08.069
Diffusive Molecular Dynamics (DMD) is a class of recently developed computational models for the simulation of long-term diffusive mass transport at atomistic length scales. Compared to previous atomistic models, e.g., transition state theory based accelerated molecular dynamics, DMD allows the use of larger time-step sizes, but has a higher computational complexity at each time-step due to the need to solve a nonlinear optimization problem at every time-step. This paper presents two numerical methods to accelerate DMD based simulations. First, we show that when a many-body potential function, e.g., embedded atom method (EAM), is employed, the cost of DMD is dominated by the computation of the mean of the potential function and its derivatives, which are high-dimensional random variables. To reduce the cost, we explore both first- and second-order mean field approximations. Specifically, we show that the first-order approximation, which uses a point estimate to calculate the mean, can reduce the cost by two to three orders of magnitude, but may introduce relatively large error in the solution. We show that adding an approximate second-order correction term can significantly reduce the error without much increase in computational cost. Second, we show that DMD can be significantly accelerated through subcycling time integration, as the cost of integrating the empirical diffusion equation is much lower than that of the optimization solver. To assess the DMD model and the numerical approximation methods, we present two groups of numerical experiments that simulate the diffusion of hydrogen in palladium nanoparticles. In particular, we show that the computational framework is capable of capturing the propagation of an atomically sharp phase boundary over a time window of more than 30 seconds. The effects of the proposed numerical methods on solution accuracy and computation time are also assessed quantitatively.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/hq0ce-jax03Proliferation of twinning in hexagonal close-packed metals: Application to magnesium
https://resolver.caltech.edu/CaltechAUTHORS:20171221-151321326
Authors: {'items': [{'id': 'Sun-Dingyi', 'name': {'family': 'Sun', 'given': 'D.'}}, {'id': 'Ponga-M', 'name': {'family': 'Ponga', 'given': 'M.'}, 'orcid': '0000-0001-5058-1454'}, {'id': 'Bhattacharya-K', 'name': {'family': 'Bhattacharya', 'given': 'K.'}, 'orcid': '0000-0003-2908-5469'}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'M.'}, 'orcid': '0000-0001-5877-4824'}]}
Year: 2018
DOI: 10.1016/j.jmps.2017.12.009
Plastic deformation of metallic alloys usually takes place through slip, but occasionally involves twinning. In particular, twinning is important in hexagonal close packed (HCP) materials where the easy slip systems are insufficient to accommodate arbitrary deformations. While deformation by slip mechanisms is reasonably well understood, comparatively less is known about deformation by twinning. Indeed, the identification of relevant twinning modes remains an art. In this paper, we develop a framework combining a fundamental kinematic definition of twins with large-scale atomistic calculations to predict twinning modes of crystalline materials. We apply this framework to magnesium where there are two accepted twin modes, tension and compression, but a number of anomalous observations. Remarkably, our framework shows that there is a very large number of twinning modes that are important in magnesium. Thus, in contrast to the traditional view that plastic deformation is kinematically partitioned between a few modes, our results suggest that deformation in HCP materials is the result of an energetic and kinetic competition between numerous possibilities. Consequently, our findings suggest that the commonly used models of deformation need to be extended in order to take into account a broader and richer variety of twin modes, which, in turn, opens up new avenues for improving the mechanical properties.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/8bvbe-ead24Long-term atomistic simulation of hydrogen absorption in palladium nanocubes using a diffusive molecular dynamics method
https://resolver.caltech.edu/CaltechAUTHORS:20180221-092513945
Authors: {'items': [{'id': 'Sun-Xingsheng', 'name': {'family': 'Sun', 'given': 'Xingsheng'}}, {'id': 'Ariza-P', 'name': {'family': 'Ariza', 'given': 'Pilar'}, 'orcid': '0000-0003-0266-0216'}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'Michael'}, 'orcid': '0000-0001-5877-4824'}, {'id': 'Wang-Kevin-G', 'name': {'family': 'Wang', 'given': 'Kevin G.'}}]}
Year: 2018
DOI: 10.1016/j.ijhydene.2018.01.169
Understanding the transport of hydrogen within metallic nanomaterials is crucial for the advancement of energy storage and the mitigation of hydrogen embrittlement. Using nanosized palladium particles as a model, recent experimental studies have revealed several interesting phenomena that occur over long time periods. The time scale of these phenomena is beyond the capability of established atomistic models such as molecular dynamics. In this work, we present the application of a new approach, referred to as diffusive molecular dynamics (DMD), to the simulation of long-term diffusive mass transport at the atomic scale. Specifically, we simulate the absorption of hydrogen by palladium nanocubes with edge lengths in the range of 4 nm and 16 nm. We find that the absorption process is dominated by the initiation and propagation of an atomistically sharp α/β Pd-H phase boundary, with thickness in the range of 0.2 to 1.0 nm, which separates an α phase core from a β phase shell. The evolution of phase boundary and the resulting local lattice deformation are described in this paper in detail. The effects of size on both equilibrium and kinetic properties are also assessed.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/sg2z7-egz27Data-Driven Computing in Dynamics
https://resolver.caltech.edu/CaltechAUTHORS:20171101-121627090
Authors: {'items': [{'id': 'Kirchdoerfer-T', 'name': {'family': 'Kirchdoerfer', 'given': 'T.'}}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'M.'}, 'orcid': '0000-0001-5877-4824'}]}
Year: 2018
DOI: 10.1002/nme.5716
We formulate extensions to Data Driven Computing for both distance minimizing and entropy maximizing schemes to incorporate time integration. Previous works focused on formulating both types of solvers in the presence of static equilibrium constraints. Here formulations assign data points a variable relevance depending on distance to the solution and on maximum-entropy weighting, with distance minimizing schemes discussed as a special case. The resulting schemes consist of the minimization of a suitably-defined free energy over phase space subject to compatibility and a time-discretized momentum conservation constraint. We present selected numerical tests that establish the convergence properties of both types of Data Driven solvers and solutions.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/zencs-p2246The anomalous yield behavior of fused silica glass
https://resolver.caltech.edu/CaltechAUTHORS:20180201-135857640
Authors: {'items': [{'id': 'Schill-W', 'name': {'family': 'Schill', 'given': 'W.'}}, {'id': 'Heyden-S', 'name': {'family': 'Heyden', 'given': 'S.'}, 'orcid': '0000-0002-7035-7975'}, {'id': 'Conti-S', 'name': {'family': 'Conti', 'given': 'S.'}, 'orcid': '0000-0001-7987-9174'}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'M.'}, 'orcid': '0000-0001-5877-4824'}]}
Year: 2018
DOI: 10.1016/j.jmps.2018.01.004
We develop a critical-state model of fused silica plasticity on the basis of data mined from molecular dynamics (MD) calculations. The MD data is suggestive of an irreversible densification transition in volumetric compression resulting in permanent, or plastic, densification upon unloading. The MD data also reveals an evolution towards a critical state of constant volume under pressure-shear deformation. The trend towards constant volume is from above, when the glass is overconsolidated, or from below, when it is underconsolidated. We show that these characteristic behaviors are well-captured by a critical state model of plasticity, where the densification law for glass takes the place of the classical consolidation law of granular media and the locus of constant-volume states defines the critical-state line. A salient feature of the critical-state line of fused silica, as identified from the MD data, that renders its yield behavior anomalous is that it is strongly non-convex, owing to the existence of two well-differentiated phases at low and high pressures. We argue that this strong non-convexity of yield explains the patterning that is observed in molecular dynamics calculations of amorphous solids deforming in shear. We employ an explicit and exact rank-2 envelope construction to upscale the microscopic critical-state model to the macroscale. Remarkably, owing to the equilibrium constraint the resulting effective macroscopic behavior is still characterized by a non-convex critical-state line. Despite this lack of convexity, the effective macroscopic model is stable against microstructure formation and defines well-posed boundary-value problems.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/fhfpr-3dd67CTH shock physics simulation of non-linear material effects within an aerospace CFRP fastener assembly due to direct lightning attachment
https://resolver.caltech.edu/CaltechAUTHORS:20180404-092418928
Authors: {'items': [{'id': 'Kirchdoerfer-T', 'name': {'family': 'Kirchdoerfer', 'given': 'T.'}}, {'id': 'Liebscher-A', 'name': {'family': 'Liebscher', 'given': 'A.'}}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'M.'}, 'orcid': '0000-0001-5877-4824'}]}
Year: 2018
DOI: 10.1016/j.compstruct.2017.11.061
This study examines detailed CTH simulation results of a carbon fiber composite panel assembly where the binding titanium fastener joint is the attachment point of a direct lightning strike. A refined COMSOL Multiphysics electromagnetics calculation is performed on the undeformed installed fastener geometry to obtain current and electric field solutions in time using SAE ARP5412B lightning test waveforms. Electro-mechanical coupling is achieved through the use of Joule heating resulting from J·E, the power per unit volume dispersed throughout the structure due to the lightning energy transport. The shock physics code CTH is used to model the fluid-structure calculations which involve highly non-linear and high temperature effects. Experimental data, in the form of material effects images, are used for validation of material and equation of state selections. Discussion of the effects created by the lightning energy depositions focuses primarily on gas conditions in the inner spaces surrounding the fastener and the associated local geometrical changes. The spatiotemporal pressure evolution within the fastener assembly cavities are compared with experimental results and the importance of modeling chemistry changes in future work are discussed within the conclusion.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/cgp7g-5zf23Diffusive molecular dynamics simulations of lithiation of silicon nanopillars
https://resolver.caltech.edu/CaltechAUTHORS:20180312-142155426
Authors: {'items': [{'id': 'Mendez-Granado-J-P', 'name': {'family': 'Mendez', 'given': 'J. P.'}, 'orcid': '0000-0002-9493-0879'}, {'id': 'Ponga-M', 'name': {'family': 'Ponga', 'given': 'M.'}, 'orcid': '0000-0001-5058-1454'}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'M.'}, 'orcid': '0000-0001-5877-4824'}]}
Year: 2018
DOI: 10.1016/j.jmps.2018.03.008
We report diffusive molecular dynamics simulations concerned with the lithiation of Si nano-pillars, i. e., nano-sized Si rods held at both ends by rigid supports. The duration of the lithiation process is of the order of miliseconds, well outside the range of molecular dynamics but readily accessible to diffusive molecular dynamics. The simulations predict an alloy Li_(15)Si_4 at the fully lithiated phase, exceedingly large and transient volume increments up to 300% due to the weakening of Si-Si iterations, a crystalline-to-amorphous-to-lithiation phase transition governed by interface kinetics, high misfit strains and residual stresses resulting in surface cracks and severe structural degradation in the form of extensive porosity, among other effects.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/xx1tm-s3x03Data-Driven Problems in Elasticity
https://resolver.caltech.edu/CaltechAUTHORS:20180131-140932556
Authors: {'items': [{'id': 'Conti-S', 'name': {'family': 'Conti', 'given': 'S.'}, 'orcid': '0000-0001-7987-9174'}, {'id': 'Müller-S', 'name': {'family': 'Müller', 'given': 'S.'}}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'M.'}, 'orcid': '0000-0001-5877-4824'}]}
Year: 2018
DOI: 10.1007/s00205-017-1214-0
We consider a new class of problems in elasticity, referred to as Data-Driven problems, defined on the space of strain-stress field pairs, or phase space. The problem consists of minimizing the distance between a given material data set and the subspace of compatible strain fields and stress fields in equilibrium. We find that the classical solutions are recovered in the case of linear elasticity. We identify conditions for convergence of Data-Driven solutions corresponding to sequences of approximating material data sets. Specialization to constant material data set sequences in turn establishes an appropriate notion of relaxation. We find that relaxation within this Data-Driven framework is fundamentally different from the classical relaxation of energy functions. For instance, we show that in the Data-Driven framework the relaxation of a bistable material leads to material data sets that are not graphs.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/07gtm-g5m85Charge carrier transport across grain boundaries in graphene
https://resolver.caltech.edu/CaltechAUTHORS:20180518-133908702
Authors: {'items': [{'id': 'Mendez-Granado-J-P', 'name': {'family': 'Mendez', 'given': 'J. P.'}, 'orcid': '0000-0002-9493-0879'}, {'id': 'Arca-F', 'name': {'family': 'Arca', 'given': 'F.'}}, {'id': 'Ramos-J', 'name': {'family': 'Ramos', 'given': 'J.'}}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'M.'}, 'orcid': '0000-0001-5877-4824'}, {'id': 'Ariza-M-P', 'name': {'family': 'Ariza', 'given': 'M. P.'}, 'orcid': '0000-0003-0266-0216'}]}
Year: 2018
DOI: 10.1016/j.actamat.2018.05.019
We evaluate the charge carrier transmission across asymmetric grain boundaries (GB) in a graphene lattice within the Landauer-Büttiker formalism. We employ a tight-binding model for C-based materials that accounts for lattice strain introduced by topological defects, such as grain boundaries. In particular, we investigate electronic transmission across grain boundaries found to be stable up to high temperatures. Our calculations suggest that the introduction of GBs generally preserves the zero-transport gap property of pristine graphene. However, only some specific asymmetric GBs open a moderate transport gap, which can be as high as ≈ 1.15 eV. We find that the GBs that introduce a transport gap are characterized by the existence of a mismatch along the GB. Indeed, the magnitude of this mismatch appears to be the main structural variable that determines the transport gap size, with greater mismatch resulting in larger transport gaps. Finally, we find that the presence of GBs reduces considerably electron transmission, and less so hole transmission.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/8akrv-ezs43Strength of tantalum shocked at ultrahigh pressures
https://resolver.caltech.edu/CaltechAUTHORS:20180706-105716928
Authors: {'items': [{'id': 'Stebner-A-P', 'name': {'family': 'Stebner', 'given': 'Aaron P.'}}, {'id': 'Wehrenberg-C', 'name': {'family': 'Wehrenberg', 'given': 'Christopher'}}, {'id': 'Li-Bo', 'name': {'family': 'Li', 'given': 'Bo'}, 'orcid': '0000-0002-8019-8891'}, {'id': 'Randall-G-C', 'name': {'family': 'Randall', 'given': 'Greg C.'}, 'orcid': '0000-0002-8375-9041'}, {'id': 'John-K', 'name': {'family': 'John', 'given': 'Kristen'}}, {'id': 'Hudish-G-A', 'name': {'family': 'Hudish', 'given': 'Grant A.'}}, {'id': 'Maddox-B', 'name': {'family': 'Maddox', 'given': 'Brian'}}, {'id': 'Farrell-M', 'name': {'family': 'Farrell', 'given': 'Michael'}}, {'id': 'Park-Hye-Sook', 'name': {'family': 'Park', 'given': 'Hye-Sook'}}, {'id': 'Remington-B', 'name': {'family': 'Remington', 'given': 'Bruce'}}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'Michael'}, 'orcid': '0000-0001-5877-4824'}, {'id': 'Ravichandran-G', 'name': {'family': 'Ravichandran', 'given': 'G.'}, 'orcid': '0000-0002-2912-0001'}]}
Year: 2018
DOI: 10.1016/j.msea.2018.06.105
High purity polycrystalline tantalum (Ta) was shocked through 1 to 3.5 Mbar pressures creating Richtmyer-Meshkov unstable interfaces that were used to determine the dynamic material strength. The experiments were performed on the Omega laser at the University of Rochester Laboratory for Laser Energetics. Prior to shock, the driven surfaces of the tantalum targets where coined with a sinusoidal pattern. The targets were recovered post-shock, and the growth of the sinusoid amplitudes was used to characterize the relative extent of plastic deformation as a function of laser energy. Analogous data were extracted prior to the experiments from phenomenological Von Mises plasticity simulations that considered equation of state tables for Ta. The simulations showed the best agreement with the experiments (less than 5% difference between mean ripple growth measures) for shock pressures ranging from 1.2 to 2.7 Mbar. A fluid model studied as a function of viscosity was also used to qualitatively indicate the sensitivity of the experiments to strength. These results verify the ability to use a phenomenological, equation of state based model to simulate very high-strain rate, high-pressure deformation of tantalum.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/vvz7g-p4b12Optimizing information transmission rates drives brain gyrification
https://resolver.caltech.edu/CaltechAUTHORS:20181212-142046456
Authors: {'items': [{'id': 'Heyden-Stefanie', 'name': {'family': 'Heyden', 'given': 'S.'}, 'orcid': '0000-0002-7035-7975'}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'M.'}, 'orcid': '0000-0001-5877-4824'}]}
Year: 2018
DOI: 10.1098/rspa.2018.0527
We investigate the functional optimality of the cerebral cortex of an adult human brain geometry. Unlike most competing models, we postulate that the cerebral cortex formation is driven by the objective of maximizing the total information transmission rate. Starting from a random path model, we show that this optimization problem is related to the Steklov eigenvalue problem. Combining realistic brain geometries with the finite-element method, we calculate the underlying Steklov eigenvalues and eigenfunctions. By comparison to a convex hull approximation, we show that the adult human brain geometry indeed reduces the Steklov eigenvalue spectrum and thus increases the rate at which information is exchanged between points on the cerebral cortex. With a view to possible clinical applications, the leading Steklov eigenfunctions and the resulting induced magnetic fields are computed and reported.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/8gcw1-2y337Kinematics of elasto-plasticity: Validity and limits of applicability of F = F^eF^p for general three-dimensional deformations
https://resolver.caltech.edu/CaltechAUTHORS:20180806-110927280
Authors: {'items': [{'id': 'Reina-C', 'name': {'family': 'Reina', 'given': 'Celia'}}, {'id': 'Fokoua-Djodom-L', 'name': {'family': 'Fokoua Djodom', 'given': 'Landry'}}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'Michael'}, 'orcid': '0000-0001-5877-4824'}, {'id': 'Conti-S', 'name': {'family': 'Conti', 'given': 'Sergio'}, 'orcid': '0000-0001-7987-9174'}]}
Year: 2018
DOI: 10.1016/j.jmps.2018.07.006
This article provides a multiscale justification of the multiplicative decomposition F=F^eF^p for three-dimensional elasto-plastic deformations, and sets its limits of applicability via a careful examination of the assumptions involved in the derivation. The analysis starts from the mesoscopic characterization of the kinematics at the level of discrete dislocations, where F_ϵ, F_ϵ^e and F_ϵ^p are uniquely defined, and the relationships F_ϵ≃F_ϵ^eF_ϵ^p and det F_ϵ^p≃1 are well-justified almost everywhere in the domain. The upscaling to the macroscale (i.e., F=F^eF^p and det F^p=1, with F, F^e and F^p defined as the limits of the analogous quantities at the mesoscale) is then rigorously derived on the basis of the following assumptions: sup_ϵ∥F_ϵ^e∥L^g(Ω)<∞ with 1 < g < ∞, sup_ϵ∥F_ϵ^p∥L∞(Ω)<∞,sup_ϵ|Curl F_ϵ^p|(Ω)<∞, and det F_ϵ^p=1. These may be interpreted, in suitable scenarios, as bounded local energy density and dissipation, finite density of dislocations and incompressibility of the plastic deformation, respectively. Although these assumptions are expected to hold in many single crystal elasto-plastic deformations, they may be violated in certain cases of physical relevance. Illustrative examples where each of the individual assumptions fails in turn are presented and their implications regarding finite multiplicative elasto-plasticity at the macroscale are examined in detail.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/m41hj-0js07A variational approach to Navier-Stokes
