Search Menu
DOE PAGES title logo U.S. Department of Energy
Office of Scientific and Technical Information
Search Scholarly Publications

Title: A review of predictive nonlinear theories for multiscale modeling of heterogeneous materials

Abstract

Since the beginning of the industrial age, material performance and design have been in the midst of innovation of many disruptive technologies. Today's electronics, space, medical, transportation, and other industries are enriched by development, design and deployment of composite, heterogeneous and multifunctional materials. As a result, materials innovation is now considerably outpaced by other aspects from component design to product cycle. Here in this article, we review predictive nonlinear theories for multiscale modeling of heterogeneous materials. Deeper attention is given to multiscale modeling in space and to computational homogenization in addressing challenging materials science questions. Moreover, we discuss a state-of-the-art platform in predictive image-based, multiscale modeling with co-designed simulations and experiments that executes on the world's largest supercomputers. Such a modeling framework consists of experimental tools, computational methods, and digital data strategies. Once fully completed, this collaborative and interdisciplinary framework can be the basis of Virtual Materials Testing standards and aids in the development of new material formulations. Moreover, it will decrease the time to market of innovative products.

Authors:
 [1];  [2];  [2];  [1]
+ Show Author Affiliations
  1. University of Notre Dame, IN (United States)
  2. Eindhoven University of Technology (Netherlands)
Publication Date:
Research Org.:
University of Notre Dame, IN (United States)
Sponsoring Org.:
USDOE Office of Science (SC); USDOE National Nuclear Security Administration (NNSA); European Research Council (ERC)
OSTI Identifier:
1533953
Alternate Identifier(s):
OSTI ID: 1397825
Grant/Contract Number:  
NA0002377; 339392
Resource Type:
Accepted Manuscript
Journal Name:
Journal of Computational Physics
Additional Journal Information:
Journal Volume: 330; Journal Issue: C; Journal ID: ISSN 0021-9991
Publisher:
Elsevier
Country of Publication:
United States
Language:
English
Subject:
42 ENGINEERING; predictive science; image-based multiscale modeling; computational homogenization; high performance computing; co-designed simulations and experiments; verification and validation; model reduction; big data

Citation Formats

Matouš, Karel, Geers, Marc G.D., Kouznetsova, Varvara G., and Gillman, Andrew. A review of predictive nonlinear theories for multiscale modeling of heterogeneous materials. United States: N. p., 2017. Web. doi:10.1016/j.jcp.2016.10.070.
Copy to clipboard
Matouš, Karel, Geers, Marc G.D., Kouznetsova, Varvara G., & Gillman, Andrew. A review of predictive nonlinear theories for multiscale modeling of heterogeneous materials. United States. https://doi.org/10.1016/j.jcp.2016.10.070
Copy to clipboard
Matouš, Karel, Geers, Marc G.D., Kouznetsova, Varvara G., and Gillman, Andrew. Wed . "A review of predictive nonlinear theories for multiscale modeling of heterogeneous materials". United States. https://doi.org/10.1016/j.jcp.2016.10.070. https://www.osti.gov/servlets/purl/1533953.
Copy to clipboard
@article{osti_1533953,
title = {A review of predictive nonlinear theories for multiscale modeling of heterogeneous materials},
author = {Matouš, Karel and Geers, Marc G.D. and Kouznetsova, Varvara G. and Gillman, Andrew},
abstractNote = {Since the beginning of the industrial age, material performance and design have been in the midst of innovation of many disruptive technologies. Today's electronics, space, medical, transportation, and other industries are enriched by development, design and deployment of composite, heterogeneous and multifunctional materials. As a result, materials innovation is now considerably outpaced by other aspects from component design to product cycle. Here in this article, we review predictive nonlinear theories for multiscale modeling of heterogeneous materials. Deeper attention is given to multiscale modeling in space and to computational homogenization in addressing challenging materials science questions. Moreover, we discuss a state-of-the-art platform in predictive image-based, multiscale modeling with co-designed simulations and experiments that executes on the world's largest supercomputers. Such a modeling framework consists of experimental tools, computational methods, and digital data strategies. Once fully completed, this collaborative and interdisciplinary framework can be the basis of Virtual Materials Testing standards and aids in the development of new material formulations. Moreover, it will decrease the time to market of innovative products.},
doi = {10.1016/j.jcp.2016.10.070},
journal = {Journal of Computational Physics},
number = C,
volume = 330,
place = {United States},
year = {Wed Feb 01 00:00:00 EST 2017},
month = {Wed Feb 01 00:00:00 EST 2017}
}
Copy to clipboard
Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record
https://doi.org/10.1016/j.jcp.2016.10.070
Copyright Statement
Other availability
Search WorldCat Search WorldCat to find libraries that may hold this journal
Citation Metrics:
Cited by: 300 works
Citation information provided by
Web of Science
Save / Share:
Export Metadata
Save to My Library
You must Sign In or Create an Account in order to save documents to your library.

