Monograph records
https://feeds.library.caltech.edu/people/Ortiz-M/monograph.rss
A Caltech Library Repository Feedhttp://www.rssboard.org/rss-specificationpython-feedgenenTue, 16 Apr 2024 14:04:57 +0000The 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.edu/records/sz75e-ve313The 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.edu/records/rx3ef-rng15A 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.edu/records/1md8a-azn77Mixed 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.edu/records/qk400-6e176A 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.edu/records/m0p7y-jsw88An 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.edu/records/62t2m-kw964The 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.edu/records/5z6sb-8mt94A 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.edu/records/bdcqh-baf67A 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.edu/records/xszec-cvc22Optimal 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.edu/records/5j8b4-b5n05The 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.edu/records/qffgv-kme54Concurrent 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.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.edu/records/9zdx5-0jx90Accurate 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.edu/records/gb81e-r3t46Model-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.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.edu/records/se8kp-9jq86A 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.edu/records/v4gz3-8sb56The 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.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.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.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.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.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.edu/records/2zv0d-40h73