https://resolver.caltech.edu/CaltechAUTHORS:20180302-070321462
Authors: {'items': [{'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'Michael'}, 'orcid': '0000-0001-5877-4824'}, {'id': 'Schmidt-B', 'name': {'family': 'Schmidt', 'given': 'Bernd'}}, {'id': 'Stefanelli-U', 'name': {'family': 'Stefanelli', 'given': 'Ulisse'}}]}
Year: 2018
DOI: 10.1088/1361-6544/aae722
We present a variational resolution of the incompressible Navier–Stokes system by means of stabilized weighted-inertia-dissipation-energy (WIDE) functionals. The minimization of these parameter-dependent functionals corresponds to an elliptic-in-time regularization of the system. By passing to the limit in the regularization parameter along subsequences of WIDE minimizers one recovers a classical Leray–Hopf weak solution.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/a0rrt-pmp68A line-free method of monopoles for 3D dislocation dynamics
https://resolver.caltech.edu/CaltechAUTHORS:20180925-152150158
Authors: {'items': [{'id': 'Deffo-A', 'name': {'family': 'Deffo', 'given': 'A.'}}, {'id': 'Ariza-M-P', 'name': {'family': 'Ariza', 'given': 'M. P.'}, 'orcid': '0000-0003-0266-0216'}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'M.'}, 'orcid': '0000-0001-5877-4824'}]}
Year: 2019
DOI: 10.1016/j.jmps.2018.09.001
We develop an approximation scheme for three-dimensional dislocation dynamics in which the dislocation line density is concentrated at points, or monopoles. Every monopole carries a Burgers vector and an element of line. The monopoles move according to mobility kinetics driven by elastic and applied forces. The divergence constraint, expressing the requirement that the monopoles approximate a boundary, is enforced weakly. The fundamental difference with traditional approximation schemes based on segments is that in the present approach an explicit linear connectivity, or 'sequence', between the monopoles need not be defined. Instead, the monopoles move as an unstructured point set subject to the weak divergence constraint. In this sense, the new paradigm is 'line-free', i. e., it sidesteps the need to track dislocation lines. This attribute offers significant computational advantages in terms of simplicity, robustness and efficiency, as demonstrated by means of selected numerical examples.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/yhk8f-w0s36Topology Optimization of Solid Rocket Fuel
https://resolver.caltech.edu/CaltechAUTHORS:20190530-074847285
Authors: {'items': [{'id': 'Kirchdoerfer-T', 'name': {'family': 'Kirchdoerfer', 'given': 'Trenton'}}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'Michael'}, 'orcid': '0000-0001-5877-4824'}, {'id': 'Stewart-D-S', 'name': {'family': 'Stewart', 'given': 'Donald S.'}}]}
Year: 2019
DOI: 10.2514/1.J057807
This paper investigates possible improvements in the combustion properties of multicomponent solid propellants through the application of topology optimization methods to representative volume element (RVE) of HMX-aluminum fuel. Design objectives for the material include increased thermal conductivity and reduced amounts of induced strains under thermal loads. The targeted increases in thermal conductivity generate designs that increase burn propagation rates, whereas the reductions in structural compliance minimize relative displacements within the design cell. Novel domain-filter treatments are also developed to better control the boundary effects on the resulting designs. A family of wire-like solutions is found to provide optimal combustion and structural properties. Burn performance estimates showed 52 and 33% improvements in burn propagation speeds relative to previous designs at, respectively, 20 and 200 atm.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/gjd1x-2rb40Atomistic Modeling and Analysis of Hydride Phase Transformation in Palladium Nanoparticles
https://resolver.caltech.edu/CaltechAUTHORS:20190107-130600369
Authors: {'items': [{'id': 'Sun-X', 'name': {'family': 'Sun', 'given': 'X.'}}, {'id': 'Ariza-M-P', 'name': {'family': 'Ariza', 'given': 'M. P.'}, 'orcid': '0000-0003-0266-0216'}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'M.'}, 'orcid': '0000-0001-5877-4824'}, {'id': 'Wang-Kevin-G', 'name': {'family': 'Wang', 'given': 'K. G.'}}]}
Year: 2019
DOI: 10.1016/j.jmps.2019.01.006
Palladium-hydrogen (Pd-H) is a prototypical system for studying solute-induced phase transformation in various energy conversion and storage applications. While the behaviors of bulk Pd-H have been studied extensively, the detailed atomic picture of hydride phase transformation within individual Pd nanoparticles is still unclear. In this work, we employ a novel atomistic computational model, referred to as Diffusive Molecular Dynamics (DMD), to characterize the H absorption dynamics in Pd nanoparticles of spherical, octahedral and cubic shapes. The DMD model couples a non-equilibrium thermodynamic model with a discrete diffusion law, which allows it to reach diffusive time scales with atomic resolution. The model is capable of capturing the propagation of an atomistically sharp hydride phase boundary. A remarkable feature of the phase boundary structure that is predicted by the calculations is the emergence of misfit dislocations distributed over the interface. These dislocations relieve the elastic residual stresses induced by the change of volume that accompanies the phase transformation. Shape effects are also investigated in this work. More specifically, in both spherical and octahedral nanoparticles, we observe stacking faults during the H absorption process while the phase boundary in the cubic nanoparticle remains coherent. The spatial distribution of the stacking faults in the spherical sample is investigated in detail using an elastic core-shell model. We also identify the mechanisms that enable the movement of the stacking faults as they track the propagation of the phase boundary. Finally, we find that the rate of H absorption is reduced by the formation and movement of the stacking faults.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/jze6v-9b908Fractional strain-gradient plasticity
https://resolver.caltech.edu/CaltechAUTHORS:20190225-123840084
Authors: {'items': [{'id': 'Dahlberg-C-F-O', 'name': {'family': 'Dahlberg', 'given': 'C. F. O.'}, 'orcid': '0000-0002-9509-2811'}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'M.'}, 'orcid': '0000-0001-5877-4824'}]}
Year: 2019
DOI: 10.1016/j.euromechsol.2019.02.006
We develop a strain-gradient plasticity theory based on fractional derivatives of plastic strain and assess its ability to reproduce the scaling laws and size effects uncovered by the recent experiments of Mu et al. (2014, 2016, 2017) on copper thin layers undergoing plastically constrained simple shear. We show that the size-scaling discrepancy between conventional strain-gradient plasticity and the experimental data is resolved if the inhomogeneity of the plastic strain distribution is quantified by means of fractional derivatives of plastic strain. In particular, the theory predicts that the size scaling exponent is equal to the fractional order of the plastic-strain derivatives, which establishes a direct connection between the size scaling of the yield stress and fractionality.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/m219w-cjn24Topology and polarity of dislocation cores dictate the mechanical strength of monolayer MoS_2
https://resolver.caltech.edu/CaltechAUTHORS:20190114-093259803
Authors: {'items': [{'id': 'Wu-Jianyang', 'name': {'family': 'Wu', 'given': 'Jianyang'}}, {'id': 'Gong-Hao', 'name': {'family': 'Gong', 'given': 'Hao'}}, {'id': 'Zhang-Zhisen', 'name': {'family': 'Zhang', 'given': 'Zhisen'}}, {'id': 'He-Jianying', 'name': {'family': 'He', 'given': 'Jianying'}}, {'id': 'Ariza-P', 'name': {'family': 'Ariza', 'given': 'Pilar'}, 'orcid': '0000-0003-0266-0216'}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'Michael'}, 'orcid': '0000-0001-5877-4824'}, {'id': 'Zhang-Zhiliang', 'name': {'family': 'Zhang', 'given': 'Zhiliang'}}]}
Year: 2019
DOI: 10.1016/j.apmt.2018.12.019
In contrast to homoelemental graphene showing common dislocation dipole with pentagon-heptagon (5|7) core, heteroelemental MoS2 is observed to contain diverse dislocation cores that tune the chemical and physical properties. Yet, how the inevitable dislocation cores in MoS_2 affect the mechanical behaviours remains virtually unexplored. Herein, we report direct atomistic simulations of mechanical characteristics of isolated dislocation-embedded MoS_2 monolayers under tensile load. All isolated dislocation cores in MoS_2 monolayer rise polar stress-concentration, while those with larger Burgers vector are less energetically-favorable configurations but show local wrinkling behaviour. It is revealed that the intrinsic tensile strength of MoS_2 is dictated by topology and polarity of dislocation cores. There is a strong inverse correlation between the maximum residual stresses induced by the dislocation cores and the strength of MoS_2 monolayers. Mechanical failure initiates from the bond at dislocation polygon on which side there is a missing atomic chain. Armchair-oriented 4|8 dislocation exhibits sole brittle failure, however, dual brittle/ductile fractures occur in zigzag-oriented dislocations; Mo-S-Mo angle-oriented crack is brittle, while the S-Mo-S angle-oriented crack becomes ductile. Our findings shed sights on mechanical design of heteroelemental 2D materials via dislocation engineering for practical application.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/24z3s-8bk05Functional optimality of the sulcus pattern of the human brain
https://resolver.caltech.edu/CaltechAUTHORS:20180604-073442987
Authors: {'items': [{'id': 'Heyden-S', 'name': {'family': 'Heyden', 'given': 'S.'}, 'orcid': '0000-0002-7035-7975'}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'M.'}, 'orcid': '0000-0001-5877-4824'}]}
Year: 2019
DOI: 10.1093/imammb/dqy007
We develop a mathematical model of information transmission across the biological neural network of the human brain. The overall function of the brain consists of the emergent processes resulting from the spread of information through the neural network. The capacity of the brain is therefore related to the rate at which it can transmit information through the neural network. The particular transmission model under consideration allows for information to be transmitted along multiple paths between points of the cortex. The resulting transmission rates are governed by potential theory. According to this theory, the brain has preferred and quantized transmission modes that correspond to eigenfunctions of the classical Steklov eigenvalue problem, with the reciprocal eigenvalues quantifying the corresponding transmission rates. We take the model as a basis for testing the hypothesis that the sulcus pattern of the human brain has evolved to maximize the rate of transmission of information between points in the cerebral cortex. We show that the introduction of sulci, or cuts, in an otherwise smooth domain indeed increases the overall transmission rate. We demonstrate this result by means of numerical experiments concerned with a spherical domain with a varying number of slits on its surface.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/p7j0c-3g708Model-Free Data-Driven inelasticity
https://resolver.caltech.edu/CaltechAUTHORS:20190304-093042764
Authors: {'items': [{'id': 'Eggersmann-Robert', 'name': {'family': 'Eggersmann', 'given': 'R.'}}, {'id': 'Kirchdoerfer-Trenton', 'name': {'family': 'Kirchdoerfer', 'given': 'T'}}, {'id': 'Reese-Stefanie', 'name': {'family': 'Reese', 'given': 'S.'}}, {'id': 'Stainier-Laurent', 'name': {'family': 'Stainier', 'given': 'L.'}, 'orcid': '0000-0001-6719-6616'}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'M.'}, 'orcid': '0000-0001-5877-4824'}]}
Year: 2019
DOI: 10.1016/j.cma.2019.02.016
We extend the Data-Driven formulation of problems in elasticity of Kirchdoerfer and Ortiz (2016) to inelasticity. This extension differs fundamentally from Data-Driven problems in elasticity in that the material data set evolves in time as a consequence of the history dependence of the material. We investigate three representational paradigms for the evolving material data sets: (i) materials with memory, i. e., conditioning the material data set to the past history of deformation; (ii) differential materials, i. e., conditioning the material data set to short histories of stress and strain; and (iii) history variables, i. e., conditioning the material data set to ad hoc variables encoding partial information about the history of stress and strain. We also consider combinations of the three paradigms thereof and investigate their ability to represent the evolving data sets of different classes of inelastic materials, including viscoelasticity, viscoplasticity and plasticity. We present selected numerical examples that demonstrate the range and scope of Data-Driven inelasticity and the numerical performance of implementations thereof.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/ge474-k6162Steric Interference in Bilayer Graphene with Point Dislocations
https://resolver.caltech.edu/CaltechAUTHORS:20190716-082655936
Authors: {'items': [{'id': 'Arca-Francisco', 'name': {'family': 'Arca', 'given': 'Francisco'}}, {'id': 'Mendez-Granado-Juan-Pedro', 'name': {'family': 'Mendez', 'given': 'Juan Pedro'}, 'orcid': '0000-0002-9493-0879'}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'Michael'}, 'orcid': '0000-0001-5877-4824'}, {'id': 'Ariza-Pilar', 'name': {'family': 'Ariza', 'given': 'Pilar'}, 'orcid': '0000-0003-0266-0216'}]}
Year: 2019
DOI: 10.3390/nano9071012
PMCID: PMC6669646
We present evidence of strong steric interference in bilayer graphene containing offset point dislocations. Calculations are carried out with Large-scale Atomic/Molecular Massively Parallel Simulator (LAMMPS) using the Long-Range Carbon Bond-Order Potential (LCBOP) potential of Los et al.. We start by validating the potential in the harmonic response by comparing the predicted phonon dispersion curves to experimental data and other potentials. The requisite force constants are derived by linearization of the potential and are presented in full form. We then continue to validate the potential in applications involving the formation of dislocation dipoles and quadrupoles in monolayer configurations. Finally, we evaluate a number of dislocation quadrupole configurations in monolayer and bilayer graphene and document strong steric interactions due to out-of-plane displacements when the dislocations on the individual layers are sufficiently offset with respect to each other.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/9dxn4-vpy13Model-free data-driven methods in mechanics: material data identification and solvers
https://resolver.caltech.edu/CaltechAUTHORS:20190604-153039944
Authors: {'items': [{'id': 'Stainier-Laurent', 'name': {'family': 'Stainier', 'given': 'Laurent'}, 'orcid': '0000-0001-6719-6616'}, {'id': 'Leygue-Adrien', 'name': {'family': 'Leygue', 'given': 'Adrien'}, 'orcid': '0000-0003-0714-822X'}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'Michael'}, 'orcid': '0000-0001-5877-4824'}]}
Year: 2019
DOI: 10.1007/s00466-019-01731-1
This paper presents an integrated model-free data-driven approach to solid mechanics, allowing to perform numerical simulations on structures on the basis of measures of displacement fields on representative samples, without postulating a specific constitutive model. A material data identification procedure, allowing to infer strain–stress pairs from displacement fields and boundary conditions, is used to build a material database from a set of mutiaxial tests on a non-conventional sample. This database is in turn used by a data-driven solver, based on an algorithm minimizing the distance between manifolds of compatible and balanced mechanical states and the given database, to predict the response of structures of the same material, with arbitrary geometry and boundary conditions. Examples illustrate this modelling cycle and demonstrate how the data-driven identification method allows importance sampling of the material state space, yielding faster convergence of simulation results with increasing database size, when compared to synthetic material databases with regular sampling patterns.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/8th0c-ymb67Selective Ablation of Cancer Cells with Low Intensity Pulsed Ultrasound
https://resolver.caltech.edu/CaltechAUTHORS:20191002-094950438
Authors: {'items': [{'id': 'Mittelstein-David-R', 'name': {'family': 'Mittelstein', 'given': 'David R.'}, 'orcid': '0000-0001-8747-0483'}, {'id': 'Ye-Jian', 'name': {'family': 'Ye', 'given': 'Jian'}, 'orcid': '0000-0002-7168-0117'}, {'id': 'Schibber-Erika-F', 'name': {'family': 'Schibber', 'given': 'Erika F.'}, 'orcid': '0000-0002-6629-297X'}, {'id': 'Roychoudhury-Ankita', 'name': {'family': 'Roychoudhury', 'given': 'Ankita'}}, {'id': 'Troyas-Leyre', 'name': {'family': 'Troyas Martinez', 'given': 'Leyre'}, 'orcid': '0000-0003-4512-0666'}, {'id': 'Fekrazad-M-Houmam', 'name': {'family': 'Fekrazad', 'given': 'M. Houman'}}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'Michael'}, 'orcid': '0000-0001-5877-4824'}, {'id': 'Lee-Peter-P', 'name': {'family': 'Lee', 'given': 'Peter P.'}, 'orcid': '0000-0002-2660-4377'}, {'id': 'Shapiro-M-G', 'name': {'family': 'Shapiro', 'given': 'Mikhail G.'}, 'orcid': '0000-0002-0291-4215'}, {'id': 'Gharib-M', 'name': {'family': 'Gharib', 'given': 'Morteza'}, 'orcid': '0000-0003-0754-4193'}]}
Year: 2020
DOI: 10.1063/1.5128627
Ultrasound can be focused into deep tissues with millimeter precision to perform noninvasive ablative therapy for diseases such as cancer. In most cases, this ablation uses high intensity ultrasound to deposit nonselective thermal or mechanical energy at the ultrasound focus, damaging both healthy bystander tissue and cancer cells. Here, we describe an alternative low intensity (I_(SPTA) < 5 W/cm²) pulsed ultrasound approach that leverages the distinct mechanical properties of neoplastic cells to achieve inherent cancer selectivity. We show that ultrasound applied at a frequency of 0.5–0.67 MHz and a pulse duration of >20 ms causes selective disruption of a panel of breast, colon, and leukemia cancer cell models in suspension without significantly damaging healthy immune or red blood cells. Mechanistic experiments reveal that the formation of acoustic standing waves and the emergence of cell-seeded cavitation lead to cytoskeletal disruption, expression of apoptotic markers, and cell death. The inherent selectivity of this low intensity pulsed ultrasound approach offers a potentially safer and thus more broadly applicable alternative to nonselective high intensity ultrasound ablation.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/tnhgj-me123Symmetric Div-Quasiconvexity and the Relaxation of Static Problems
https://resolver.caltech.edu/CaltechAUTHORS:20190805-150303687
Authors: {'items': [{'id': 'Conti-Sergio', 'name': {'family': 'Conti', 'given': 'S.'}, 'orcid': '0000-0001-7987-9174'}, {'id': 'Müller-Sebastian', 'name': {'family': 'Müller', 'given': 'S.'}}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'M.'}, 'orcid': '0000-0001-5877-4824'}]}
Year: 2020
DOI: 10.1007/s00205-019-01433-1
We consider problems of static equilibrium in which the primary unknown is the stress field and the solutions maximize a complementary energy subject to equilibrium constraints. A necessary and sufficient condition for the sequential lower-semicontinuity of such functionals is symmetric divdiv-quasiconvexity; a special case of Fonseca and Müller's A-quasiconvexity with A=div acting on R^(n×n)_(sym). We specifically consider the example of the static problem of plastic limit analysis and seek to characterize its relaxation in the non-standard case of a non-convex elastic domain. We show that the symmetric div-quasiconvex envelope of the elastic domain can be characterized explicitly for isotropic materials whose elastic domain depends on pressure p and Mises effective shear stress q. The envelope then follows from a rank-2 hull construction in the (p, q)-plane. Remarkably, owing to the equilibrium constraint, the relaxed elastic domain can still be strongly non-convex, which shows that convexity of the elastic domain is not a requirement for existence in plasticity.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/1164a-3vx87Rigorous Uncertainty Quantification and Design with Uncertain Material Models
https://resolver.caltech.edu/CaltechAUTHORS:20191028-142036143
Authors: {'items': [{'id': 'Sun-Xingsheng', 'name': {'family': 'Sun', 'given': 'X.'}}, {'id': 'Kirchdoerfer-T', 'name': {'family': 'Kirchdoerfer', 'given': 'T.'}}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'M.'}, 'orcid': '0000-0001-5877-4824'}]}
Year: 2020
DOI: 10.1016/j.ijimpeng.2019.103418