Works referenced in this record:

Extension of the Nonuniform Transformation Field Analysis to linear viscoelastic composites in the presence of aging and swelling
journal, June 2014

A POD-EIM reduced two-scale model for crystal growth
journal, July 2014

The coarse-graining approach to statistical mechanics: how blissful is our ignorance?
journal, March 2002

  • Ridderbos, Katinka
  • Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics, Vol. 33, Issue 1
  • DOI: 10.1016/S1355-2198(01)00037-5

FE2 multiscale in linear elasticity based on parametrized microscale models using proper generalized decomposition
journal, April 2013

  • El Halabi, F.; González, D.; Chico, A.
  • Computer Methods in Applied Mechanics and Engineering, Vol. 257
  • DOI: 10.1016/j.cma.2013.01.011

Computational homogenization of soft matter friction: Isogeometric framework and elastic boundary layers
journal, September 2014

  • Temizer, İ.
  • International Journal for Numerical Methods in Engineering, Vol. 100, Issue 13
  • DOI: 10.1002/nme.4778

Mathematical homogenization of nonperiodic heterogeneous media subjected to large deformation transient loading
journal, November 2008

  • Fish, Jacob; Fan, Rong
  • International Journal for Numerical Methods in Engineering, Vol. 76, Issue 7
  • DOI: 10.1002/nme.2355

Modeling of failure in composites by X-FEM and level sets within a multiscale framework
journal, January 2008

  • Hettich, Thomas; Hund, Andrea; Ramm, Ekkehard
  • Computer Methods in Applied Mechanics and Engineering, Vol. 197, Issue 5
  • DOI: 10.1016/j.cma.2007.07.017

Ab-initio simulations of materials using VASP: Density-functional theory and beyond
journal, October 2008

  • Hafner, Jürgen
  • Journal of Computational Chemistry, Vol. 29, Issue 13
  • DOI: 10.1002/jcc.21057

Nonlinear asymptotic homogenization and the effective behavior of layered thermoelectric composites
journal, August 2013

  • Yang, Y.; Ma, F. Y.; Lei, C. H.
  • Journal of the Mechanics and Physics of Solids, Vol. 61, Issue 8
  • DOI: 10.1016/j.jmps.2013.03.006

Direct numerical simulations in solid mechanics for understanding the macroscale effects of microscale material variability
journal, April 2015

  • Bishop, Joseph E.; Emery, John M.; Field, Richard V.
  • Computer Methods in Applied Mechanics and Engineering, Vol. 287
  • DOI: 10.1016/j.cma.2015.01.017

The influence of scale size on the stability of periodic solids and the role of associated higher order gradient continuum models
journal, November 1996

Coupling of scales in a multiscale simulation using neural networks
journal, November 2008

Three-dimensional reconstruction of statistically optimal unit cells of polydisperse particulate composites from microtomography
journal, December 2009

A 3D computational homogenization model for porous material and parameters identification
journal, January 2015

Damage evolution in particulate composite materials
journal, March 2003

Strain-driven homogenization of inelastic microstructures and composites based on an incremental variational formulation
journal, January 2002

  • Miehe, Christian
  • International Journal for Numerical Methods in Engineering, Vol. 55, Issue 11
  • DOI: 10.1002/nme.515

Surrogate modeling of multiscale models using kernel methods: KERNEL SURROGATE MULTISCALE MODELS
journal, November 2014

  • Wirtz, D.; Karajan, N.; Haasdonk, B.
  • International Journal for Numerical Methods in Engineering, Vol. 101, Issue 1
  • DOI: 10.1002/nme.4767

A multi-level computational model for multi-scale damage analysis in composite and porous materials
journal, April 2001

  • Ghosh, Somnath; Lee, Kyunghoon; Raghavan, Prasanna
  • International Journal of Solids and Structures, Vol. 38, Issue 14
  • DOI: 10.1016/S0020-7683(00)00167-0

Acceleration of material‐dominated calculations via phase‐space simplicial subdivision and interpolation
journal, March 2015

  • Klusemann, B.; Ortiz, M.
  • International Journal for Numerical Methods in Engineering, Vol. 103, Issue 4
  • DOI: 10.1002/nme.4887

High-performance model reduction techniques in computational multiscale homogenization
journal, July 2014

  • Hernández, J. A.; Oliver, J.; Huespe, A. E.
  • Computer Methods in Applied Mechanics and Engineering, Vol. 276
  • DOI: 10.1016/j.cma.2014.03.011

Fracture simulations using large-scale molecular dynamics
journal, May 1995

Computational multiscale modelling of heterogeneous material layers
journal, April 2009

Measurement of three-dimensional microstructure in a LiCoO2 positive electrode
journal, April 2011

Computational homogenization for nonlinear conduction in heterogeneous materials using model reduction
journal, June 2008

An adaptive method for homogenization in orthotropic nonlinear elasticity
journal, July 2007

  • Temizer, İ.; Wriggers, P.
  • Computer Methods in Applied Mechanics and Engineering, Vol. 196, Issue 35-36
  • DOI: 10.1016/j.cma.2007.03.017

