Book Section records
https://feeds.library.caltech.edu/people/Ortiz-M/book_section.rss
A Caltech Library Repository Feedhttp://www.rssboard.org/rss-specificationpython-feedgenenTue, 16 Apr 2024 14:04:57 +0000Localization 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.edu/records/wvc5y-a5d43Two-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.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.edu/records/4gb8w-gdf75Nanomechanics 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.edu/records/5ck70-j6f85Frictional 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.edu/records/dfvmy-se793Variational 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.edu/records/rjkw8-cfh80Experimental 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.edu/records/fde8n-wwd04Variational 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.edu/records/dksq3-t4x69An 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.edu/records/30x8v-bnd79A 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.edu/records/64d44-9gx48Validation 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.edu/records/pjwqf-qv757Finite 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.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.edu/records/wppwn-yq492A 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.edu/records/c17q0-vxx53Finite 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.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.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.edu/records/8cgf8-z0521Dissipative 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.edu/records/kbb2q-gk954HOLMES: 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.edu/records/jqfxj-8t304Coupled 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.edu/records/29tac-6zx33Linear 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.edu/records/kv9tb-zp895Modeling 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.edu/records/mr74c-7qt42Atomistic 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.edu/records/2zsfw-g6848Data-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.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.edu/records/k0ms6-ffs72Accurate 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.edu/records/nc59f-2jz76