We assess a method of quantification of margins and uncertainties (QMU) in applications where the main source of uncertainty is an imperfect knowledge or characterization of the material behavior. The aim of QMU is to determine adequate design margins given quantified uncertainties and a desired level of confidence in the design. We quantify uncertainties through rigorous probability bounds computed by exercising an existing deterministic code in order to sample the mean response and identify worst-case combinations of parameters. The resulting methodology is non-intrusive and can be wrapped around existing solvers. The use of rigorous probability bounds ensures that the resulting designs are conservative to within a desired level of confidence. We assess the QMU framework by means of an application concerned with sub-ballistic impact of AZ31B Mg alloy plates. We assume the design specification to be a maximum allowable backface deflection of the plate. As a simple scenario, we specifically assume that, under the conditions of interest, the plate is well-characterized by the Johnson-Cook model, but the parameters of the model are uncertain. In calculations, we use the commercial finite-element package LS-Dyna and DAKOTA Version 6.7. The assessment demonstrates the feasibility of the approach and how it results in high-confidence designs that are well-within the practical range of engineering application.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/c4j5c-yeb56Spontaneous twinning as an accommodation mechanism in monolayer graphene
https://resolver.caltech.edu/CaltechAUTHORS:20191205-090217849
Authors: {'items': [{'id': 'Arca-F', 'name': {'family': 'Arca', 'given': 'F.'}}, {'id': 'Mendez-Granado-J-P', 'name': {'family': 'Mendez', 'given': 'J. P.'}, 'orcid': '0000-0002-9493-0879'}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'M.'}, 'orcid': '0000-0001-5877-4824'}, {'id': 'Ariza-M-P', 'name': {'family': 'Ariza', 'given': 'M. P.'}, 'orcid': '0000-0003-0266-0216'}]}
Year: 2020
DOI: 10.1016/j.euromechsol.2019.103923
We present numerical evidence that twinning operates as an accommodation and relaxation mechanism in graphene. We show that twins may arise spontaneously in graphene layers containing arrays of dislocations and that twinning results in a significant reduction in energy. We verify that the twinning relations are satisfied across the interfaces, which are thereby identified as bona fides twin boundaries. We additionally verify that the twin boundaries are thermally stable up to high temperatures.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/5dnfk-nxa44Size Scaling of Plastic Deformation in Simple Shear: Fractional Strain-Gradient Plasticity and Boundary Effects in Conventional Strain-Gradient Plasticity
https://resolver.caltech.edu/CaltechAUTHORS:20200430-120230708
Authors: {'items': [{'id': 'Dahlberg-C-F-O', 'name': {'family': 'Dahlberg', 'given': 'Carl F. O.'}}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'Michael'}, 'orcid': '0000-0001-5877-4824'}]}
Year: 2020
DOI: 10.1115/1.4045872
A recently developed model based on fractional derivatives of plastic strain is compared with conventional strain-gradient plasticity (SGP) models. Specifically, the experimental data and observed model discrepancies in the study by Mu et al. (2016, "Dependence of Confined Plastic Flow of Polycrystalline Cu Thin Films on Microstructure," MRS Com. Res. Let. 20, pp. 1–6) are considered by solving the constrained simple shear problem. Solutions are presented both for a conventional SGP model and a model extension introducing an energetic interface. The interface allows us to relax the Dirichlet boundary condition usually assumed to prevail when solving this problem with the SGP model. We show that the particular form of a relaxed boundary condition does not change the underlying size scaling of the yield stress and consequently does not resolve the scaling issue. Furthermore, we show that the fractional strain-gradient plasticity model predicts a yield stress with a scaling exponent that is equal to the fractional order of differentiation.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/a3tzz-kg572A dynamical model of oncotripsy by mechanical cell fatigue: selective cancer cell ablation by low-intensity pulsed ultrasound
https://resolver.caltech.edu/CaltechAUTHORS:20191223-114059821
Authors: {'items': [{'id': 'Schibber-E-F', 'name': {'family': 'Schibber', 'given': 'E. F.'}, 'orcid': '0000-0002-6629-297X'}, {'id': 'Mittelstein-D-R', 'name': {'family': 'Mittelstein', 'given': 'D. R.'}, 'orcid': '0000-0001-8747-0483'}, {'id': 'Gharib-M', 'name': {'family': 'Gharib', 'given': 'M.'}, 'orcid': '0000-0003-0754-4193'}, {'id': 'Shapiro-M-G', 'name': {'family': 'Shapiro', 'given': 'M. G.'}, 'orcid': '0000-0002-0291-4215'}, {'id': 'Lee-P-P', 'name': {'family': 'Lee', 'given': 'P. P.'}}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'M.'}, 'orcid': '0000-0001-5877-4824'}]}
Year: 2020
DOI: 10.1098/rspa.2019.0692
PMCID: PMC7209139
The method of oncotripsy, first proposed in Heyden & Ortiz (Heyden & Ortiz 2016 J. Mech. Phys. Solids 92, 164–175 (doi:10.1016/j.jmps.2016.04.016)), exploits aberrations in the material properties and morphology of cancerous cells in order to ablate them selectively by means of tuned low-intensity pulsed ultrasound. We propose the dynamical model of oncotripsy that follows as an application of cell dynamics, statistical mechanical theory of network elasticity and 'birth–death' kinetics to describe the processes of damage and repair of the cytoskeleton. We also develop a reduced dynamical model that approximates the three-dimensional dynamics of the cell and facilitates parametric studies, including sensitivity analysis and process optimization. We show that the dynamical model predicts—and provides a conceptual basis for understanding—the oncotripsy effect and other trends in the data of Mittelstein et al. (Mittelstein et al. 2019 Appl. Phys. Lett. 116, 013701 (doi:10.1063/1.5128627)), for cells in suspension, including the dependence of cell-death curves on cell and process parameters.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/nc5aa-k7608Large scale ab-initio simulations of dislocations
https://resolver.caltech.edu/CaltechAUTHORS:20200110-142048574
Authors: {'items': [{'id': 'Ponga-M', 'name': {'family': 'Ponga', 'given': 'Mauricio'}, 'orcid': '0000-0001-5058-1454'}, {'id': 'Bhattacharya-K', 'name': {'family': 'Bhattacharya', 'given': 'Kaushik'}, 'orcid': '0000-0003-2908-5469'}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'Michael'}, 'orcid': '0000-0001-5877-4824'}]}
Year: 2020
DOI: 10.1016/j.jcp.2020.109249
We present a novel methodology to compute relaxed dislocations core configurations, and their energies in crystalline metallic materials using large-scale ab-intio simulations. The approach is based on MacroDFT, a coarse-grained density functional theory method that accurately computes the electronic structure with sub-linear scaling resulting in a tremendous reduction in cost. Due to its implementation in real-space, MacroDFT has the ability to harness petascale resources to study materials and alloys through accurate ab-initio calculations. Thus, the proposed methodology can be used to investigate dislocation cores and other defects where long range elastic effects play an important role, such as in dislocation cores, grain boundaries and near precipitates in crystalline materials. We demonstrate the method by computing the relaxed dislocation cores in prismatic dislocation loops and dislocation segments in magnesium (Mg). We also study the interaction energy with a line of Aluminum (Al) solutes. Our simulations elucidate the essential coupling between the quantum mechanical aspects of the dislocation core and the long range elastic fields that they generate. In particular, our quantum mechanical simulations are able to describe the logarithmic divergence of the energy in the far field as is known from classical elastic theory. In order to reach such scaling, the number of atoms in the simulation cell has to be exceedingly large, and cannot be achieved with the state-of-the-art density functional theory implementations.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/c8912-wt574Supergiant elasticity and fracture of 3D spirally wound MoS₂
https://resolver.caltech.edu/CaltechAUTHORS:20200326-080855730
Authors: {'items': [{'id': 'Wu-Jianyang', 'name': {'family': 'Wu', 'given': 'Jianyang'}}, {'id': 'He-Jianying', 'name': {'family': 'He', 'given': 'Jianying'}}, {'id': 'Ariza-Pilar', 'name': {'family': 'Ariza', 'given': 'Pilar'}, 'orcid': '0000-0003-0266-0216'}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'Michael'}, 'orcid': '0000-0001-5877-4824'}, {'id': 'Zhang-Zhiliang', 'name': {'family': 'Zhang', 'given': 'Zhiliang'}}]}
Year: 2020
DOI: 10.1007/s10704-020-00427-5
Recently experimentally synthesized three-dimensional (3D) MoS₂MoS₂ spiral is a new kind of helical structure with technically robust properties. Among them, the mechanical properties of such appealing materials are indispensable but remain unexplored. Here, the stretching characteristics of 3D spirally wound MoS₂MoS₂ as a new type of mechanical nanospring are explored by using large-scale molecular dynamic (MD) simulations. It is revealed that the MoS₂MoS₂ spiral structures not only exhibit unique sawtooth-like tensile responses inaccessible from conventional springs, but also hold high stretching deformation capabilities. Surprisingly, there is a critical inner radius which induces a jump of elasticity but not in the tensile strength; below it yields elastic strain of less than 320%, while above which the elastic strain is over 1900%. The supergiant elasticity is primarily caused by the sliding–reorientation action, stepwise opening and elastic deformation of nanoribbons of MoS₂MoS₂ spirals. Moreover, imposed strain energy is mainly absorbed by the inner edges of MoS₂MoS₂ spirals, and MoS₂MoS₂ spirals catastrophically fail at the corner of the inner hexagon-edge of buckled MoS₂MoS₂ nanoribbons that are more stress-concentrated. This study provides important insights into facile design of MoS₂MoS₂ spiral-based nanosprings with supergiant elongation capability for practical applications.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/r8hzn-nmt32Effect of polypropylene fibers on the fracture behavior of heated ultra-high performance concrete
https://resolver.caltech.edu/CaltechAUTHORS:20191203-154217834
Authors: {'items': [{'id': 'Ríos-J-D', 'name': {'family': 'Ríos', 'given': 'J. D.'}}, {'id': 'Cifuentes-Bulte-Héctor', 'name': {'family': 'Cifuentes', 'given': 'H.'}, 'orcid': '0000-0001-6302-418X'}, {'id': 'Leiva-C', 'name': {'family': 'Leiva', 'given': 'C.'}}, {'id': 'Ariza-Maria-Pilar', 'name': {'family': 'Ariza', 'given': 'M. P.'}, 'orcid': '0000-0003-0266-0216'}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'M.'}, 'orcid': '0000-0001-5877-4824'}]}
Year: 2020
DOI: 10.1007/s10704-019-00407-4
In this work we assess the effect of the addition of polypropylene (PP) fibers in a heated ultra-high-performance fiber reinforced concrete (UHPFRC). To this end, three sets of specimens with identical cementitious materials were manufactured: plain concrete, a concrete reinforced exclusively with steel fibers and a concrete reinforced with steel and polypropylene fibers. The mechanical and fracture properties of each concrete at temperatures ranging from room temperature to 300∘C were determined. A thorough appraisal of the thermal effect on the microstructure was also carried out by means of an X-ray scan analysis. Based on the testing data, the relation between the macroscopic response, including mechanical and fracture behavior, and the microscopic structure, i.e., size and number of pores and their distribution, is ascertained. The results show that the addition of PP fibers significantly increases the maximum pore size and slightly increases the total porosity. Furthermore, the partial melting of polypropylene fibers at 300∘C, in combination with the rise in porosity, reduces thermal damage and results in similar behavior at low and high temperatures, room temperature and 300∘C, respectively.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/ee535-rsa86Ice Penetration by a Bluff-Body Melting Probe
https://resolver.caltech.edu/CaltechAUTHORS:20210218-171550599
Authors: {'items': [{'id': 'Weinberg-Kerstin', 'name': {'family': 'Weinberg', 'given': 'Kerstin'}}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'Michael'}, 'orcid': '0000-0001-5877-4824'}]}
Year: 2020
DOI: 10.1115/1.4046633
We analyze the operation of melting probes as a Stefan problem for the liquid/solid interface surrounding the probe. We assume that the liquid layer is thin and, therefore, amenable to analysis by the lubrication theory. The resulting Stefan problem is solvable in the closed form. The solution determines the dependence of the penetration speed on the temperature differential between the probe and the surrounding ice, the size, shape and weight of the probe, the viscosity of liquid water and the thermal properties of solid ice.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/b2ae7-ydf19Shear localization as a mesoscopic stress-relaxation mechanism in fused silica glass at high strain rates
https://resolver.caltech.edu/CaltechAUTHORS:20200320-094313784
Authors: {'items': [{'id': 'Schill-W', 'name': {'family': 'Schill', 'given': 'W.'}}, {'id': 'Mendez-Granado-J-P', 'name': {'family': 'Mendez', 'given': 'J. P.'}, 'orcid': '0000-0002-9493-0879'}, {'id': 'Stainier-Laurent', 'name': {'family': 'Stainier', 'given': 'L.'}, 'orcid': '0000-0001-6719-6616'}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'M.'}, 'orcid': '0000-0001-5877-4824'}]}
Year: 2020
DOI: 10.1016/j.jmps.2020.103940
Molecular dynamics (MD) simulations of fused silica glass deforming in pressure-shear, while revealing useful insights into processes unfolding at the atomic level, fail spectacularly in that they grossly overestimate the magnitude of the stresses relative to those observed, e. g., in plate-impact experiments. We interpret this gap as evidence of relaxation mechanisms that operate at mesoscopic lengthscales and which, therefore, are not taken into account in atomic-level calculations. We specifically hypothesize that the dominant mesoscopic relaxation mechanism is shear banding. We evaluate this hypothesis by first generating MD data over the relevant range of temperature and strain rate and then carrying out continuum shear-banding calculations in a plate-impact configuration using a critical-state plasticity model fitted to the MD data. The main outcome of the analysis is a knock-down factor due to shear banding that effectively brings the predicted level of stress into alignment with experimental observation, thus resolving the predictive gap of MD calculations.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/vydc9-dg157Data-Driven Finite Elasticity
https://resolver.caltech.edu/CaltechAUTHORS:20200313-132836970
Authors: {'items': [{'id': 'Conti-Sergio', 'name': {'family': 'Conti', 'given': 'S.'}, 'orcid': '0000-0001-7987-9174'}, {'id': 'Müller-Sebastian', 'name': {'family': 'Müller', 'given': 'S.'}}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'M.'}, 'orcid': '0000-0001-5877-4824'}]}
Year: 2020
DOI: 10.1007/s00205-020-01490-x
We extend to finite elasticity the Data-Driven formulation of geometrically linear elasticity presented in Conti et al. (Arch Ration Mech Anal 229:79–123, 2018). The main focus of this paper concerns the formulation of a suitable framework in which the Data-Driven problem of finite elasticity is well-posed in the sense of existence of solutions. We confine attention to deformation gradients F ∈ L^p(Ω;R^(n x n)) and first Piola-Kirchhoff stresses P ∈ L^q(Ω;R^(n x n)), with (p,q) ∈ (1, ∞) and 1/p + 1/q = 1. We assume that the material behavior is described by means of a material data set containing all the states (F, P) that can be attained by the material, and develop germane notions of coercivity and closedness of the material data set. Within this framework, we put forth conditions ensuring the existence of solutions. We exhibit specific examples of two- and three-dimensional material data sets that fit the present setting and are compatible with material frame indifference.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/k6vxp-dqp71Transcranial Focused Ultrasound Generates Skull-Conducted Shear Waves: Computational Model and Implications for Neuromodulation
https://resolver.caltech.edu/CaltechAUTHORS:20200420-131214393
Authors: {'items': [{'id': 'Salahshoor-Hossein', 'name': {'family': 'Salahshoor', 'given': 'Hossein'}}, {'id': 'Shapiro-M-G', 'name': {'family': 'Shapiro', 'given': 'Mikhail G.'}, 'orcid': '0000-0002-0291-4215'}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'Michael'}, 'orcid': '0000-0001-5877-4824'}]}
Year: 2020
DOI: 10.1063/5.0011837
PMCID: PMC7386437
Focused ultrasound (FUS) is an established technique for non-invasive surgery and has recently attracted considerable attention as a potential method for non-invasive neuromodulation. While the pressure waves in FUS procedures have been extensively studied in this context, the accompanying shear waves are often neglected due to the relatively high shear compliance of soft tissues. However, in bony structures such as the skull, acoustic pressure can also induce significant shear waves that could propagate outside the ultrasound focus. Here, we investigate wave propagation in the human cranium by means of a finite-element model that accounts for the anatomy, elasticity, and viscoelasticity of the skull and brain. We show that, when a region on the scalp is subjected to FUS, the skull acts as a waveguide for shear waves that propagate with a speed close to 1500 m/s, reaching off-target structures such as the cochlea. In particular, when a sharp onset of FUS is introduced in a zone proximal to the intersection of the parietal and temporal cranium, the bone-propagated shear waves reach the inner ear in about 40 μs, leading to cumulative displacements of about 1 μm. We further quantify the effect of ramped and sharp application of FUS on the cumulative displacements in the inner ear. Our results help explain the off-target auditory responses observed during neuromodulation experiments and inform the development of mitigation and sham control strategies.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/v4qcx-njq83Charge-carrier transmission across twins in graphene
https://resolver.caltech.edu/CaltechAUTHORS:20200708-075007084
Authors: {'items': [{'id': 'Arca-Francisco', 'name': {'family': 'Arca', 'given': 'F.'}, 'orcid': '0000-0003-2473-4589'}, {'id': 'Mendez-Granado-Juan-Pedro', 'name': {'family': 'Mendez', 'given': 'J. P.'}, 'orcid': '0000-0002-9493-0879'}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'M.'}, 'orcid': '0000-0001-5877-4824'}, {'id': 'Ariza-Maria-Pilar', 'name': {'family': 'Ariza', 'given': 'M. P.'}, 'orcid': '0000-0003-0266-0216'}]}
Year: 2020
DOI: 10.1088/1361-648x/aba0d9
Twinning is a known accommodation mechanism of graphene that results in low-energy microstructures or twins. In view of their mechanical stability, twins suggest themselves as a possible means of introducing extended defects in graphene leading to the opening of transmission band gaps. We investigate charge-carrier transmission across the twin structures in graphene using the Landauer-Büttiker (LB) formalism in combination with a tight-binding model. We verify the approach by means of selected comparisons with Density Functional Theory (DFT) and non-equilibrium Green's function (NEGF) calculations using the code SIESTA and TRANSIESTA. The calculations reveal that graphene twins open transport gaps depending on the twin geometry up to maximum of 1.15 eV. As previously reported for grain boundaries, we find that localized states arise at dislocation cores in the twin boundaries that introduce peaks near the Fermi level.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/d9mrw-dzb86Data-driven fracture mechanics
https://resolver.caltech.edu/CaltechAUTHORS:20200910-100202726
Authors: {'items': [{'id': 'Carrara-Pietro', 'name': {'family': 'Carrara', 'given': 'P.'}, 'orcid': '0000-0003-4740-1306'}, {'id': 'De-Lorenzis-Laura', 'name': {'family': 'De Lorenzis', 'given': 'L.'}, 'orcid': '0000-0003-2748-3287'}, {'id': 'Stainier-Laurent', 'name': {'family': 'Stainier', 'given': 'L.'}, 'orcid': '0000-0001-6719-6616'}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'M.'}, 'orcid': '0000-0001-5877-4824'}]}
Year: 2020
DOI: 10.1016/j.cma.2020.113390
We present a new data-driven paradigm for variational brittle fracture mechanics. The fracture-related material modeling assumptions are removed and the governing equations stemming from variational principles are combined with a set of discrete data points, leading to a model-free data-driven method of solution. The solution at a given load step is identified as the point within the data set that best satisfies either the Kuhn–Tucker conditions stemming from the variational fracture problem or global minimization of a suitable energy functional, leading to data-driven counterparts of both the local and the global minimization approaches of variational fracture mechanics. Both formulations are tested on different test configurations with and without noise and for Griffith and R-curve type fracture behavior.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/b3kg0-v1855Mollified finite element approximants of arbitrary order and smoothness