Issues in Computational Fluid Dynamics Code Verification and Validation
journal, May 1998

  • Oberkampf, William L.; Blottner, Frederick G.
  • AIAA Journal, Vol. 36, Issue 5
  • DOI: 10.2514/2.456

Prediction of Landfalling Hurricanes with the Advanced Hurricane WRF Model
journal, June 2008

  • Davis, Christopher; Wang, Wei; Chen, Shuyi S.
  • Monthly Weather Review, Vol. 136, Issue 6
  • DOI: 10.1175/2007MWR2085.1

Continuum Micromechanics: Survey
journal, August 2002

Analysis and adaptive modeling of highly heterogeneous elastic structures
journal, September 1997

  • Oden, J. Tinsley; Zohdi, Tarek I.
  • Computer Methods in Applied Mechanics and Engineering, Vol. 148, Issue 3-4
  • DOI: 10.1016/S0045-7825(97)00032-7

Continuum micro-mechanics of elastoplastic polycrystals
journal, April 1965

MultiScale First-Order and Second-Order Computational Homogenization of Microstructures towards Continua
journal, January 2003

  • Geers, Marc; Kouznetsova, V. G.; Brekelmans, W. A. M.
  • International Journal for Multiscale Computational Engineering, Vol. 1, Issue 4
  • DOI: 10.1615/IntJMultCompEng.v1.i4.40

Dislocation processes in the deformation of nanocrystalline aluminium by molecular-dynamics simulation
journal, September 2002

  • Yamakov, Vesselin; Wolf, Dieter; Phillpot, Simon R.
  • Nature Materials, Vol. 1, Issue 1
  • DOI: 10.1038/nmat700

computational homogenization for the thermo-mechanical analysis of heterogeneous solids
journal, December 2008

  • Özdemir, I.; Brekelmans, W. A. M.; Geers, M. G. D.
  • Computer Methods in Applied Mechanics and Engineering, Vol. 198, Issue 3-4
  • DOI: 10.1016/j.cma.2008.09.008

A numerical approximation to the elastic properties of sphere-reinforced composites
journal, October 2002

Nonlinear Computational Homogenization Method for the Evaluation of Eddy Currents in Soft Magnetic Composites
journal, February 2014

  • Niyonzima, Innocent; Sabariego, Ruth V.; Dular, Patrick
  • IEEE Transactions on Magnetics, Vol. 50, Issue 2
  • DOI: 10.1109/TMAG.2013.2286413

Numerical homogenization of mesoscopic loss in poroelastic media
journal, January 2015

A homogenization approach for characterization of the fluid–solid coupling parameters in Biot׳s equations for acoustic poroelastic materials
journal, September 2015

Performance of the Unstructured-Mesh, SWAN+ADCIRC Model in Computing Hurricane Waves and Surge
journal, November 2011

  • Dietrich, J. C.; Tanaka, S.; Westerink, J. J.
  • Journal of Scientific Computing, Vol. 52, Issue 2
  • DOI: 10.1007/s10915-011-9555-6

Performance of a distributed memory finite difference atmospheric general circulation model
journal, October 1995

Hierarchically parallel coupled finite strain multiscale solver for modeling heterogeneous layers: HIERARCHICALLY PARALLEL MULTISCALE SOLVER
journal, August 2014

  • Mosby, Matthew; Matouš, Karel
  • International Journal for Numerical Methods in Engineering, Vol. 102, Issue 3-4
  • DOI: 10.1002/nme.4755

Simulated Micromechanical Models Using Artificial Neural Networks
journal, July 2001

Magnesium interatomic potential for simulating plasticity and fracture phenomena
journal, December 2014

  • Wu, Z.; Francis, M. F.; Curtin, W. A.
  • Modelling and Simulation in Materials Science and Engineering, Vol. 23, Issue 1
  • DOI: 10.1088/0965-0393/23/1/015004

Microstructure-statistics-property relations of anisotropic polydisperse particulate composites using tomography
journal, February 2013

Data-parallel lower-upper relaxation method for the Navier-Stokes equations
journal, July 1996

  • Wright, Michael J.; Candler, Graham V.; Prampolini, Marco
  • AIAA Journal, Vol. 34, Issue 7
  • DOI: 10.2514/3.13242

Determination of the size of the representative volume element for random composites: statistical and numerical approach
journal, June 2003

Bridging the scales in nano engineering and science
journal, September 2006

Computational coarse graining of a randomly forced one-dimensional Burgers equation
journal, March 2008

  • Ahuja, Sunil; Yakhot, Victor; Kevrekidis, Ioannis G.
  • Physics of Fluids, Vol. 20, Issue 3
  • DOI: 10.1063/1.2856212

Computational homogenisation of periodic cellular materials: Application to structural modelling
journal, April 2015

Geometrical structure of disordered sphere packings
journal, June 2005

Minimal kinematic boundary conditions for simulations of disordered microstructures
journal, January 2005

Discrete Element Method Simulations for Complex Granular Flows
journal, January 2015

Two scale analysis of heterogeneous elastic-plastic materials with asymptotic homogenization and Voronoi cell finite element model
journal, May 1996

  • Ghosh, Somnath; Lee, Kyunghoon; Moorthy, Suresh
  • Computer Methods in Applied Mechanics and Engineering, Vol. 132, Issue 1-2
  • DOI: 10.1016/0045-7825(95)00974-4

A method for interpolating on manifolds structural dynamics reduced-order models
journal, November 2009

  • Amsallem, David; Cortial, Julien; Carlberg, Kevin
  • International Journal for Numerical Methods in Engineering, Vol. 80, Issue 9
  • DOI: 10.1002/nme.2681

Apparent and effective physical properties of heterogeneous materials: Representativity of samples of two materials from food industry
journal, July 2006

  • Kanit, Toufik; N’Guyen, Franck; Forest, Samuel
  • Computer Methods in Applied Mechanics and Engineering, Vol. 195, Issue 33-36
  • DOI: 10.1016/j.cma.2005.07.022

Using microstructure reconstruction to model mechanical behavior in complex microstructures
journal, August 2006

Recent Developments in High Performance Computing for Remote Sensing: A Review
journal, September 2011

  • Lee, Craig A.; Gasster, Samuel D.; Plaza, Antonio
  • IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing, Vol. 4, Issue 3
  • DOI: 10.1109/JSTARS.2011.2162643

Multiscale framework for behavior prediction in granular media
journal, June 2009

Estimation of Local Modeling Error and Goal-Oriented Adaptive Modeling of Heterogeneous Materials
journal, October 2000

  • Oden, J. Tinsley; Vemaganti, Kumar S.
  • Journal of Computational Physics, Vol. 164, Issue 1
  • DOI: 10.1006/jcph.2000.6585

Reconstructing random media
journal, January 1998

Multi-scale constitutive modelling of heterogeneous materials with a gradient-enhanced computational homogenization scheme
journal, January 2002

  • Kouznetsova, V.; Geers, M. G. D.; Brekelmans, W. A. M.
  • International Journal for Numerical Methods in Engineering, Vol. 54, Issue 8
  • DOI: 10.1002/nme.541

Structural Damage Analysis of Masonry Walls using Computational Homogenization
journal, April 2007

  • Massart, T. J.; Peerlings, R. H. J.; Geers, M. G. D.
  • International Journal of Damage Mechanics, Vol. 16, Issue 2
  • DOI: 10.1177/1056789506064943

The Design and Implementation of FFTW3
journal, February 2005

Numerical modelling of the effective conductivities of composites with arbitrarily shaped inclusions and highly conducting interface
journal, October 2008

Variational Principles for Inhomogeneous Non-linear Media
journal, January 1985

  • Talbot, D. R. S.; Willis, J. R.
  • IMA Journal of Applied Mathematics, Vol. 35, Issue 1
  • DOI: 10.1093/imamat/35.1.39

Size of a Representative Volume Element in a Second-Order Computational Homogenization Framework
journal, January 2004

  • Kouznetsova, V. G.; Geers, Professor, Marc G. D.; Brekelmans, W. A. M.
  • International Journal for Multiscale Computational Engineering, Vol. 2, Issue 4
  • DOI: 10.1615/IntJMultCompEng.v2.i4.50

Wavelet Methods in Computational Fluid Dynamics
journal, January 2010

Computational homogenization based on a weak format of micro-periodicity for RVE-problems
journal, January 2011

  • Larsson, F.; Runesson, K.; Saroukhani, S.
  • Computer Methods in Applied Mechanics and Engineering, Vol. 200, Issue 1-4
  • DOI: 10.1016/j.cma.2010.06.023

Relating inhomogeneous deformation to local texture in zirconium through grain-scale digital image correlation strain mapping experiments
journal, January 2012

Homogenization and multiscale stability analysis in finite magneto-electro-elasticity. Application to soft matter EE, ME and MEE composites
journal, March 2016

  • Miehe, Christian; Vallicotti, Daniel; Teichtmeister, Stephan
  • Computer Methods in Applied Mechanics and Engineering, Vol. 300
  • DOI: 10.1016/j.cma.2015.10.013

P3DFFT: A Framework for Parallel Computations of Fourier Transforms in Three Dimensions
journal, January 2012

  • Pekurovsky, Dmitry
  • SIAM Journal on Scientific Computing, Vol. 34, Issue 4
  • DOI: 10.1137/11082748X

A nonlinear manifold-based reduced order model for multiscale analysis of heterogeneous hyperelastic materials
journal, May 2016

Concurrent Processing and Complexity of Temporally Encoded Neuronal Messages in Visual Perception
journal, August 1991

  • McClurkin, John W.; Optican, Lance M.; Richmond, Barry J.
  • Science, Vol. 253, Issue 5020
  • DOI: 10.1126/science.1908118