https://resolver.caltech.edu/CaltechAUTHORS:20201210-083948637
Authors: {'items': [{'id': 'Febrianto-Eky', 'name': {'family': 'Febrianto', 'given': 'Eky'}, 'orcid': '0000-0002-5354-2589'}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'Michael'}, 'orcid': '0000-0001-5877-4824'}, {'id': 'Cirak-Fehmi', 'name': {'family': 'Cirak', 'given': 'Fehmi'}, 'orcid': '0000-0002-9274-6904'}]}
Year: 2021
DOI: 10.1016/j.cma.2020.113513
The approximation properties of the finite element method can often be substantially improved by choosing smooth high-order basis functions. It is extremely difficult to devise such basis functions for partitions consisting of arbitrarily shaped polytopes. We propose the mollified basis functions of arbitrary order and smoothness for partitions consisting of convex polytopes. On each polytope an independent local polynomial approximant of arbitrary order is assumed. The basis functions are defined as the convolutions of the local approximants with a mollifier. The mollifier is chosen to be smooth, to have a compact support and a unit volume. The approximation properties of the obtained basis functions are governed by the local polynomial approximation order and mollifier smoothness. The convolution integrals are evaluated numerically first by computing the boolean intersection between the mollifier and the polytope and then applying the divergence theorem to reduce the dimension of the integrals. The support of a basis function is given as the Minkowski sum of the respective polytope and the mollifier. The breakpoints of the basis functions, i.e. locations with non-infinite smoothness, are not necessarily aligned with polytope boundaries. Furthermore, the basis functions are not boundary interpolating so that we apply boundary conditions with the non-symmetric Nitsche method as in immersed/embedded finite elements. The presented numerical examples confirm the optimal convergence of the proposed approximation scheme for Poisson and elasticity problems.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/kkman-46j95Model-free data-driven computational mechanics enhanced by tensor voting
https://resolver.caltech.edu/CaltechAUTHORS:20201015-152733627
Authors: {'items': [{'id': 'Eggersmann-Robert', 'name': {'family': 'Eggersmann', 'given': 'Robert'}}, {'id': 'Stainier-Laurent', 'name': {'family': 'Stainier', 'given': 'Laurent'}, 'orcid': '0000-0001-6719-6616'}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'Michael'}, 'orcid': '0000-0001-5877-4824'}, {'id': 'Reese-Stefanie', 'name': {'family': 'Reese', 'given': 'Stefanie'}}]}
Year: 2021
DOI: 10.1016/j.cma.2020.113499
The data-driven computing paradigm initially introduced by Kirchdoerfer and Ortiz (2016) is extended by incorporating locally linear tangent spaces into the data set. These tangent spaces are constructed by means of the tensor voting method introduced by Mordohai and Medioni (2010) which improves the learning of the underlying structure of a data set. Tensor voting is an instance-based machine learning technique which accumulates votes from the nearest neighbors to build up second-order tensors encoding tangents and normals to the underlying data structure. The here proposed second-order data-driven paradigm is a plug-in method for distance-minimizing as well as entropy-maximizing data-driven schemes. Like its predecessor (Kirchdoerfer and Ortiz, 2016), the resulting method aims to minimize a suitably defined free energy over phase space subject to compatibility and equilibrium constraints. The method's implementation is straightforward and numerically efficient since the data structure analysis is performed in an offline step. Selected numerical examples are presented that establish the higher-order convergence properties of the data-driven solvers enhanced by tensor voting for ideal and noisy data sets.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/qcjth-1jj29Molecular dynamics study of the shock response of polyurea
https://resolver.caltech.edu/CaltechAUTHORS:20201012-103540350
Authors: {'items': [{'id': 'Manav-Manav', 'name': {'family': 'Manav', 'given': 'M.'}, 'orcid': '0000-0002-8498-4144'}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'M.'}, 'orcid': '0000-0001-5877-4824'}]}
Year: 2021
DOI: 10.1016/j.polymer.2020.123109
We leverage the phase segregated microstructure of polyurea to study its shock response using molecular dynamics (MD) simulation. The two phase segregated domains, the hard and the soft domains, are investigated separately. The shock response of the domains is studied using a multiscale shock-simulation approach that allows simulation of low pressure shocks. Both domains exhibit an unconventional behavior at low shock velocities that is typically associated with polymers. The shock response of the hard domain is marked by energy dissipation due to hydrogen bond breaking. Moreover, the radial distribution function suggests a severe distortion in the ring structure of aromatic moieties in the hard domain at high shock pressure. Finally, the shock Hugoniot of polyurea, obtained by combining the response of the two domains using a mixing rule, shows excellent match with experimental data.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/38psz-tnt81Data-Driven Multiscale Modeling in Mechanics
https://resolver.caltech.edu/CaltechAUTHORS:20201123-120506132
Authors: {'items': [{'id': 'Karapiperis-Konstantinos', 'name': {'family': 'Karapiperis', 'given': 'K.'}, 'orcid': '0000-0002-6796-8900'}, {'id': 'Stainier-Laurent', 'name': {'family': 'Stainier', 'given': 'L.'}, 'orcid': '0000-0001-6719-6616'}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'M.'}, 'orcid': '0000-0001-5877-4824'}, {'id': 'Andrade-J-E', 'name': {'family': 'Andrade', 'given': 'J. E.'}}]}
Year: 2021
DOI: 10.1016/j.jmps.2020.104239
We present a Data-Driven framework for multiscale mechanical analysis of materials. The proposed framework relies on the Data-Driven formulation in mechanics (Kirchdoerfer and Ortiz 2016), with the material data being directly extracted from lower-scale computations. Particular emphasis is placed on two key elements: the parametrization of material history, and the optimal sampling of the mechanical state space. We demonstrate an application of the framework in the prediction of the behavior of sand, a prototypical complex history-dependent material. In particular, the model is able to predict the material response under complex nonmonotonic loading paths, and compares well against plane strain and triaxial compression shear banding experiments.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/b2s76-b8s23Experimental Validation of the Attenuation Properties in the Sonic Range of Metaconcrete Containing Two Types of Resonant Inclusions
https://resolver.caltech.edu/CaltechAUTHORS:20201102-091525367
Authors: {'items': [{'id': 'Briccola-Deborah', 'name': {'family': 'Briccola', 'given': 'D.'}}, {'id': 'Cuni-M', 'name': {'family': 'Cuni', 'given': 'M.'}}, {'id': 'De-Juli-A', 'name': {'family': 'De Juli', 'given': 'A.'}}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'M.'}, 'orcid': '0000-0001-5877-4824'}, {'id': 'Pandolfi-Anna', 'name': {'family': 'Pandolfi', 'given': 'A.'}, 'orcid': '0000-0002-7084-7456'}]}
Year: 2021
DOI: 10.1007/s11340-020-00668-4
Background: Metaconcrete is a new concept of concrete, showing marked attenuation properties under impact and blast loading, where traditional aggregates are partially replaced by resonant bi-material inclusions. In a departure from conventional mechanical metamaterials, the inclusions are dispersed randomly as cast in the material. The behavior of metaconcrete at supersonic frequencies has been investigated theoretically and numerically and confirmed experimentally.
Objective: The feasibility of metaconcrete to achieve wave attenuation at low frequencies demands further experimental validation. The present study is directed at characterizing dynamically, in the range of the low sonic frequencies, the—possibly synergistic—effect of combinations of different types of inclusions on the attenuation properties of metaconcrete.
Methods: Dynamic tests are conducted on cylindrical metaconcrete specimens cast with two types of spherical inclusions, made of a steel core and a polymeric coating. The two inclusions differ in terms of size and coating material: type 1 inclusions are 22 mm diameter with 1.35 mm PDMS coating; type 2 inclusions are 24 mm diameter with 2 mm layer natural rubber coating. Linear frequency sweeps in the low sonic range (< 10 kHz), tuned to numerically estimated inclusion eigenfrequencies, are applied to the specimens through a mechanical actuator. The transmitted waves are recorded by transducers and Fast-Fourier transformed (FFT) to bring the attenuation spectrum of the material into full display.
Results: Amplitude reductions of transmitted signals are markedly visible for any metaconcrete specimens in the range of the inclusion resonant frequencies, namely, 3,400-3,500 Hz for the PDMS coating inclusions and near 3,200 Hz for the natural rubber coating inclusions. Specimens with mixed inclusions provide a rather uniform attenuation in a limited range of frequencies, independently of the inclusion density, while specimens with a single inclusion type are effective over larger frequency ranges. With respect to conventional concrete, metaconcrete reduces up to 90% the amplitude of the transmitted signal within the attenuation bands.
Conclusions: Relative to conventional concrete, metaconcrete strongly attenuates waves over frequency bands determined by the resonant frequencies of the inclusions. The present dynamical tests conducted in the sonic range of frequencies quantify the attenuation properties of the metaconcrete cast with two types inclusions, providing location, range and intensity of the attenuation bands, which are dependent on the physical-geometric features of the inclusions.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/mbyt5-3pb27Applications of the J-integral to dynamical problems in geotechnical engineering
https://resolver.caltech.edu/CaltechAUTHORS:20210216-140504716
Authors: {'items': [{'id': 'Garcia-Suarez-Joaquin', 'name': {'family': 'Garcia-Suarez', 'given': 'J.'}, 'orcid': '0000-0001-8830-4348'}, {'id': 'Asimaki-D', 'name': {'family': 'Asimaki', 'given': 'D.'}, 'orcid': '0000-0002-3008-8088'}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'M.'}, 'orcid': '0000-0001-5877-4824'}]}
Year: 2021
DOI: 10.1016/j.jmps.2021.104353
We formulate a path-independent J-integral for the elastodynamic problem expressed in the frequency domain. We show that the path-independence of the integral can be exploited in order to derive ansatz-free identities and rigorous inequalities in certain problems arising in geotechnical engineering. By way of illustration, we specifically consider the problem of assessing seismic pressures on retaining walls. We show that the bounds for the earth thrust derived from the frequency-domain dynamic -integral improve upon previous heuristic and conjectured bounds.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/pnmxy-g7385A semi-discrete line-free method of monopoles for dislocation dynamics
https://resolver.caltech.edu/CaltechAUTHORS:20210317-151949384
Authors: {'items': [{'id': 'Ariza-Maria-Pilar', 'name': {'family': 'Ariza', 'given': 'M. P.'}, 'orcid': '0000-0003-0266-0216'}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'M.'}, 'orcid': '0000-0001-5877-4824'}]}
Year: 2021
DOI: 10.1016/j.eml.2021.101267
We develop a semi-discrete particle method for Volterra dislocation currents in which the particles, or monopoles, represent an element of line and carry a Burgers vector. The monopoles move according to mobility kinetics driven by elastic and applied forces. The divergence constraint of Volterra dislocation currents is enforced weakly through mesh-free interpolation and an explicit linear connectivity, or 'sequence', between the monopoles need not be defined. In this sense, the method is 'line-free', i. e., it sidesteps the need to track dislocation lines. This attribute offers significant computational advantages in terms of simplicity, robustness and efficiency, especially as regards the tracking of complex dislocation patterns, including topological transitions. We illustrate the range and scope of the method, by means of an example of application concerned with the plastic hardening of nano-sized grains under monotonic loading.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/rsz7k-0jp35Finite element solver for data-driven finite strain elasticity
https://resolver.caltech.edu/CaltechAUTHORS:20210423-164852906
Authors: {'items': [{'id': 'Platzer-Auriane', 'name': {'family': 'Platzer', 'given': 'Auriane'}, 'orcid': '0000-0002-0244-9632'}, {'id': 'Leygue-Adrien', 'name': {'family': 'Leygue', 'given': 'Adrien'}, 'orcid': '0000-0003-0714-822X'}, {'id': 'Stainier-Laurent', 'name': {'family': 'Stainier', 'given': 'Laurent'}, 'orcid': '0000-0001-6719-6616'}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'Michael'}, 'orcid': '0000-0001-5877-4824'}]}
Year: 2021
DOI: 10.1016/j.cma.2021.113756
A nominal finite element solver is proposed for data-driven finite strain elasticity. It bypasses the need for a constitutive model by considering a database of deformation gradient/first Piola–Kirchhoff stress tensors pairs. The boundary value problem is reformulated as the constrained minimization problem of the distance between (i) the mechanical states, i.e. strain–stress, in the body and (ii) the material states coming from the database. The corresponding constraints are of two types: kinematical, i.e. displacement–strain relation, and mechanical, i.e. conservation linear and angular momenta. The solver uses alternated minimization: the material states are determined from a local search in the database using an efficient tree-based nearest neighbor search algorithm, and the mechanical states result from a standard constrained minimization addressed with an augmented Lagrangian approach. The performance of the solver is demonstrated by means of 2D sanity check examples: the data-driven solution converges to the classical finite element solution when the material database increasingly approximates the constitutive model. In addition, we demonstrate that the balance of angular momentum, which was classically not taken into account in previous data-driven studies, must be enforced as a constraint to ensure the convergence of the method.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/bhy5c-bye50Concurrent goal-oriented materials-by-design
https://resolver.caltech.edu/CaltechAUTHORS:20210713-212259269
Authors: {'items': [{'id': 'Sun-Xingsheng', 'name': {'family': 'Sun', 'given': 'Xingsheng'}, 'orcid': '0000-0003-1527-789X'}, {'id': 'Liu-Burigede', 'name': {'family': 'Liu', 'given': 'Burigede'}, 'orcid': '0000-0002-6518-3368'}, {'id': 'Bhattacharya-K', 'name': {'family': 'Bhattacharya', 'given': 'Kaushik'}, 'orcid': '0000-0003-2908-5469'}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'Michael'}, 'orcid': '0000-0001-5877-4824'}]}
Year: 2021
DOI: 10.48550/arXiv.2106.06074
The development of new materials and structures for extreme conditions including impact remains a continuing challenge despite steady advances. Design is currently accomplished using a sequential approach: an optimal material is first developed using the process-structure-properties paradigm, where performance is measured against a blended measure. Then, the structure is optimized while holding the material properties fixed. In this paper, we propose an alternative concurrent and goal-oriented optimization approach where both the material properties and the structure are optimized simultaneously against an overall system-wide performance measure. We develop a non-intrusive, high-performance computational framework based on DAKOTA and GMSH and use it to study the ballistic impact of a double-layer plate of strong AZ31B magnesium alloy and soft polyurea. We show that the proposed concurrent and goal-oriented optimization strategy can provide significant advantage over the traditional sequential optimization approach.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/3nqk7-yhe03Model-free Data-Driven Inference
https://resolver.caltech.edu/CaltechAUTHORS:20210719-210156414
Authors: {'items': [{'id': 'Conti-Sergio', 'name': {'family': 'Conti', 'given': 'S.'}, 'orcid': '0000-0001-7987-9174'}, {'id': 'Hoffmann-Franca', 'name': {'family': 'Hoffmann', 'given': 'F.'}, 'orcid': '0000-0002-1182-5521'}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'M.'}, 'orcid': '0000-0001-5877-4824'}]}
Year: 2021
DOI: 10.48550/arXiv.2106.02728
We present a model-free data-driven inference method that enables inferences
on system outcomes to be derived directly from empirical data without the need
for intervening modeling of any type, be it modeling of a material law or
modeling of a prior distribution of material states. We specifically consider
physical systems with states characterized by points in a phase space
determined by the governing field equations. We assume that the system is
characterized by two likelihood measures: one µ_D measuring the likelihood
of observing a material state in phase space; and another µ_E measuring the
likelihood of states satisfying the field equations, possibly under random
actuation. We introduce a notion of intersection between measures which can be
interpreted to quantify the likelihood of system outcomes. We provide
conditions under which the intersection can be characterized as the athermal
limit µ∞ of entropic regularizations µ_β, or thermalizations,
of the product measure µ = µ_D x µ_E as β → +∞. We
also supply conditions under which µ∞ can be obtained as the athermal
limit of carefully thermalized (µ_h,β_h) sequences of empirical data
sets (µ_h) approximating weakly an unknown likelihood function µ. In
particular, we find that the cooling sequence β_h → +∞ must be
slow enough, corresponding to quenching, in order for the proper limit
µ∞ to be delivered. Finally, we derive explicit analytic expressions
for expectations E[f] of outcomes f that are explicit in the data,
thus demonstrating the feasibility of the model-free data-driven paradigm as
regards making convergent inferences directly from the data without recourse to
intermediate modeling steps.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/9zdx5-0jx90Nonequilibrium thermomechanics of Gaussian phase packet crystals: Application to the quasistatic quasicontinuum method
https://resolver.caltech.edu/CaltechAUTHORS:20210518-103040351
Authors: {'items': [{'id': 'Gupta-Prateek', 'name': {'family': 'Gupta', 'given': 'Prateek'}, 'orcid': '0000-0003-3666-0257'}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'Michael'}, 'orcid': '0000-0001-5877-4824'}, {'id': 'Kochmann-D-M', 'name': {'family': 'Kochmann', 'given': 'Dennis M.'}, 'orcid': '0000-0002-9112-6615'}]}
Year: 2021
DOI: 10.1016/j.jmps.2021.104495
The quasicontinuum (QC) method was originally introduced to bridge across length scales by coarse-graining an atomistic ensemble to significantly larger continuum scales at zero temperature, thus overcoming the crucial length-scale limitation of classical atomic-scale simulation techniques while solely relying on atomic-scale input (in the form of interatomic potentials). An associated challenge lies in bridging across time scales to overcome the time-scale limitations of atomistics at finite temperature. To address the biggest challenge, bridging across both length and time scales, only a few techniques exist, and most of those are limited to conditions of constant temperature. Here, we present a new general strategy for the space–time coarsening of an atomistic ensemble, which introduces thermomechanical coupling. Specifically, we evolve the statistics of an atomistic ensemble in phase space over time by applying the Liouville equation to an approximation of the ensemble's probability distribution (which further admits a variational formulation). To this end, we approximate a crystalline solid as a lattice of lumped correlated Gaussian phase packets occupying atomic lattice sites, and we investigate the resulting quasistatics and dynamics of the system. By definition, phase packets account for the dynamics of crystalline lattices at finite temperature through the statistical variances of atomic momenta and positions. We show that momentum–space correlation allows for an exchange between potential and kinetic contributions to the crystal's Hamiltonian. Consequently, local adiabatic heating due to atomic site motion is captured. Moreover, in the quasistatic limit, the governing equations reduce to the minimization of thermodynamic potentials (similar to maximum-entropy formulation previously introduced for finite-temperature QC), and they yield the local equation of state, which we derive for isothermal, isobaric, and isentropic conditions. Since our formulation without interatomic correlations precludes irreversible heat transport, we demonstrate its combination with thermal transport models to describe realistic atomic-level processes, and we discuss opportunities for capturing atomic-level thermal transport by including interatomic correlations in the Gaussian phase packet formulation. Overall, our Gaussian phase packet approach offers a promising avenue for finite-temperature non-equilibrium quasicontinuum techniques, which may be combined with thermal transport models and extended to other approximations of the probability distribution as well as to exploit the variational structure.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/7njpe-mks78Hierarchical multiscale quantification of material uncertainty