Experimental and computational investigation of progressive damage accumulation in CFRP composites
journal, May 2013

Extraction of morphological quantities from a digitized medium
journal, June 1995

  • Coker, David A.; Torquato, Salvatore
  • Journal of Applied Physics, Vol. 77, Issue 12
  • DOI: 10.1063/1.359134

Neural network models of potential energy surfaces
journal, September 1995

  • Blank, Thomas B.; Brown, Steven D.; Calhoun, August W.
  • The Journal of Chemical Physics, Vol. 103, Issue 10
  • DOI: 10.1063/1.469597

Multiscale thermomechanical contact: Computational homogenization with isogeometric analysis
journal, December 2013

  • Temizer, İ
  • International Journal for Numerical Methods in Engineering, Vol. 97, Issue 8
  • DOI: 10.1002/nme.4604

Size and temperature effects on the fracture mechanisms of silicon nanowires: Molecular dynamics simulations
journal, September 2010

Multiscale model for predicting damage evolution in composites due to impact loading
journal, October 2008

Fast Parallel Algorithms for Short-Range Molecular Dynamics
journal, March 1995

Visual learning and recognition of 3-d objects from appearance
journal, January 1995

  • Murase, Hiroshi; Nayar, Shree K.
  • International Journal of Computer Vision, Vol. 14, Issue 1
  • DOI: 10.1007/BF01421486

A micromechanics-based nonlocal constitutive equation and estimates of representative volume element size for elastic composites
journal, April 1996

Berechnung der elastischen Konstanten des Vielkristalls aus den Konstanten des Einkristalls
journal, August 1958

Computational homogenization in dissipative electro-mechanics of functional materials
journal, December 2013

  • Zäh, Dominic; Miehe, Christian
  • Computer Methods in Applied Mechanics and Engineering, Vol. 267
  • DOI: 10.1016/j.cma.2013.09.012

A hard X-ray nanoprobe beamline for nanoscale microscopy
journal, September 2012

  • Winarski, Robert P.; Holt, Martin V.; Rose, Volker
  • Journal of Synchrotron Radiation, Vol. 19, Issue 6
  • DOI: 10.1107/S0909049512036783

Overall behaviour of heterogeneous elastoviscoplastic materials: effect of microstructural modelling
journal, August 2000

A mixed finite element procedure of gradient Cosserat continuum for second-order computational homogenisation of granular materials
journal, July 2014

Verification and validation in computational fluid dynamics
journal, April 2002

Computational plasticity for composite structures based on mathematical homogenization: Theory and practice
journal, August 1997

  • Fish, Jacob; Shek, Kamlun; Pandheeradi, Muralidharan
  • Computer Methods in Applied Mechanics and Engineering, Vol. 148, Issue 1-2
  • DOI: 10.1016/S0045-7825(97)00030-3

Response Surfaces, Mixtures, and Ridge Analyses
journal, January 2007

  • Box, George E. P.; Draper, Norman R.
  • Wiley Series in Probability and Statistics
  • DOI: 10.1002/0470072768

Homogenization estimates for multi-scale nonlinear composites
journal, November 2011

Eigendeformation-based reduced order homogenization for failure analysis of heterogeneous materials
journal, January 2007

  • Oskay, Caglar; Fish, Jacob
  • Computer Methods in Applied Mechanics and Engineering, Vol. 196, Issue 7
  • DOI: 10.1016/j.cma.2006.08.015

Equation of State Calculations by Fast Computing Machines
journal, June 1953

  • Metropolis, Nicholas; Rosenbluth, Arianna W.; Rosenbluth, Marshall N.
  • The Journal of Chemical Physics, Vol. 21, Issue 6
  • DOI: 10.1063/1.1699114

Multi‐scale computational homogenization–localization for propagating discontinuities using X‐FEM
journal, February 2015

  • Bosco, E.; Kouznetsova, V. G.; Geers, M. G. D.
  • International Journal for Numerical Methods in Engineering, Vol. 102, Issue 3-4
  • DOI: 10.1002/nme.4838

A computational homogenization approach for Li-ion battery cells: Part 1 – formulation
journal, April 2014

Constitutive modeling of geomaterials from non-uniform material tests
journal, January 1998

Knowledge‐Based Modeling of Material Behavior with Neural Networks
journal, January 1991

In Situ Experiments with X ray Tomography: an Attractive Tool for Experimental Mechanics
journal, January 2010

The variational multiscale method—a paradigm for computational mechanics
journal, November 1998

  • Hughes, Thomas J. R.; Feijóo, Gonzalo R.; Mazzei, Luca
  • Computer Methods in Applied Mechanics and Engineering, Vol. 166, Issue 1-2
  • DOI: 10.1016/S0045-7825(98)00079-6

Modeling heterogeneous materials via two-point correlation functions. II. Algorithmic details and applications
journal, March 2008

Density‐functional thermochemistry. III. The role of exact exchange
journal, April 1993

  • Becke, Axel D.
  • The Journal of Chemical Physics, Vol. 98, Issue 7, p. 5648-5652
  • DOI: 10.1063/1.464913