https://resolver.caltech.edu/CaltechAUTHORS:20210225-132735184
Authors: {'items': [{'id': 'Liu-Burigede', 'name': {'family': 'Liu', 'given': 'Burigede'}, 'orcid': '0000-0002-6518-3368'}, {'id': 'Sun-Xingsheng', 'name': {'family': 'Sun', 'given': 'Xingsheng'}}, {'id': 'Bhattacharya-K', 'name': {'family': 'Bhattacharya', 'given': 'Kaushik'}, 'orcid': '0000-0003-2908-5469'}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'Michael'}, 'orcid': '0000-0001-5877-4824'}]}
Year: 2021
DOI: 10.1016/j.jmps.2021.104492
The macroscopic behavior of many materials is complex and the end result of mechanisms that operate across a broad range of disparate scales. An imperfect knowledge of material behavior across scales is a source of epistemic uncertainty of the overall material behavior. However, assessing this uncertainty is difficult due to the complex nature of material response and the prohibitive computational cost of integral calculations. In this paper, we exploit the multiscale and hierarchical nature of material response to develop an approach to quantify the overall uncertainty of material response without the need for integral calculations. Specifically, we bound the uncertainty at each scale and then combine the partial uncertainties in a way that provides a bound on the overall or integral uncertainty. The bound provides a conservative estimate on the uncertainty. Importantly, this approach does not require integral calculations that are prohibitively expensive. We demonstrate the framework on the problem of ballistic impact of a polycrystalline magnesium plate. Magnesium and its alloys are of current interest as promising light-weight structural and protective materials. Finally, we remark that the approach can also be used to study the sensitivity of the overall response to particular mechanisms at lower scales in a materials-by-design approach.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/cx5h6-8ef30Efficient data structures for model-free data-driven computational mechanics
https://resolver.caltech.edu/CaltechAUTHORS:20210225-132741960
Authors: {'items': [{'id': 'Eggersmann-Robert', 'name': {'family': 'Eggersmann', 'given': 'Robert'}}, {'id': 'Stainier-Laurent', 'name': {'family': 'Stainier', 'given': 'Laurent'}, 'orcid': '0000-0001-6719-6616'}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'Michael'}, 'orcid': '0000-0001-5877-4824'}, {'id': 'Reese-Stefanie', 'name': {'family': 'Reese', 'given': 'Stefanie'}}]}
Year: 2021
DOI: 10.1016/j.cma.2021.113855
The data-driven computing paradigm initially introduced by Kirchdoerfer & Ortiz (2016) enables finite element computations in solid mechanics to be performed directly from material data sets, without an explicit material model. From a computational effort point of view, the most challenging task is the projection of admissible states at material points onto their closest states in the material data set. In this study, we compare and develop several possible data structures for solving the nearest-neighbor problem. We show that approximate nearest-neighbor (ANN) algorithms can accelerate material data searches by several orders of magnitude relative to exact searching algorithms. The approximations are suggested by—and adapted to—the structure of the data-driven iterative solver and result in no significant loss of solution accuracy. We assess the performance of the ANN algorithm with respect to material data set size with the aid of a 3D elasticity test case. We show that computations on a single processor with up to one billion material data points are feasible within a few seconds execution time with a speed up of more than 10⁶ with respect to exact k-d trees.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/x2qtq-53t11Data-driven rate-dependent fracture mechanics
https://resolver.caltech.edu/CaltechAUTHORS:20210722-144956534
Authors: {'items': [{'id': 'Carrara-Pietro', 'name': {'family': 'Carrara', 'given': 'P.'}, 'orcid': '0000-0003-4740-1306'}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'M.'}, 'orcid': '0000-0001-5877-4824'}, {'id': 'De-Lorenzis-Laura', 'name': {'family': 'De Lorenzis', 'given': 'L.'}, 'orcid': '0000-0003-2748-3287'}]}
Year: 2021
DOI: 10.1016/j.jmps.2021.104559
We extend the model-free data-driven paradigm for rate-independent fracture mechanics proposed in Carrara et al. (2020), to rate-dependent fracture and sub-critical fatigue. The problem is formulated by combining the balance governing equations stemming from variational principles with a set of data points that encodes the fracture constitutive behavior of the material. The solution is found as the data point that best satisfies the meta-stability condition as given by the variational procedure and following a distance minimization approach based on closest-point-projection. The approach is tested on different setups adopting different types of rate-dependent fracture and fatigue models affected or not by white noise.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/1hfm0-tmc61Hydrogen-induced transgranular to intergranular fracture transition in bi-crystalline nickel
https://resolver.caltech.edu/CaltechAUTHORS:20210722-162827192
Authors: {'items': [{'id': 'Ding-Yu', 'name': {'family': 'Ding', 'given': 'Yu'}}, {'id': 'Yu-Haiyang', 'name': {'family': 'Yu', 'given': 'Haiyang'}, 'orcid': '0000-0002-2419-6736'}, {'id': 'Zhao-Kai', 'name': {'family': 'Zhao', 'given': 'Kai'}, 'orcid': '0000-0003-2645-7917'}, {'id': 'Lin-Meichao', 'name': {'family': 'Lin', 'given': 'Meichao'}}, {'id': 'Xiao-Senbo', 'name': {'family': 'Xiao', 'given': 'Senbo'}}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'Michael'}, 'orcid': '0000-0001-5877-4824'}, {'id': 'He-Jianying', 'name': {'family': 'He', 'given': 'Jianying'}}, {'id': 'Zhang-Zhiliang', 'name': {'family': 'Zhang', 'given': 'Zhiliang'}}]}
Year: 2021
DOI: 10.1016/j.scriptamat.2021.114122
It is known that hydrogen can influence the dislocation plasticity and fracture mode transition of metallic materials, however, the nanoscale interaction mechanism between hydrogen and grain boundary largely remains illusive. By uniaxial straining of bi-crystalline Ni with a Σ5(210)[001] grain boundary, a transgranular to intergranular fracture transition facilitated by hydrogen is elucidated by atomistic modeling, and a specific hydrogen-controlled plasticity mechanism is revealed. Hydrogen is found to form a local atmosphere in the vicinity of grain boundary, which induces a local stress concentration and inhibits the subsequent stress relaxation at the grain boundary during deformation. It is this local stress concentration that promotes earlier dislocation emission, twinning evolution, and generation of more vacancies that facilitate nanovoiding. The nucleation and growth of nanovoids finally leads to intergranular fracture at the grain boundary, in contrast to the transgranular fracture of hydrogen-free sample.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/ymw3h-3pm04Data-Driven nonlocal mechanics: Discovering the internal length scales of materials
https://resolver.caltech.edu/CaltechAUTHORS:20210908-171123194
Authors: {'items': [{'id': 'Karapiperis-Konstantinos', 'name': {'family': 'Karapiperis', 'given': 'K.'}, 'orcid': '0000-0002-6796-8900'}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'M.'}, 'orcid': '0000-0001-5877-4824'}, {'id': 'Andrade-J-E', 'name': {'family': 'Andrade', 'given': 'J. E.'}}]}
Year: 2021
DOI: 10.1016/j.cma.2021.114039
Nonlocal effects permeate most microstructured materials, including granular media, metals and foams. The quest for predictive nonlocal mechanical theories with well-defined internal length scales has been ongoing for more than a century since the seminal work of the Cosserats. We present here a novel framework for the nonlocal analysis of material behavior, which bypasses the need to define any internal length scale. This is achieved by extending the Data-Driven paradigm in mechanics, originally introduced for simple continua, into generalized continua. The problem is formulated directly on a material data set, comprised of higher-order kinematics and their conjugate kinetics, which are identified from experiments or inferred from lower scale computations. The case of a micropolar continuum is used as a vehicle to introduce the framework, which may also be adapted to strain-gradient and micromorphic media. Two applications are presented: a micropolar elastic plate with a hole, which is used to demonstrate the convergence properties of the method, and the shear banding problem of a triaxially compressed sample of quartz sand, which is used to demonstrate the applicability of the method in the case of complex history-dependent material behavior.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/mvx1v-5qg28A comparative accuracy and convergence study of eigenerosion and phase-field models of fracture
https://resolver.caltech.edu/CaltechAUTHORS:20210225-132738559
Authors: {'items': [{'id': 'Pandolfi-Anna', 'name': {'family': 'Pandolfi', 'given': 'A.'}, 'orcid': '0000-0002-7084-7456'}, {'id': 'Weinberg-Kerstin', 'name': {'family': 'Weinberg', 'given': 'K.'}, 'orcid': '0000-0002-2213-8401'}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'M.'}, 'orcid': '0000-0001-5877-4824'}]}
Year: 2021
DOI: 10.1016/j.cma.2021.114078
We compare the accuracy, convergence rate and computational cost of eigenerosion (EE) and phase-field (PF) methods. For purposes of comparison, we specifically consider the standard test case of a center-crack panel loaded in biaxial tension and assess the convergence of the energy error as the length scale parameter and mesh size tend to zero simultaneously. The panel is discretized by means of a regular mesh consisting of standard bilinear or Q1 elements. The exact stresses from the known analytical linear elastic solution are applied to the boundary. All element integrals over the interior and the boundary of the domain are evaluated exactly using the symbolic computation program Mathematica. When the EE inelastic energy is enhanced by means of Richardson extrapolation, EE is found to converge at twice the rate of PF and to exhibit much better accuracy. In addition, EE affords a one-order-of-magnitude computational speed-up over PF.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/t4gcf-zfc87Accurate approximations of density functional theory for large systems with applications to defects in crystalline solids
https://resolver.caltech.edu/CaltechAUTHORS:20220119-233956787
Authors: {'items': [{'id': 'Bhattacharya-K', 'name': {'family': 'Bhattacharya', 'given': 'Kaushik'}, 'orcid': '0000-0003-2908-5469'}, {'id': 'Gavini-Vikram', 'name': {'family': 'Gavini', 'given': 'Vikram'}, 'orcid': '0000-0002-9451-2300'}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'Michael'}, 'orcid': '0000-0001-5877-4824'}, {'id': 'Ponga-Mauricio', 'name': {'family': 'Ponga', 'given': 'Mauricio'}, 'orcid': '0000-0001-5058-1454'}, {'id': 'Suryanarayana-Phanish', 'name': {'family': 'Suryanarayana', 'given': 'Phanish'}, 'orcid': '0000-0001-5172-0049'}]}
Year: 2021
DOI: 10.48550/arXiv.2112.06016
This chapter presents controlled approximations of Kohn-Sham density functional theory (DFT) that enable very large scale simulations. The work is motivated by the study of defects in crystalline solids, though the ideas can be used in other applications. The key idea is to formulate DFT as a minimization problem over the density operator, and to cast spatial and spectral discretization as systematically convergent approximations. This enables efficient and adaptive algorithms that solve the equations of DFT with no additional modeling, and up to desired accuracy, for very large systems, with linear and sublinear scaling. Various approaches based on such approximations are presented, and their numerical performance demonstrated through selected examples. These examples also provide important insight about the mechanics and physics of defects in crystalline solids.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/gb81e-r3t46Mechanics of ultrasonic neuromodulation in a mouse subject
https://resolver.caltech.edu/CaltechAUTHORS:20210929-163841106
Authors: {'items': [{'id': 'Salahshoor-Hossein', 'name': {'family': 'Salahshoor', 'given': 'Hossein'}, 'orcid': '0000-0002-7264-7650'}, {'id': 'Guo-Hongsun', 'name': {'family': 'Guo', 'given': 'Hongsun'}}, {'id': 'Shapiro-M-G', 'name': {'family': 'Shapiro', 'given': 'Mikhail G.'}, 'orcid': '0000-0002-0291-4215'}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'Michael'}, 'orcid': '0000-0001-5877-4824'}]}
Year: 2022
DOI: 10.1016/j.eml.2021.101539
PMCID: PMC10760995
Ultrasound neuromodulation (UNM), where a region in the brain is targeted by focused ultrasound (FUS), which, in turn, causes excitation or inhibition of neural activity, has recently received considerable attention as a promising tool for neuroscience. Despite its great potential, several aspects of UNM are still unknown. An important question pertains to the off-target sensory effects of UNM and their dependence on stimulation frequency. To understand these effects, we have developed a finite-element model of a mouse, including elasticity and viscoelasticity, and used it to interrogate the response of mouse models to focused ultrasound (FUS). We find that, while some degree of focusing and magnification of the signal is achieved within the brain, the induced pressure-wave pattern is complex and delocalized. In addition, we find that the brain is largely insulated, or 'cloaked', from shear waves by the cranium and that the shear waves are largely carried away from the skull by the vertebral column, which acts as a waveguide. We find that, as expected, this waveguide mechanism is strongly frequency dependent, which may contribute to the frequency dependence of UNM effects. Our calculations further suggest that off-target skin locations experience displacements and stresses at levels that, while greatly attenuated from the source, could nevertheless induce sensory responses in the subject.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/q7vbx-5eb89Mechanics of ultrasonic neuromodulation in a mouse subject
https://resolver.caltech.edu/CaltechAUTHORS:20210929-163841106
Authors: {'items': [{'id': 'Salahshoor-Hossein', 'name': {'family': 'Salahshoor', 'given': 'Hossein'}, 'orcid': '0000-0002-7264-7650'}, {'id': 'Guo-Hongsun', 'name': {'family': 'Guo', 'given': 'Hongsun'}}, {'id': 'Shapiro-M-G', 'name': {'family': 'Shapiro', 'given': 'Mikhail G.'}, 'orcid': '0000-0002-0291-4215'}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'Michael'}, 'orcid': '0000-0001-5877-4824'}]}
Year: 2022
DOI: 10.1016/j.eml.2021.101539
Ultrasound neuromodulation (UNM), where a region in the brain is targeted by focused ultrasound (FUS), which, in turn, causes excitation or inhibition of neural activity, has recently received considerable attention as a promising tool for neuroscience. Despite its great potential, several aspects of UNM are still unknown. An important question pertains to the off-target sensory effects of UNM and their dependence on stimulation frequency. To understand these effects, we have developed a finite-element model of a mouse, including elasticity and viscoelasticity, and used it to interrogate the response of mouse models to focused ultrasound (FUS). We find that, while some degree of focusing and magnification of the signal is achieved within the brain, the induced pressure-wave pattern is complex and delocalized. In addition, we find that the brain is largely insulated, or 'cloaked', from shear waves by the cranium and that the shear waves are largely carried away from the skull by the vertebral column, which acts as a waveguide. We find that, as expected, this waveguide mechanism is strongly frequency dependent, which may contribute to the frequency dependence of UNM effects. Our calculations further suggest that off-target skin locations experience displacements and stresses at levels that, while greatly attenuated from the source, could nevertheless induce sensory responses in the subject.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/2c8jb-mkg02Multiscale modeling of materials: Computing, data science, uncertainty and goal-oriented optimization
https://resolver.caltech.edu/CaltechAUTHORS:20220121-968309000
Authors: {'items': [{'id': 'Kovachki-Nikola-B', 'name': {'family': 'Kovachki', 'given': 'Nikola'}, 'orcid': '0000-0002-3650-2972'}, {'id': 'Liu-Burigede', 'name': {'family': 'Liu', 'given': 'Burigede'}, 'orcid': '0000-0002-6518-3368'}, {'id': 'Sun-Xingsheng', 'name': {'family': 'Sun', 'given': 'Xingsheng'}, 'orcid': '0000-0003-1527-789X'}, {'id': 'Zhou-Hao', 'name': {'family': 'Zhou', 'given': 'Hao'}, 'orcid': '0000-0002-6011-6422'}, {'id': 'Bhattacharya-K', 'name': {'family': 'Bhattacharya', 'given': 'Kaushik'}, 'orcid': '0000-0003-2908-5469'}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'Michael'}, 'orcid': '0000-0001-5877-4824'}, {'id': 'Stuart-A-M', 'name': {'family': 'Stuart', 'given': 'Andrew'}, 'orcid': '0000-0001-9091-7266'}]}
Year: 2022
DOI: 10.1016/j.mechmat.2021.104156
The recent decades have seen various attempts at accelerating the process of developing materials targeted towards specific applications. The performance required for a particular application leads to the choice of a particular material system whose properties are optimized by manipulating its underlying microstructure through processing. The specific configuration of the structure is then designed by characterizing the material in detail, and using this characterization along with physical principles in system level simulations and optimization. These have been advanced by multiscale modeling of materials, high-throughput experimentations, materials data-bases, topology optimization and other ideas. Still, developing materials for extreme applications involving large deformation, high strain rates and high temperatures remains a challenge. This article reviews a number of recent methods that advance the goal of designing materials targeted by specific applications.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/cjvbg-kbb29A Proof of Taylor Scaling for Curvature-Driven Dislocation Motion Through Random Arrays of Obstacles
https://resolver.caltech.edu/CaltechAUTHORS:20210719-210159826
Authors: {'items': [{'id': 'Courte-Luca', 'name': {'family': 'Courte', 'given': 'Luca'}}, {'id': 'Dondl-Patrick-W', 'name': {'family': 'Dondl', 'given': 'Patrick'}, 'orcid': '0000-0003-3035-7230'}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'Michael'}, 'orcid': '0000-0001-5877-4824'}]}
Year: 2022
DOI: 10.1007/s00205-022-01765-5
We prove Taylor scaling for dislocation lines characterized by line-tension and moving by curvature under the action of an applied shear stress in a plane containing a random array of obstacles. Specifically, we show—in the sense of optimal scaling—that the critical applied shear stress for yielding, or percolation-like unbounded motion of the dislocation, scales in proportion to the square root of the obstacle density. For sufficiently small obstacle densities, Taylor scaling dominates the linear-scaling that results from purely energetic considerations and, therefore, characterizes the dominant rate-limiting mechanism in that regime.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/seaet-sjc76A spatially adaptive phase-field model of fracture
https://resolver.caltech.edu/CaltechAUTHORS:20220517-424411000
Authors: {'items': [{'id': 'Phansalkar-Dhananjay', 'name': {'family': 'Phansalkar', 'given': 'Dhananjay'}, 'orcid': '0000-0001-7870-1446'}, {'id': 'Weinberg-Kerstin', 'name': {'family': 'Weinberg', 'given': 'Kerstin'}, 'orcid': '0000-0002-2213-8401'}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'Michael'}, 'orcid': '0000-0001-5877-4824'}, {'id': 'Leyendecker-Sigrid', 'name': {'family': 'Leyendecker', 'given': 'Sigrid'}}]}
Year: 2022
DOI: 10.1016/j.cma.2022.114880
Phase-field models of fracture introduce smeared cracks of width commensurate with a regularisation length parameter ϵ and obeying a minimum energy principle. Mesh adaptivity naturally suggests itself as a means of supplying spatial resolution where needed while simultaneously keeping the computational size of the model as small as possible. Here, a variational-based spatial adaptivity is proposed for a phase-field model of fracture.
An extension of the conventional phase-field model is achieved by allowing spatial variation of the regularisation length ϵ in the energy functional. Similar to the displacement and phase fields, the optimal regularisation length is obtained by minimising the energy functional. This extended phase-field model serves as the foundation for an adaptive mesh refinement strategy, in which the mesh size is determined locally by the optimal regularisation length. The resulting solution procedure is implemented in the framework of the finite element library FEniCS. According to the selected numerical experiment, the spatially adaptive phase-field model converges marginally faster than the conventional phase-field model but with a vastly superior constant, resulting in significant computational savings.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/msk4z-vwr43Model-Free Data-Driven Viscoelasticity in the Frequency Domain
https://resolver.caltech.edu/CaltechAUTHORS:20220707-204105977
Authors: {'items': [{'id': 'Salahshoor-Hossein', 'name': {'family': 'Salahshoor', 'given': 'Hossein'}, 'orcid': '0000-0002-7264-7650'}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'Michael'}, 'orcid': '0000-0001-5877-4824'}]}
Year: 2022
DOI: 10.48550/arXiv.arXiv.2205.06674
We develop a Data-Driven framework for the simulation of wave propagation in viscoelastic solids directly from dynamic testing material data, including data from Dynamic Mechanical Analysis (DMA), nano-indentation, Dynamic Shear Testing (DST) and Magnetic Resonance Elastography (MRE), without the need for regression or material modeling. The problem is formulated in the frequency domain and the method of solution seeks to minimize a distance between physically admissible histories of stress and strain, in the sense of compatibility and equilibrium, and the material data. We metrize the space of histories by means of the flat-norm of their Fourier transform, which allows consideration of infinite wave trains such as harmonic functions. Another significant advantage of the flat norm is that it allows the response of the system at one frequency to be inferred from data at nearby frequencies. We demonstrate and verify the approach by means of two test cases, a polymeric truss structure characterized by DMA data and a 3D soft gel sample characterized by MRE data. The examples demonstrate the ease of implementation of the Data-Driven scheme within conventional commercial codes and its robust convergence properties, both with respect to the solver and the data.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/m6jkz-cej08Geometric effects in gas vesicle buckling under ultrasound
https://resolver.caltech.edu/CaltechAUTHORS:20220706-965638000
Authors: {'items': [{'id': 'Salahshoor-Hossein', 'name': {'family': 'Salahshoor', 'given': 'Hossein'}, 'orcid': '0000-0002-7264-7650'}, {'id': 'Yao-Yuxing', 'name': {'family': 'Yao', 'given': 'Yuxing'}, 'orcid': '0000-0003-0337-6372'}, {'id': 'Dutka-Przemysław', 'name': {'family': 'Dutka', 'given': 'Przemysław'}, 'orcid': '0000-0003-3819-1618'}, {'id': 'Nyström-Nivin-N', 'name': {'family': 'Nyström', 'given': 'Nivin N.'}, 'orcid': '0000-0001-6288-6060'}, {'id': 'Jin-Zhiyang', 'name': {'family': 'Jin', 'given': 'Zhiyang'}, 'orcid': '0000-0002-4411-6991'}, {'id': 'Min-Ellen', 'name': {'family': 'Min', 'given': 'Ellen'}}, {'id': 'Malounda-Dina', 'name': {'family': 'Malounda', 'given': 'Dina'}, 'orcid': '0000-0001-7086-9877'}, {'id': 'Jensen-G-J', 'name': {'family': 'Jensen', 'given': 'Grant J.'}, 'orcid': '0000-0003-1556-4864'}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'Michael'}, 'orcid': '0000-0001-5877-4824'}, {'id': 'Shapiro-M-G', 'name': {'family': 'Shapiro', 'given': 'Mikhail G.'}, 'orcid': '0000-0002-0291-4215'}]}
Year: 2022
DOI: 10.1101/2022.06.27.497663
Acoustic reporter genes based on gas vesicles (GVs) have enabled the use of ultrasound to noninvasively visualize cellular function in vivo. The specific detection of GV signals relative to background acoustic scattering in tissues is facilitated by nonlinear ultrasound imaging techniques taking advantage of the sonomechanical buckling of GVs. However, the effect of geometry on the buckling behavior of GVs under exposure to ultrasound has not been studied. To understand such geometric effects, we developed computational models of GVs of various lengths and diameters and used finite element simulations to predict their threshold buckling pressures and post-buckling deformations. We demonstrated that the GV diameter has an inverse cubic relation to the threshold buckling pressure, whereas length has no substantial effect. To complement these simulations, we experimentally probed the effect of geometry on the mechanical properties of GVs and the corresponding nonlinear ultrasound signals. The results of these experiments corroborate our computational predictions. This study provides fundamental insights into how geometry affects the sonomechanical properties of GVs, which, in turn, can inform further engineering of these nanostructures for high-contrast, nonlinear ultrasound imaging.STATEMENT OF SIGNIFICANCEGas vesicles (GVs) are an emerging class of genetically encodable and engineerable imaging agents for ultrasound whose sonomechanical buckling generates nonlinear contrast to enable sensitive and specific imaging in highly scattering biological systems. Though the effect of protein composition on GV buckling has been studied, the effect of geometry has not previously been addressed. This study reveals that geometry, especially GV diameter, significantly alters the threshold acoustic pressures required to induce GV buckling. Our computational predictions and experimental results provide fundamental understanding of the relationship between GV geometry and buckling properties and underscore the utility of GVs for nonlinear ultrasound imaging. Additionally, our results provide suggestions to further engineer GVs to enable in vivo ultrasound imaging with greater sensitivity and higher contrast.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/se8kp-9jq86Strain-tuning of transport gaps and semiconductor-to-conductor phase transition in twinned graphene
https://resolver.caltech.edu/CaltechAUTHORS:20220513-557834000
Authors: {'items': [{'id': 'Arca-Francisco', 'name': {'family': 'Arca', 'given': 'F.'}, 'orcid': '0000-0003-2473-4589'}, {'id': 'Mendez-Granado-Juan-Pedro', 'name': {'family': 'Mendez', 'given': 'J. P.'}, 'orcid': '0000-0002-9493-0879'}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'M.'}, 'orcid': '0000-0001-5877-4824'}, {'id': 'Ariza-Maria-Pilar', 'name': {'family': 'Ariza', 'given': 'M. P.'}, 'orcid': '0000-0003-0266-0216'}]}
Year: 2022
DOI: 10.1016/j.actamat.2022.117987
We show, through the use of the Landauer-Büttiker (LB) formalism and a tight-binding (TB) model, that the transport gap of twinned graphene can be tuned through the application of a uniaxial strain in the direction normal to the twin band. Remarkably, we find that the transport gap E_(gap) bears a square-root dependence on the control parameter ϵₓ − ϵ꜀,, where ϵₓ is the applied uniaxial strain and ϵ꜀ ~ 19% is a critical strain. We interpret this dependence as evidence of criticality underlying a continuous phase transition, with ϵₓ − ϵ꜀ playing the role of control parameter and the transport gap E_(gap) playing the role of order parameter. For ϵₓ < ϵ꜀, the transport gap is non-zero and the material is semiconductor, whereas for ϵₓ > ϵ꜀ the transport gap closes to zero and the material becomes conductor, which evinces a semiconductor-to-conductor phase transition. The computed critical exponent of 1/2 places the transition in the meanfield universality class, which enables far-reaching analogies with other systems in the same class.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/yfyj7-n7904A model-free Data-Driven paradigm for in situ patient-specific prediction of human brain response to ultrasound stimulation
https://resolver.caltech.edu/CaltechAUTHORS:20230322-367761000.29
Authors: {'items': [{'id': 'Salahshoor-Hossein', 'name': {'family': 'Salahshoor', 'given': 'Hossein'}, 'orcid': '0000-0002-7264-7650'}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'Michael'}, 'orcid': '0000-0001-5877-4824'}]}
Year: 2022
DOI: 10.1101/2022.09.01.506248
We present a class of model-free Data-Driven solvers that effectively enable the utilization of in situ and in vivo imaging data directly in full-scale calculations of the mechanical response of the human brain to ultrasound stimulation, entirely bypassing the need for analytical modeling or regression of the data. We demonstrate the approach, including its ability to make detailed spatially-resolved patient-specific predictions of wave patterns, using public-domain MRI images, MRE data and commercially available solid-mechanics software.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/v4gz3-8sb56Hydrogen-enhanced grain boundary vacancy stockpiling causes transgranular to intergranular fracture transition
https://resolver.caltech.edu/CaltechAUTHORS:20220817-896609000
Authors: {'items': [{'id': 'Ding-Yu', 'name': {'family': 'Ding', 'given': 'Yu'}}, {'id': 'Yu-Haiyang', 'name': {'family': 'Yu', 'given': 'Haiyang'}, 'orcid': '0000-0002-2419-6736'}, {'id': 'Lin-Meichao', 'name': {'family': 'Lin', 'given': 'Meichao'}}, {'id': 'Zhao-Kai', 'name': {'family': 'Zhao', 'given': 'Kai'}, 'orcid': '0000-0003-2645-7917'}, {'id': 'Xiao-Senbo', 'name': {'family': 'Xiao', 'given': 'Senbo'}}, {'id': 'Vinogradov-Alexei', 'name': {'family': 'Vinogradov', 'given': 'Alexei'}, 'orcid': '0000-0001-9585-2801'}, {'id': 'Qiao-Lijie', 'name': {'family': 'Qiao', 'given': 'Lijie'}}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'Michael'}, 'orcid': '0000-0001-5877-4824'}, {'id': 'He-Jianying', 'name': {'family': 'He', 'given': 'Jianying'}}, {'id': 'Zhang-Zhiliang', 'name': {'family': 'Zhang', 'given': 'Zhiliang'}}]}
Year: 2022
DOI: 10.1016/j.actamat.2022.118279
The attention to hydrogen embrittlement (HE) has been intensified recently in the light of hydrogen as a carbon-free energy carrier. Despite worldwide research, the multifaceted HE mechanism remains a matter of debate. Here we report an atomistic study of the coupled effect of hydrogen and deformation temperature on the pathway to intergranular fracture of nickel. Uniaxial straining is applied to nickel Σ5(210)[001] and Σ9(1-10)[22-1] grain boundaries with or without pre-charged hydrogen at various temperatures. Without hydrogen, vacancy generation at grain boundary is limited and transgranular fracture mode dominates. When charged, hydrogen as a booster can enhance strain-induced vacancy generation by up to ten times. This leads to the superabundant vacancy stockpiling at the grain boundary, which agglomerates and nucleates intergranular nanovoids eventually causing intergranular fracture. While hydrogen tends to persistently enhance vacancy concentration, temperature plays an intriguing dual role as either an enhancer or an inhibitor for vacancy stockpiling. These results show good agreement with recent positron annihilation spectroscopy experiments. An S-shaped quantitative correlation between the proportion of intergranular fracture and vacancy concentration was for the first time derived, highlighting the existence of a critical vacancy concentration, beyond which fracture mode will be completely intergranular.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/3msg4-ky970Model-free Data-Driven inference in computational mechanics
https://resolver.caltech.edu/CaltechAUTHORS:20221128-494241100.30
Authors: {'items': [{'id': 'Prume-Erik', 'name': {'family': 'Prume', 'given': 'E.'}, 'orcid': '0000-0002-2227-7540'}, {'id': 'Reese-Stefanie', 'name': {'family': 'Reese', 'given': 'S.'}, 'orcid': '0000-0003-4760-8358'}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'M.'}, 'orcid': '0000-0001-5877-4824'}]}
Year: 2023
DOI: 10.1016/j.cma.2022.115704
We extend the model-free Data-Driven computing paradigm to solids and structures that are stochastic due to intrinsic randomness in the material behavior. The behavior of such materials is characterized by a likelihood measure instead of a constitutive relation. We specifically assume that the material likelihood measure is known only through an empirical point-data set in material or phase space. The state of the solid or structure is additionally subject to compatibility and equilibrium constraints. The problem is then to infer the likelihood of a given structural outcome of interest. In this work, we present a Data-Driven method of inference that determines likelihoods of outcomes from the empirical material data and that requires no material or prior modeling. In particular, the computation of expectations is reduced to explicit sums over local material data sets and to quadratures over admissible states, i.e., states satisfying compatibility and equilibrium. The complexity of the material data-set sums is linear in the number of data points and in the number of members in the structure. Efficient population annealing procedures and fast search algorithms for accelerating the calculations are presented. The scope, cost and convergence properties of the method are assessed with the aid selected applications and benchmark tests.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/hrwm9-jgx52Extended molecular dynamics: Seamless temporal coarse-graining and transition between deterministic and probabilistic paradigms
https://authors.library.caltech.edu/records/q92ct-ja103
Authors: {'items': [{'id': 'Romero-Ignacio', 'name': {'family': 'Romero', 'given': 'Ignacio'}, 'orcid': '0000-0003-0364-6969'}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'Michael'}, 'orcid': '0000-0001-5877-4824'}]}
Year: 2023
DOI: 10.1016/j.euromechsol.2022.104858
<p>This article explores the formulation of evolution equations for atomistic systems where the time resolution is controlled at will. Based on a time-rescaled version of Hamilton's equations of motion, the equations of motion of these systems are derived with adjustable time <a href="https://www.sciencedirect.com/topics/engineering/granularity">granularity</a>. Also, using the <a href="https://www.sciencedirect.com/topics/engineering/liouville">Liouville</a> formalism for <a href="https://www.sciencedirect.com/topics/engineering/hamiltonian">Hamiltonian</a> mechanics, the evolution equations are recast in probabilistic terms, opening the door to variational, Galerkin-type projections. The resulting approximation provides the governing equations for the average motion of the system as well as the evolution of a temperature-like variable that modulates the thermal, unresolved, vibrations of each particle. The balance between the resolved and unresolved motions is, by construction, adjustable at every instant and fully reversible. This kind of models can be used to study the behavior of atomistic systems at different time scales.</p>https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/q92ct-ja103Model-free Data-Driven viscoelasticity in the frequency domain
https://resolver.caltech.edu/CaltechAUTHORS:20221117-155430600.5
Authors: {'items': [{'id': 'Salahshoor-Hossein', 'name': {'family': 'Salahshoor', 'given': 'Hossein'}, 'orcid': '0000-0002-7264-7650'}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'Michael'}, 'orcid': '0000-0001-5877-4824'}]}
Year: 2023
DOI: 10.1016/j.cma.2022.115657
We develop a Data-Driven framework for the simulation of wave propagation in viscoelastic solids directly from dynamic testing material data, including data from Dynamic Mechanical Analysis (DMA), nano-indentation, Dynamic Shear Testing (DST) and Magnetic Resonance Elastography (MRE), without the need for regression or material modeling. The problem is formulated in the frequency domain and the method of solution seeks to minimize a distance between physically admissible histories of stress and strain, in the sense of compatibility and equilibrium, and the material data. We metrize the space of histories by means of the flat-norm of their Fourier transform, which allows consideration of infinite wave trains such as harmonic functions. Another significant advantage of the flat norm is that it allows the response of the system at one frequency to be inferred from data at nearby frequencies. We demonstrate and verify the approach by means of two test cases, a polymeric truss structure characterized by DMA data and a 3D soft gel sample characterized by MRE data. The examples demonstrate the ease of implementation of the Data-Driven scheme within conventional commercial codes and its robust convergence properties, both with respect to the solver and the data.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/j4wfj-pak77Model-Free and Prior-Free Data-Driven Inference in Mechanics
https://resolver.caltech.edu/CaltechAUTHORS:20230203-893210800.26
Authors: {'items': [{'id': 'Conti-Sergio', 'name': {'family': 'Conti', 'given': 'Sergio'}, 'orcid': '0000-0001-7987-9174'}, {'id': 'Hoffmann-Franca', 'name': {'family': 'Hoffmann', 'given': 'Franca'}, 'orcid': '0000-0002-1182-5521'}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'Michael'}, 'orcid': '0000-0001-5877-4824'}]}
Year: 2023
DOI: 10.1007/s00205-022-01836-7
We present a model-free data-driven inference method that enables inferences on system outcomes to be derived directly from empirical data without the need for intervening modeling of any type, be it modeling of a material law or modeling of a prior distribution of material states. We specifically consider physical systems with states characterized by points in a phase space determined by the governing field equations. We assume that the system is characterized by two likelihood measures: one μ_D measuring the likelihood of observing a material state in phase space; and another μ_E measuring the likelihood of states satisfying the field equations, possibly under random actuation. We introduce a notion of intersection between measures which can be interpreted to quantify the likelihood of system outcomes. We provide conditions under which the intersection can be characterized as the athermal limit μ_∞ of entropic regularizations μ_B, or thermalizations, of the product measure μ = μ_D x μ_E as β → +∞. We also supply conditions under which μ_∞ can be obtained as the athermal limit of carefully thermalized (μ_[h,β_(h)]) sequences of empirical data sets (μ_h) approximating weakly an unknown likelihood function μ. In particular, we find that the cooling sequence β_h → +∞ must be slow enough, corresponding to annealing, in order for the proper limit μ_∞ to be delivered. Finally, we derive explicit analytic expressions for expectations E[⨍] of outcomes ⨍ that are explicit in the data, thus demonstrating the feasibility of the model-free data-driven paradigm as regards making convergent inferences directly from the data without recourse to intermediate modeling steps.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/enztv-57g67Extension of the spatially adaptive phase-field model to various forms of fracture
https://authors.library.caltech.edu/records/rz7ym-6yh29
Authors: {'items': [{'name': {'family': 'Phansalkar', 'given': 'Dhananjay'}, 'orcid': '0000-0001-7870-1446'}, {'id': 'Jadhav-Deepak-B', 'name': {'family': 'Jadhav', 'given': 'Deepak B.'}}, {'id': 'Weinberg-Kerstin', 'name': {'family': 'Weinberg', 'given': 'Kerstin'}, 'orcid': '0000-0002-2213-8401'}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'Michael'}, 'orcid': '0000-0001-5877-4824'}, {'id': 'Leyendecker-Sigrid', 'name': {'family': 'Leyendecker', 'given': 'Sigrid'}, 'orcid': '0000-0002-8585-2725'}]}
Year: 2023
DOI: 10.1016/j.finmec.2022.100161