Flow simulation and high performance computing
journal, December 1996

  • Tezduyar, T.; Aliabadi, S.; Behr, M.
  • Computational Mechanics, Vol. 18, Issue 6
  • DOI: 10.1007/BF00350249

On the crushing of aluminum open-cell foams: Part I. Experiments
journal, February 2009

Three-Dimensional Reconstruction of Statistically Optimal Unit Cells of Multimodal Particulate Composites
journal, January 2010

Kernel principal component analysis for stochastic input model generation
journal, August 2011

Multiscale modelling of particle debonding in reinforced elastomers subjected to finite deformations
journal, January 2005

  • Matouš, Karel; Geubelle, Philippe H.
  • International Journal for Numerical Methods in Engineering, Vol. 65, Issue 2
  • DOI: 10.1002/nme.1446

Computational homogenization of nonlinear elastic materials using neural networks: NEURAL NETWORKS-BASED COMPUTATIONAL HOMOGENIZATION
journal, June 2015

  • Le, B. A.; Yvonnet, J.; He, Q. -C.
  • International Journal for Numerical Methods in Engineering, Vol. 104, Issue 12
  • DOI: 10.1002/nme.4953

New variational principles in plasticity and their application to composite materials
journal, November 1992

In situ X-ray synchrotron tomographic imaging during the compression of hyper-elastic polymeric materials
journal, September 2015

  • Patterson, Brian M.; Cordes, Nikolaus L.; Henderson, Kevin
  • Journal of Materials Science, Vol. 51, Issue 1
  • DOI: 10.1007/s10853-015-9355-8

Transient computational homogenization for heterogeneous materials under dynamic excitation
journal, November 2013

  • Pham, K.; Kouznetsova, V. G.; Geers, M. G. D.
  • Journal of the Mechanics and Physics of Solids, Vol. 61, Issue 11
  • DOI: 10.1016/j.jmps.2013.07.005

DIRECT NUMERICAL SIMULATION: A Tool in Turbulence Research
journal, January 1998

An enhanced multi-scale approach for masonry wall computations with localization of damage
journal, January 2007

  • Massart, T. J.; Peerlings, R. H. J.; Geers, M. G. D.
  • International Journal for Numerical Methods in Engineering, Vol. 69, Issue 5
  • DOI: 10.1002/nme.1799

Molecular dynamics using atomic-resolution structure reveal structural fluctuations that may lead to polymerization of human Cu Zn superoxide dismutase
journal, June 2007

  • Strange, R. W.; Yong, C. W.; Smith, W.
  • Proceedings of the National Academy of Sciences, Vol. 104, Issue 24
  • DOI: 10.1073/pnas.0703857104

Billion vortex particle direct numerical simulations of aircraft wakes
journal, February 2008

  • Chatelain, Philippe; Curioni, Alessandro; Bergdorf, Michael
  • Computer Methods in Applied Mechanics and Engineering, Vol. 197, Issue 13-16
  • DOI: 10.1016/j.cma.2007.11.016

Bridging multiple structural scales with a generalized finite element method: BRIDGING SCALES WITH GFEM
journal, June 2014

  • Plews, J. A.; Duarte, C. A.
  • International Journal for Numerical Methods in Engineering, Vol. 102, Issue 3-4
  • DOI: 10.1002/nme.4703

Metallic-covalent interatomic potential for carbon in iron
journal, October 2008

A second-moment incremental formulation for the mean-field homogenization of elasto-plastic composites
journal, March 2011

Modeling hurricane waves and storm surge using integrally-coupled, scalable computations
journal, January 2011

A model for the dissociative adsorption of N2O on Cu(100) using a continuous potential energy surface
journal, March 2010

Representative volume element size for elastic composites: A numerical study
journal, September 1997

The effective mechanical properties of nonlinear isotropic composites
journal, January 1991

Second-order homogenization estimates for nonlinear composites incorporating field fluctuations: I—theory
journal, April 2002

APPLIED PHYSICS: Enhanced: Moore's Law Forever?
journal, January 2003

Generalized multiscale finite element methods (GMsFEM)
journal, October 2013

Key computational modeling issues in Integrated Computational Materials Engineering
journal, January 2013

  • Panchal, Jitesh H.; Kalidindi, Surya R.; McDowell, David L.
  • Computer-Aided Design, Vol. 45, Issue 1
  • DOI: 10.1016/j.cad.2012.06.006

The heterogeneous multiscale method
journal, April 2012

Simulation of the multi-scale convergence in computational homogenization approaches
journal, April 2000

  • Terada, Kenjiro; Hori, Muneo; Kyoya, Takashi
  • International Journal of Solids and Structures, Vol. 37, Issue 16
  • DOI: 10.1016/S0020-7683(98)00341-2

Non-Local Computational Homogenization of Periodic Masonry
journal, January 2011

Average stress in matrix and average elastic energy of materials with misfitting inclusions
journal, May 1973