<p>The phase field approach has proved to be efficient and has received ample attention amongst the available techniques to model fracture. However, high computational cost still imposes substantial difficulties in the phase-field simulation of fractures. This contribution is based on a recently proposed variational approach for spatial adaptivity in a phase-field model of fracture. The main idea is to consider the <a href="https://www.sciencedirect.com/topics/engineering/regularization">regularisation</a> length ϵ as a space-dependent variable in the argument of the energy functional. We extend this now by implementing a strain energy split to ensure that only the tensile energy drives the <a href="https://www.sciencedirect.com/topics/engineering/crack-propagation">crack propagation</a>. The displacement, phase field, and optimal regularisation length are then determined locally by minimisation of the modified energy functional. Subsequently, the computed optimal regularisation length is used to refine the mesh size locally. The resultant solution procedure is implemented in the finite element library FEniCS. Numerical investigations on selected examples of different fracture modes demonstrate that the spatially adaptive phase field model has a comparable convergence rate, but a subjacent energy convergence curve resulting in significant computational savings. Moreover, it also computes the peak force more accurately illustrating its potential for usage in practical applications.</p>https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/rz7ym-6yh29Mesh d-refinement: A data-based computational framework to account for complex material response
https://authors.library.caltech.edu/records/69x94-b3n22
Authors: {'items': [{'id': 'Wattel-Sacha-Z', 'name': {'family': 'Wattel', 'given': 'Sacha'}, 'orcid': '0000-0002-5117-9915'}, {'id': 'Molinari-Jean-François', 'name': {'family': 'Molinari', 'given': 'Jean-François'}, 'orcid': '0000-0002-1728-1844'}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'Michael'}, 'orcid': '0000-0001-5877-4824'}, {'id': 'Garcia-Suarez-Joaquin', 'name': {'family': 'Garcia-Suarez', 'given': 'Joaquin'}, 'orcid': '0000-0002-1728-1844'}]}
Year: 2023
DOI: 10.1016/j.mechmat.2023.104630
<p>Model-free data-driven <a href="https://www.sciencedirect.com/topics/engineering/computational-mechanics">computational mechanics</a> (DDCM) is a new paradigm for simulations in solid mechanics. The modeling step associated to the definition of a material constitutive law is circumvented through the introduction of an abstract phase space in which, following a pre-defined rule, physically-admissible states are matched to observed material response data (coming from either experiments or lower-scale simulations). In terms of computational resources, the search procedure that performs these matches is the most onerous step in the algorithm. One of the main advantages of DDCM is the fact that it avoids regression-based, bias-prone constitutive modeling. However, many materials do display a simple linear response in the small-strain regime while also presenting complex behavior after a certain deformation threshold. Motivated by this fact, we present a novel refinement technique that turns regular elements (equipped with a linear-elastic constitutive law) into data-driven ones if they are expected to surpass the threshold known to trigger material non-linear response. We term this technique "data refinement", "d-refinement" for short. It works both with data-driven elements based on either DDCM or strain–stress relations learned from data using neural networks. Starting from an initially regular FEM <a href="https://www.sciencedirect.com/topics/engineering/meshes">mesh</a>, the proposed algorithm detects where the refinement is needed and iterates until all elements presumed to display non-linearity become data-driven ones. Insertion criteria are discussed. The scheme is well-suited for simulations that feature non-linear response in relatively small portions of the domain while the rest remains linear-elastic. The method is validated against a traditional incremental solver (i.e., Newton–Raphson method) and we show that the d-refinement framework can outperform it in terms of speed at no loss of accuracy. We provide an application that showcases the advantage of the new method: bridging scales in architected metamaterials. For this application, we also succinctly outline how d-refinement can be used in conjunction with a neural network trained on <a href="https://www.sciencedirect.com/topics/engineering/microscale">microscale</a> data.</p>https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/69x94-b3n22Computation of effective elastic moduli of rocks using hierarchical homogenization
https://resolver.caltech.edu/CaltechAUTHORS:20230404-258305700.8
Authors: {'items': [{'id': 'Ahmad-Rasool', 'name': {'family': 'Ahmad', 'given': 'Rasool'}, 'orcid': '0000-0002-4154-6902'}, {'id': 'Liu-Mingliang', 'name': {'family': 'Liu', 'given': 'Mingliang'}, 'orcid': '0000-0002-5783-4490'}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'Michael'}, 'orcid': '0000-0001-5877-4824'}, {'id': 'Mukerji-Tapan', 'name': {'family': 'Mukerji', 'given': 'Tapan'}, 'orcid': '0000-0003-1711-1850'}, {'id': 'Cai-Wei', 'name': {'family': 'Cai', 'given': 'Wei'}, 'orcid': '0000-0001-5919-8734'}]}
Year: 2023
DOI: 10.1016/j.jmps.2023.105268
This work focuses on computing the homogenized elastic properties of rocks from 3D micro-computed-tomography (micro-CT) scanned images. The accurate computation of homogenized properties of rocks, archetypal random media, requires both resolution of intricate underlying microstructure and large field of view, resulting in huge micro-CT images. Homogenization entails solving the local elasticity problem computationally which can be prohibitively expensive for a huge image. To mitigate this problem, we use a renormalization method inspired scheme, the hierarchical homogenization method, where a large image is partitioned into smaller subimages. The individual subimages are separately homogenized using periodic boundary conditions, and then assembled into a much smaller intermediate image. The intermediate image is again homogenized, subject to the periodic boundary condition, to find the final homogenized elastic constant of the original image. An FFT-based elasticity solver is used to solve the associated periodic elasticity problem. The error in the homogenized elastic constant is empirically shown to follow a power law scaling with exponent -1 with respect to the subimage size across all five microstructures of rocks. We further show that the inclusion of surrounding materials during the homogenization of the small subimages reduces error in the final homogenized elastic moduli while still respecting the power law with the exponent of -1. This power law scaling is then exploited to determine a better approximation of the large heterogeneous microstructures based on Richardson extrapolation.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/c6pc2-pgt81A data‐driven solver scheme for inelastic problems
https://authors.library.caltech.edu/records/n6551-2rx95
Authors: {'items': [{'id': 'Prume-Erik', 'name': {'family': 'Prume', 'given': 'Erik'}, 'orcid': '0000-0002-2227-7540'}, {'id': 'Stainier-Laurent', 'name': {'family': 'Stainier', 'given': 'Laurent'}, 'orcid': '0000-0001-6719-6616'}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'Michael'}, 'orcid': '0000-0001-5877-4824'}, {'id': 'Reese-Stefanie', 'name': {'family': 'Reese', 'given': 'Stefanie'}, 'orcid': '0000-0003-4760-8358'}]}
Year: 2023
DOI: 10.1002/pamm.202200153
<p>We review the data‐driven computing paradigm for inelastic problems. We extend an efficient graph search algorithm for the data search by thermodynamic constraints and a rate independent history parametrization based on the mechanical work increment. In addition, we propose a strategy how to use commercial solvers in the framework. Finally, we demonstrate the proposed method with a numerical example featuring 2‐d continuum plasticity.</p>https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/n6551-2rx95Adaptive goal-oriented data sampling in Data-Driven Computational Mechanics
https://resolver.caltech.edu/CaltechAUTHORS:20230411-695015900.6
Authors: {'items': [{'id': 'Gorgogianni-Anna', 'name': {'family': 'Gorgogianni', 'given': 'Anna'}}, {'id': 'Karapiperis-Konstantinos', 'name': {'family': 'Karapiperis', 'given': 'Konstantinos'}, 'orcid': '0000-0002-6796-8900'}, {'id': 'Stainier-Laurent', 'name': {'family': 'Stainier', 'given': 'Laurent'}, 'orcid': '0000-0001-6719-6616'}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'Michael'}, 'orcid': '0000-0001-5877-4824'}, {'id': 'Andrade-J-E', 'name': {'family': 'Andrade', 'given': 'José E.'}, 'orcid': '0000-0003-3741-0364'}]}
Year: 2023
DOI: 10.1016/j.cma.2023.115949
Data-Driven (DD) computing is an emerging field of Computational Mechanics, motivated by recent technological advances in experimental measurements, the development of highly predictive computational models, advances in data storage and data processing, which enable the transition from a material data-scarce to a material data-rich era. The predictive capability of DD simulations is contingent on the quality of the material data set, i.e. its ability to closely sample all the strain–stress states in the phase space of a given mechanical problem. In this study, we develop a methodology for increasing the quality of an existing material data set through iterative expansions. Leveraging the formulation of the problems treated with the DD paradigm as distance minimization problems, we identify regions in phase space with poor data coverage, and target them with additional experiments or lower-scale simulations. The DD solution informs the additional experiments so that they can provide better coverage of the phase space of a given application.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/9sv03-ppf89Atomistic-scale model for the numerical analysis of the hydrogen diffusion on magnesium alloys
https://authors.library.caltech.edu/records/a0hb8-1eh80
Authors: {'items': [{'id': 'Molinos-Pérez-Miguel', 'name': {'family': 'Molinos', 'given': 'M.'}, 'orcid': '0000-0002-5073-4796'}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'Michael'}, 'orcid': '0000-0001-5877-4824'}, {'id': 'Ariza-Pilar', 'name': {'family': 'Ariza', 'given': 'M. P.'}, 'orcid': '0000-0003-0266-0216'}]}
Year: 2023
<p>Magnesium (Mg) structural alloys offer desirable properties such as low density, machinability, and high specific strength. These properties make Mg alloys advantageous for use in many structural applications but also for applications as a hydrogen storage material due to the favorable cost and high gravimetric and volumetric densities of hydrogen.</p><p>However, the susceptibility of Mg alloys to hydrogen embrittlement phenomena can lead to low ductility and low fracture toughness at room temperature, which may hinder their potential applications. Therefore, information about the behavior of magnesium and its hydrides under different pressure-temperature conditions is highly required. A theoretical framework for the simulation of hydrogen diffusion in Mg based on fully atomistic calculations using the Diffusive Molecular Dynamics (DMD) is proposed. Our model consists of the resolution of a Thermo-ChemoMechanical (TMC) coupled problem solved thorough a staggered scheme. On the one hand, the thermomechanical part considers a thermalized Angular Dependent Potential (ADP) which is best suited to model the phase transition of Mg (bcc↔hcp) caused by the formation of MgH2 at finite temperature. And, on the other hand, the chemical problem, which drives the time evolution, is solved by a diffusion equation calibrated with macroscopic information.</p>https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/a0hb8-1eh80Convergence rates for ansatz‐free data‐driven inference in physically constrained problems
https://resolver.caltech.edu/CaltechAUTHORS:20230711-988768900.18
Authors: {'items': [{'id': 'Conti-Sergio', 'name': {'family': 'Conti', 'given': 'Sergio'}, 'orcid': '0000-0001-7987-9174'}, {'id': 'Hoffmann-Franca', 'name': {'family': 'Hoffmann', 'given': 'Franca'}, 'orcid': '0000-0002-1182-5521'}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'Michael'}, 'orcid': '0000-0001-5877-4824'}]}
Year: 2023
DOI: 10.1002/zamm.202200481
We study a Data-Driven approach to inference in physical systems in a measure-theoretic framework. The systems under consideration are characterized by two measures defined over the phase space: (i) A physical likelihood measure expressing the likelihood that a state of the system be admissible, in the sense of satisfying all governing physical laws; (ii) A material likelihood measure expressing the likelihood that a local state of the material be observed in the laboratory. We assume deterministic loading, which means that the first measure is supported on a linear subspace. We additionally assume that the second measure is only known approximately through a sequence of empirical (discrete) measures. We develop a method for the quantitative analysis of convergence based on the flat metric and obtain error bounds both for annealing and the discretization or sampling procedure, leading to the determination of appropriate quantitative annealing rates. Finally, we provide an example illustrating the application of the theory to transportation networks.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/febmr-v9h61Data-driven breakage mechanics: Predicting the evolution of particle-size distribution in granular media
https://authors.library.caltech.edu/records/5s9tc-v9641
Authors: {'items': [{'id': 'Ulloa-Jacinto', 'name': {'family': 'Ulloa', 'given': 'Jacinto'}, 'orcid': '0000-0001-7616-5408'}, {'id': 'Gorgogianni-Anna', 'name': {'family': 'Gorgogianni', 'given': 'Anna'}}, {'id': 'Karapiperis-Konstantinos', 'name': {'family': 'Karapiperis', 'given': 'Konstantinos'}, 'orcid': '0000-0002-6796-8900'}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'Michael'}, 'orcid': '0000-0001-5877-4824'}, {'id': 'Andrade-J-E', 'name': {'family': 'Andrade', 'given': 'José E.'}, 'orcid': '0000-0003-3741-0364'}]}
Year: 2023
DOI: 10.1016/j.jmps.2023.105328
<p>This paper presents a model-free data-driven framework for breakage mechanics. In contrast with continuum breakage mechanics, the de facto approach for the macroscopic analysis of crushable granular media, the present framework does not require the definition of constitutive models and phenomenological assumptions, relying on <a href="https://www.sciencedirect.com/topics/engineering/material-behavior">material behavior</a> that is known only through empirical data. For this purpose, we revisit the recent developments in model-free data-driven computing for history-dependent materials and extend the main ideas to materials with particle breakage. A systematic construction of the modeling framework is presented, starting from the closed-form representation of continuum breakage mechanics and arriving at alternative model-free representations. The <a href="https://www.sciencedirect.com/topics/engineering/predictive-ability">predictive ability</a> of the data-driven framework is highlighted and contrasted with continuum breakage mechanics on different boundary value problems. Moreover, an application to a real experimental test in crushable sand is presented, where the data is furnished by high-fidelity grain-scale simulations, indicating that the proposed framework provides an accurate prediction of the mechanics of crushable materials including the state of comminution.</p>https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/5s9tc-v9641Interatomic-Potential-Free, Data-Driven Molecular Dynamics
https://authors.library.caltech.edu/records/zhqxx-0t840
Authors: {'items': [{'id': 'Bulin-J', 'name': {'family': 'Bulin', 'given': 'J.'}}, {'id': 'Hamaekers-Jan', 'name': {'family': 'Hamaekers', 'given': 'J.'}, 'orcid': '0000-0001-5399-043X'}, {'name': {'family': 'Ariza', 'given': 'M. P.'}, 'orcid': '0000-0003-0266-0216'}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'M.'}, 'orcid': '0000-0001-5877-4824'}]}
Year: 2023
DOI: 10.1016/j.cma.2023.116224
<p>We present a Data-Driven (DD) paradigm that enables molecular dynamics calculations to be performed directly from sampled force-field data such as obtained, e. g., from <i>ab initio</i> calculations, thereby eschewing the conventional step of modeling the data by empirical <a href="https://www.sciencedirect.com/topics/engineering/interatomic-potential">interatomic potentials</a> entirely. The data required by the DD solvers consists of local atomic configurations and corresponding atomic forces and is, therefore, <i>fundamental</i>, i. e., it is not beholden to any particular model. The resulting DD solvers, including a fully explicit DD-Verlet algorithm, are provably convergent and exhibit robust convergence with respect to the data in selected test cases. We present an example of application to <i>C</i>₆₀ <a href="https://www.sciencedirect.com/topics/engineering/buckminsterfullerene">buckminsterfullerenes</a> that showcases the feasibility, range and scope of the DD molecular dynamics paradigm.</p>https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/zhqxx-0t840Geometric effects in gas vesicle buckling under ultrasound
https://resolver.caltech.edu/CaltechAUTHORS:20221128-494241100.5
Authors: {'items': [{'id': 'Salahshoor-Hossein', 'name': {'family': 'Salahshoor', 'given': 'Hossein'}, 'orcid': '0000-0002-7264-7650'}, {'id': 'Yao-Yuxing', 'name': {'family': 'Yao', 'given': 'Yuxing'}, 'orcid': '0000-0003-0337-6372'}, {'id': 'Dutka-Przemysław', 'name': {'family': 'Dutka', 'given': 'Przemysław'}, 'orcid': '0000-0003-3819-1618'}, {'id': 'Nyström-Nivin-N', 'name': {'family': 'Nyström', 'given': 'Nivin N.'}, 'orcid': '0000-0001-6288-6060'}, {'id': 'Jin-Zhiyang', 'name': {'family': 'Jin', 'given': 'Zhiyang'}, 'orcid': '0000-0002-4411-6991'}, {'id': 'Min-Ellen', 'name': {'family': 'Min', 'given': 'Ellen'}}, {'id': 'Malounda-Dina', 'name': {'family': 'Malounda', 'given': 'Dina'}, 'orcid': '0000-0001-7086-9877'}, {'id': 'Jensen-G-J', 'name': {'family': 'Jensen', 'given': 'Grant J.'}, 'orcid': '0000-0003-1556-4864'}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'Michael'}, 'orcid': '0000-0001-5877-4824'}, {'id': 'Shapiro-M-G', 'name': {'family': 'Shapiro', 'given': 'Mikhail G.'}, 'orcid': '0000-0002-0291-4215'}]}
Year: 2023
DOI: 10.1016/j.bpj.2022.09.004
PMCID: PMC9674984
Acoustic reporter genes based on gas vesicles (GVs) have enabled the use of ultrasound to noninvasively visualize cellular function in vivo. The specific detection of GV signals relative to background acoustic scattering in tissues is facilitated by nonlinear ultrasound imaging techniques taking advantage of the sonomechanical buckling of GVs. However, the effect of geometry on the buckling behavior of GVs under exposure to ultrasound has not been studied. To understand such geometric effects, we developed computational models of GVs of various lengths and diameters and used finite element simulations to predict their threshold buckling pressures and postbuckling deformations. We demonstrated that the GV diameter has an inverse cubic relation to the threshold buckling pressure, whereas length has no substantial effect. To complement these simulations, we experimentally probed the effect of geometry on the mechanical properties of GVs and the corresponding nonlinear ultrasound signals. The results of these experiments corroborate our computational predictions. This study provides fundamental insights into how geometry affects the sonomechanical properties of GVs, which, in turn, can inform further engineering of these nanostructures for high-contrast, nonlinear ultrasound imaging.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/6b26e-8v344Fractional strain gradient plasticity and ductile fracture of metals