Continuum Theory of Ductile Rupture by Void Nucleation and Growth: Part I—Yield Criteria and Flow Rules for Porous Ductile Media
journal, January 1977

  • Gurson, A. L.
  • Journal of Engineering Materials and Technology, Vol. 99, Issue 1
  • DOI: 10.1115/1.3443401

Bounds and self-consistent estimates for the overall properties of anisotropic composites
journal, June 1977

Novel boundary conditions for strain localization analyses in microstructural volume elements: BCS FOR LOCALIZATION ANALYSIS IN MICROSTRUCTURES
journal, October 2011

  • Coenen, E. W. C.; Kouznetsova, V. G.; Geers, M. G. D.
  • International Journal for Numerical Methods in Engineering, Vol. 90, Issue 1
  • DOI: 10.1002/nme.3298

Computational micro-to-macro transitions of discretized microstructures undergoing small strains
journal, July 2002

Multi-scale computational homogenization of structured thin sheets
journal, May 2007

  • Geers, M. G. D.; Coenen, E. W. C.; Kouznetsova, V. G.
  • Modelling and Simulation in Materials Science and Engineering, Vol. 15, Issue 4
  • DOI: 10.1088/0965-0393/15/4/S06

Multiscale Equilibrium and Nonequilibrium Thermodynamics in Chemical Engineering
book, January 2010

FE2 multiscale approach for modelling the elastoviscoplastic behaviour of long fibre SiC/Ti composite materials
journal, March 2000

  • Feyel, Frédéric; Chaboche, Jean-Louis
  • Computer Methods in Applied Mechanics and Engineering, Vol. 183, Issue 3-4
  • DOI: 10.1016/S0045-7825(99)00224-8

Computational homogenization of rope-like technical textiles
journal, February 2015

  • Fillep, Sebastian; Mergheim, Julia; Steinmann, Paul
  • Computational Mechanics, Vol. 55, Issue 3
  • DOI: 10.1007/s00466-015-1124-7

From random microstructures to representative volume elements
journal, May 2007

  • Zeman, J.; Šejnoha, M.
  • Modelling and Simulation in Materials Science and Engineering, Vol. 15, Issue 4
  • DOI: 10.1088/0965-0393/15/4/S01

Computational homogenization in magneto-mechanics
journal, December 2013

  • Javili, A.; Chatzigeorgiou, G.; Steinmann, P.
  • International Journal of Solids and Structures, Vol. 50, Issue 25-26
  • DOI: 10.1016/j.ijsolstr.2013.08.024

Microstructure of Composite Propellants Using Simulated Packings and X-Ray Tomography
journal, January 2008

  • Gallier, Stany; Hiernard, Fabrice
  • Journal of Propulsion and Power, Vol. 24, Issue 1
  • DOI: 10.2514/1.30454

Implicit constitutive modelling for viscoplasticity using neural networks
journal, September 1998

Software debugging, testing, and verification
journal, January 2002

Effective properties of composite materials with periodic microstructure: a computational approach
journal, April 1999

  • Michel, J. C.; Moulinec, H.; Suquet, P.
  • Computer Methods in Applied Mechanics and Engineering, Vol. 172, Issue 1-4
  • DOI: 10.1016/S0045-7825(98)00227-8

Microstructure reconstructions from 2-point statistics using phase-recovery algorithms
journal, March 2008

The reduced model multiscale method (R3M) for the non-linear homogenization of hyperelastic media at finite strains
journal, April 2007

Computational homogenization at extreme scales
journal, March 2016

Homogenization-based constitutive models for magnetorheological elastomers at finite strain
journal, February 2011

  • Ponte Castañeda, P.; Galipeau, E.
  • Journal of the Mechanics and Physics of Solids, Vol. 59, Issue 2
  • DOI: 10.1016/j.jmps.2010.11.004

Computing overall elastic constants of polydisperse particulate composites from microtomographic data
journal, September 2011

  • Lee, Hyunsun; Gillman, Andrew S.; Matouš, Karel
  • Journal of the Mechanics and Physics of Solids, Vol. 59, Issue 9
  • DOI: 10.1016/j.jmps.2011.05.010

Multi-scale computational homogenization: Trends and challenges
journal, August 2010

  • Geers, M. G. D.; Kouznetsova, V. G.; Brekelmans, W. A. M.
  • Journal of Computational and Applied Mathematics, Vol. 234, Issue 7
  • DOI: 10.1016/j.cam.2009.08.077

Diffusion maps
journal, July 2006

  • Coifman, Ronald R.; Lafon, Stéphane
  • Applied and Computational Harmonic Analysis, Vol. 21, Issue 1
  • DOI: 10.1016/j.acha.2006.04.006

Finite anisotropic elasticity and material frame indifference from a nonequilibrium thermodynamics perspective
journal, June 2008

3D reconstruction and characterization of polycrystalline microstructures using a FIB–SEM system
journal, December 2006

Three-point bounds and other estimates for strongly nonlinear composites
journal, May 1998