https://authors.library.caltech.edu/records/apva3-4tf55
Authors: {'items': [{'id': 'Ariza-M-Pilar', 'name': {'family': 'Ariza', 'given': 'M. P.'}, 'orcid': '0000-0003-0266-0216'}, {'id': 'Conti-Sergio', 'name': {'family': 'Conti', 'given': 'S.'}, 'orcid': '0000-0001-7987-9174'}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'M.'}, 'orcid': '0000-0001-5877-4824'}]}
Year: 2023
DOI: 10.1016/j.euromechsol.2023.105172
<p>We present an optimal scaling analysis based on (possibly fractional) strain-gradient plasticity. The analysis yields optimal scaling laws, in the sense of upper and lower bounds of a power-law type with matching exponents, connecting macroscopic fracture properties, such as the critical elongation at failure and the specific fracture energy, to microscopic mechanisms such as cleavage and microplasticity. We show that an optimal upper bound can be derived from an exceedingly simple test deformation that opens up a sheet of parallelepipedic voids. We also show that an optimal lower bound can be obtained by relaxing compatibility between transverse fibers, which effectively renders the analysis one-dimensional. The analysis predicts a 'gating effect' of the surface energy. Specifically, a critical surface energy arises from the analysis that marks a sharp transition between brittle and ductile behavior. When the surface energy of the material exceeds the threshold value, the macroscopic specific fracture energy is predicted to rise sharply as a power of the surface energy with an exponent defined precisely by the theory.</p>https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/apva3-4tf55The energy-stepping Monte Carlo method: an exactly symmetry-preserving, a Hamiltonian Monte Carlo method with a 100% acceptance ratio
https://authors.library.caltech.edu/records/kj7yz-etf63
Authors: {'items': [{'id': 'Romero-Ignacio', 'name': {'family': 'Romero', 'given': 'Ignacio'}, 'orcid': '0000-0003-0364-6969'}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'Michael'}, 'orcid': '0000-0001-5877-4824'}]}
Year: 2023
DOI: 10.48550/arXiv.2312.07215
<p>We introduce the energy-stepping Monte Carlo (ESMC) method, a Markov chain Monte Carlo (MCMC) algorithm based on the conventional dynamical interpretation of the proposal stage but employing an energy-stepping integrator. The energy-stepping integrator is quasi-explicit, symplectic, energy-conserving, and symmetry-preserving. As a result of the exact energy conservation of energy-stepping integrators, ESMC has a 100% acceptance ratio of the proposal states. Numerical tests provide empirical evidence that ESMC affords a number of additional benefits: the Markov chains it generates have weak autocorrelation, it has the ability to explore distant characteristic sets of the sampled probability distribution and it yields smaller errors than chains sampled with Hamiltonian Monte Carlo (HMC) and similar step sizes. Finally, ESMC benefits from the exact symmetry conservation properties of the energy-stepping integrator when sampling from potentials with built-in symmetries, whether explicitly known or not.</p>https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/kj7yz-etf63Towards Quantum Computational Mechanics
https://authors.library.caltech.edu/records/9jh8m-4gn23
Authors: {'items': [{'id': 'Liu-Burigede', 'name': {'family': 'Liu', 'given': 'Burigede'}, 'orcid': '0000-0002-6518-3368'}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'Michael'}, 'orcid': '0000-0001-5877-4824'}, {'id': 'Cirak-Fehmi', 'name': {'family': 'Cirak', 'given': 'Fehmi'}, 'orcid': '0000-0002-9274-6904'}]}
Year: 2023
DOI: 10.48550/arXiv.2312.03791
<p>The rapid advancements in quantum computing as ushered in a new era for computer simulations, presenting groundbreaking opportunities across diverse disciplines. Central to this revolution is the quantum processor's capacity to entangle qubits, unlocking unprecedented possibilities for addressing computational challenges on an extreme scale, far beyond the reach of classical computing. In this study, we explore how quantum computing can be employed to enhance computational mechanics. Our focus is on the analysis of Representative Volume Element (RVE) within the framework of multiscale solid mechanics. We introduce an innovative quantum algorithm designed to solve the RVE problem. This algorithm is capable of compute RVEs of discretization size N in 𝒪(Poly log(N)) time, thus achieving an exponential speed-up over traditional classical computing approaches that typically scales linearly with N. We validate our approach with case studies including the solution of one and two dimensional Poisson's equation, as well as an RVE of a composite bar with piece-wise constant phases. We provide quantum circuit designs that requires only 𝒪(Poly log(N)) universal quantum gates,underscoring the efficiency of our approach. Our work suggests a major way in which quantum computing can be combined with and brought to bear on computational mechanics.</p>https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/9jh8m-4gn23Modeling hard-soft block copolymers as a liquid crystalline polymer
https://authors.library.caltech.edu/records/4nbfv-5rx84
Authors: {'items': [{'id': 'Manav-M', 'name': {'family': 'Manav', 'given': 'M.'}, 'orcid': '0000-0002-8498-4144'}, {'id': 'Ponga-Mauricio', 'name': {'family': 'Ponga', 'given': 'M.'}, 'orcid': '0000-0001-5058-1454'}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'M.'}, 'orcid': '0000-0001-5877-4824'}]}
Year: 2023
DOI: 10.48550/arXiv.2305.07673
<p>We report a new computational approach to model hard-soft block copolymers like polyurea as a liquid crystalline polymer to understand their microstructural evolution due to mechanical loading. The resulting microstructure closely resembles the microstructure observed in polyurea. The stress-strain relations in uniaxial compression and tension loading obtained from the model are also in close quantitative agreement with the experimental data for polyurea. We use the model to elucidate the evolution of the hard and the soft domains during loading, which is consistent with the experimental measurements characterizing microstructural evolution in polyurea.</p>https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/4nbfv-5rx84Homogenizing elastic properties of large digital rock images by combining CNN with hierarchical homogenization method
https://authors.library.caltech.edu/records/e84dq-tqj49
Authors: {'items': [{'id': 'Ahmad-Rasool', 'name': {'family': 'Ahmad', 'given': 'Rasool'}, 'orcid': '0000-0002-4154-6902'}, {'id': 'Liu-Mingliang', 'name': {'family': 'Liu', 'given': 'Mingliang'}}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'Michael'}, 'orcid': '0000-0001-5877-4824'}, {'id': 'Mukerji-Tapan', 'name': {'family': 'Mukerji', 'given': 'Tapan'}, 'orcid': '0000-0003-1711-1850'}, {'id': 'Cai-Wei', 'name': {'family': 'Cai', 'given': 'Wei'}, 'orcid': '0000-0001-5919-8734'}]}
Year: 2023
DOI: 10.48550/arXiv.2305.06519
<p>Determining effective elastic properties of rocks from their pore-scale digital images is a key goal of digital rock physics (DRP). Direct numerical simulation (DNS) of elastic behavior, however, incurs high computational cost; and surrogate machine learning (ML) model, particularly convolutional neural network (CNN), show promises to accelerate homogenization process. 3D CNN models, however, are unable to handle large images due to memory issues. To address this challenge, we propose a novel method that combines 3D CNN with hierarchical homogenization method (HHM). The surrogate 3D CNN model homogenizes only small subimages, and a DNS is used to homogenize the intermediate image obtained by assembling small subimages. The 3D CNN model is designed to output the homogenized elastic constants within the Hashin-Shtrikman (HS) bounds of the input images. The 3D CNN model is first trained on data comprising equal proportions of five sandstone (quartz mineralogy) images, and, subsequently, fine-tuned for specific rocks using transfer learning. The proposed method is applied to homogenize the rock images of size 300x300x300 and 600x600x600 voxels, and the predicted homogenized elastic moduli are shown to agree with that obtained from the brute-force DNS. The transferability of the trained 3D CNN model (using transfer learning) is further demonstrated by predicting the homogenized elastic moduli of a limestone rock with calcite mineralogy. The surrogate 3D CNN model in combination with the HHM is thus shown to be a promising tool for the homogenization of large 3D digital rock images and other random media</p>https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/e84dq-tqj49Data-Driven Games in Computational Mechanics
https://authors.library.caltech.edu/records/e3w8d-x7954
Authors: {'items': [{'id': 'Weinberg-Kerstin', 'name': {'family': 'Weinberg', 'given': 'K.'}, 'orcid': '0000-0002-2213-8401'}, {'id': 'Stainier-Laurent', 'name': {'family': 'Stainier', 'given': 'L.'}, 'orcid': '0000-0001-6719-6616'}, {'id': 'Conti-Sergio', 'name': {'family': 'Conti', 'given': 'S.'}, 'orcid': '0000-0001-7987-9174'}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'M.'}, 'orcid': '0000-0001-5877-4824'}]}
Year: 2023
DOI: 10.48550/arXiv.2305.19279
<p>We resort to game theory in order to formulate Data-Driven methods for solid mechanics in which stress and strain players pursue different objectives. The objective of the stress player is to minimize the discrepancy to a material data set, whereas the objective of the strain player is to ensure the admissibility of the mechanical state, in the sense of compatibility and equilibrium. We show that, unlike the cooperative Data-Driven games proposed in the past, the new non-cooperative Data-Driven games identify an effective material law from the data and reduce to conventional displacement boundary-value problems, which facilitates their practical implementation. However, unlike supervised machine learning methods, the proposed non-cooperative Data-Driven games are unsupervised, ansatz-free and parameter-free. In particular, the effective material law is learned from the data directly, without recourse to regression to a parameterized class of functions such as neural networks. We present analysis that elucidates sufficient conditions for convergence of the Data-Driven solutions with respect to the data. We also present selected examples of implementation and application that demonstrate the range and versatility of the approach.</p>https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/e3w8d-x7954An optimal-transport finite-particle method for mass diffusion
https://authors.library.caltech.edu/records/2zv0d-40h73
Authors: {'items': [{'id': 'Pandolfi-Anna', 'name': {'family': 'Pandolfi', 'given': 'A.'}, 'orcid': '0000-0002-7084-7456'}, {'id': 'Stainier-Laurent', 'name': {'family': 'Stainier', 'given': 'L.'}, 'orcid': '0000-0001-6719-6616'}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'M.'}, 'orcid': '0000-0001-5877-4824'}]}
Year: 2023
DOI: 10.48550/arXiv.2305.05315
<p>We formulate a class of velocity-free finite-particle methods for mass transport problems based on a time-discrete incremental variational principle that combines entropy and the cost of particle transport, as measured by the Wasserstein metric. The incremental functional is further spatially discretized into finite particles, i.e., particles characterized by a fixed spatial profile of finite width, each carrying a fixed amount of mass. The motion of the particles is then governed by a competition between the cost of transport, that aims to keep the particles fixed, and entropy maximization, that aims to spread the particles so as to increase the entropy of the system. We show how the optimal width of the particles can be determined variationally by minimization of the governing incremental functional. Using this variational principle, we derive optimal scaling relations between the width of the particles, their number and the size of the domain. We also address matters of implementation including the acceleration of the computation of diffusive forces by exploiting the Gaussian decay of the particle profiles and by instituting fast nearest-neighbor searches. We demonstrate the robustness and versatility of the finite-particle method by means of a test problem concerned with the injection of mass into a sphere. There test results demonstrate the meshless character of the method in any spatial dimension, its ability to redistribute mass particles and follow their evolution in time, its ability to satisfy flux boundary conditions for general domains based solely on a distance function, and its robust convergence characteristics.</p>https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/2zv0d-40h73Accurate Approximations of Density Functional Theory for Large Systems with Applications to Defects in Crystalline Solids
https://authors.library.caltech.edu/records/nc59f-2jz76
Authors: {'items': [{'id': 'Bhattacharya-K', 'name': {'family': 'Bhattacharya', 'given': 'Kaushik'}, 'orcid': '0000-0003-2908-5469'}, {'id': 'Gavini-Vikram', 'name': {'family': 'Gavini', 'given': 'Vikram'}, 'orcid': '0000-0002-9451-2300'}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'Michael'}, 'orcid': '0000-0001-5877-4824'}, {'id': 'Ponga-Mauricio', 'name': {'family': 'Ponga', 'given': 'Mauricio'}, 'orcid': '0000-0001-5058-1454'}, {'id': 'Suryanarayana-Phanish', 'name': {'family': 'Suryanarayana', 'given': 'Phanish'}, 'orcid': '0000-0001-5172-0049'}]}
Year: 2023
DOI: 10.1007/978-3-031-22340-2_12
<p>This chapter presents controlled approximations of Kohn–Sham density functional theory (DFT) that enable very large scale simulations. The work is motivated by the study of defects in crystalline solids, though the ideas can be used in other applications. The key idea is to formulate DFT as a minimization problem over the density operator, and to cast spatial and spectral discretization as systematically convergent approximations. This enables efficient and adaptive algorithms that solve the equations of DFT with no additional modeling, and up to desired accuracy, for very large systems, with linear and sublinear scaling. Various approaches based on such approximations are presented, and their numerical performance is demonstrated through selected examples. These examples also provide important insights into the mechanics and physics of defects in crystalline solids.</p>https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/nc59f-2jz76A simple quantitative model of neuromodulation, Part I: Ion flow through neural ion channels
https://authors.library.caltech.edu/records/eh88r-12f66
Authors: {'items': [{'id': 'Werneck-Linda', 'name': {'family': 'Werneck', 'given': 'Linda'}, 'orcid': '0009-0004-1227-6351'}, {'id': 'Han-Mertcan', 'name': {'family': 'Han', 'given': 'Mertcan'}, 'orcid': '0000-0002-3543-5894'}, {'id': 'Yildiz-Erdost', 'name': {'family': 'Yildiz', 'given': 'Erdost'}, 'orcid': '0000-0001-8086-3524'}, {'id': 'Keip-Marc-André', 'name': {'family': 'Keip', 'given': 'Marc-André'}, 'orcid': '0000-0002-5838-5201'}, {'id': 'Sitti-Metin', 'name': {'family': 'Sitti', 'given': 'Metin'}, 'orcid': '0000-0001-8249-3854'}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'Michael'}, 'orcid': '0000-0001-5877-4824'}]}
Year: 2024
DOI: 10.1016/j.jmps.2023.105457
<p>We develop a simple model of ionic current through neuronal membranes as a function of membrane potential and extracellular <a href="https://www.sciencedirect.com/topics/engineering/ion-concentration">ion concentration</a>. The model combines a simplified Poisson–Nernst–Planck (PNP) model of ion transport through individual ion channels with channel <a href="https://www.sciencedirect.com/topics/engineering/activation-function">activation functions</a> calibrated from <i>ad hoc</i> in-house experimental data. The simplified PNP model is validated against bacterial gramicidin A ion channel data. The calibrated model accounts for the transport of calcium, sodium, <a href="https://www.sciencedirect.com/topics/engineering/potassium">potassium</a>, and chloride and exhibits remarkable agreement with the experimentally measured current–voltage curves for the differentiated human neural cells. All relevant data and code related to the ion flow models are available at Werneck et al. (2023).</p>https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/eh88r-12f66Hydrogen trapping and diffusion in polycrystalline nickel: The spectrum of grain boundary segregation
https://authors.library.caltech.edu/records/spg9t-yra67
Authors: {'items': [{'id': 'Ding-Yu', 'name': {'family': 'Ding', 'given': 'Yu'}}, {'id': 'Yu-Haiyang', 'name': {'family': 'Yu', 'given': 'Haiyang'}, 'orcid': '0000-0002-2419-6736'}, {'id': 'Lin-Meichao', 'name': {'family': 'Lin', 'given': 'Meichao'}, 'orcid': '0000-0003-1234-5957'}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'Michael'}, 'orcid': '0000-0001-5877-4824'}, {'id': 'Xiao-Senbo', 'name': {'family': 'Xiao', 'given': 'Senbo'}, 'orcid': '0000-0001-7021-9591'}, {'id': 'He-Jianying', 'name': {'family': 'He', 'given': 'Jianying'}, 'orcid': '0000-0001-8485-7893'}, {'id': 'Zhang-Zhiliang', 'name': {'family': 'Zhang', 'given': 'Zhiliang'}, 'orcid': '0000-0002-9557-3455'}]}
Year: 2024
DOI: 10.1016/j.jmst.2023.07.027
<p>Hydrogen as an interstitial solute at grain boundaries (GBs) can have a catastrophic impact on the <a href="https://www.sciencedirect.com/topics/materials-science/mechanical-property">mechanical properties</a> of many metals. Despite the global research effort, the underlying hydrogen-GB interactions in <a href="https://www.sciencedirect.com/topics/materials-science/polycrystal">polycrystals</a> remain inadequately understood. In this study, using Voronoi tessellations and atomistic simulations, we elucidate the hydrogen segregation energy spectrum at the GBs of polycrystalline nickel by exploring all the topologically favorable segregation sites. Three distinct peaks in the energy spectrum are identified, corresponding to different structural fingerprints. The first peak (−0.205 eV) represents the most favorable segregation sites at GB core, while the second and third peaks account for the sites at GB surface. By incorporating a thermodynamic model, the spectrum enables the determination of the equilibrium hydrogen concentrations at GBs, unveiling a remarkable two to three orders of magnitude increase compared to the bulk hydrogen concentration reported in experimental studies. The identified structures from the GB spectrum exhibit vastly different behaviors in hydrogen segregation and diffusion, with the low-barrier channels inside GB core contributing to short-circuit diffusion, while the high energy gaps between GB and neighboring lattice serving as on-plane diffusion barriers. Mean square displacement analysis further confirms the findings, and shows that the calculated GB <a href="https://www.sciencedirect.com/topics/materials-science/diffusivity">diffusion coefficient</a> is three orders of magnitude greater than that of lattice. The present study has a significant implication for practical applications since it offers a tool to bridge the gap between atomic-scale interactions and macroscopic behaviors in <a href="https://www.sciencedirect.com/topics/materials-science/engineering-material">engineering materials</a>.</p>https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/spg9t-yra67