Asymptotic analysis of heterogeneous Cosserat media
journal, June 2001

  • Forest, Samuel; Pradel, Francis; Sab, Karam
  • International Journal of Solids and Structures, Vol. 38, Issue 26-27
  • DOI: 10.1016/S0020-7683(00)00295-X

Artificial neural network as an incremental non-linear constitutive model for a finite element code
journal, July 2003

An approach to micro-macro modeling of heterogeneous materials
journal, January 2001

  • Kouznetsova, V.; Brekelmans, W. A. M.; Baaijens, F. P. T.
  • Computational Mechanics, Vol. 27, Issue 1
  • DOI: 10.1007/s004660000212

Towards High Performance Digital Volume Correlation
journal, December 2010

3D microstructural characterization of nickel superalloys via serial-sectioning using a dual beam FIB-SEM
journal, July 2006

Computational homogenization for heat conduction in heterogeneous solids
journal, January 2007

  • Özdemir, I.; Brekelmans, W. A. M.; Geers, M. G. D.
  • International Journal for Numerical Methods in Engineering, Vol. 73, Issue 2
  • DOI: 10.1002/nme.2068

Scale transition and enforcement of RVE boundary conditions in second-order computational homogenization
journal, January 2008

  • Kaczmarczyk, Łukasz; Pearce, Chris J.; Bićanić, Nenad
  • International Journal for Numerical Methods in Engineering, Vol. 74, Issue 3
  • DOI: 10.1002/nme.2188

A class of general algorithms for multi-scale analyses of heterogeneous media
journal, July 2001

Verification and validation in computational engineering and science: basic concepts
journal, September 2004

  • Babuska, Ivo; Oden, J. Tinsley
  • Computer Methods in Applied Mechanics and Engineering, Vol. 193, Issue 36-38
  • DOI: 10.1016/j.cma.2004.03.002

A numerical method for homogenization in non-linear elasticity
journal, July 2006

X-ray nanotomography and focused-ion-beam sectioning for quantitative three-dimensional analysis of nanocomposites
journal, June 2016

  • Shuck, Christopher E.; Frazee, Mathew; Gillman, Andrew
  • Journal of Synchrotron Radiation, Vol. 23, Issue 4
  • DOI: 10.1107/S1600577516007992

Basal and prism dislocation cores in magnesium: comparison of first-principles and embedded-atom-potential methods predictions
journal, June 2009

  • Yasi, J. A.; Nogaret, T.; Trinkle, D. R.
  • Modelling and Simulation in Materials Science and Engineering, Vol. 17, Issue 5
  • DOI: 10.1088/0965-0393/17/5/055012

Insights into Current Limitations of Density Functional Theory
journal, August 2008

On mechanics and material length scales of failure in heterogeneous interfaces using a finite strain high performance solver
journal, October 2015

  • Mosby, Matthew; Matouš, Karel
  • Modelling and Simulation in Materials Science and Engineering, Vol. 23, Issue 8
  • DOI: 10.1088/0965-0393/23/8/085014

Damage accumulation in a carbon/epoxy composite: Comparison between a multiscale model and computed tomography experimental results
journal, September 2012

Bounds and estimates for linear composites with strain gradient effects
journal, December 1994

Quantification of Uncertainty in Computational Fluid Dynamics
journal, January 1997

Computational homogenization for adhesive and cohesive failure in quasi-brittle solids: COMPUTATIONAL HOMOGENIZATION FOR FAILURE IN QUASI-BRITTLE SOLIDS
journal, March 2010

  • Verhoosel, Clemens V.; Remmers, Joris J. C.; Gutiérrez, Miguel A.
  • International Journal for Numerical Methods in Engineering, Vol. 83, Issue 8-9
  • DOI: 10.1002/nme.2854

Using neural networks to represent potential surfaces as sums of products
journal, November 2006

  • Manzhos, Sergei; Carrington, Tucker
  • The Journal of Chemical Physics, Vol. 125, Issue 19
  • DOI: 10.1063/1.2387950

Challenge problems: uncertainty in system response given uncertain parameters
journal, July 2004

  • Oberkampf, William L.; Helton, Jon C.; Joslyn, Cliff A.
  • Reliability Engineering & System Safety, Vol. 85, Issue 1-3
  • DOI: 10.1016/j.ress.2004.03.002

Estimation of Modeling Error in Computational Mechanics
journal, November 2002

  • Oden, J. Tinsley; Prudhomme, Serge
  • Journal of Computational Physics, Vol. 182, Issue 2
  • DOI: 10.1006/jcph.2002.7183

A multi-scale approach to bridge microscale damage and macroscale failure: a nested computational homogenization-localization framework
journal, September 2012

  • Coenen, E. W. C.; Kouznetsova, V. G.; Bosco, E.
  • International Journal of Fracture, Vol. 178, Issue 1-2
  • DOI: 10.1007/s10704-012-9765-4

Morphology and physical properties of Fontainebleau sandstone via a tomographic analysis
journal, August 1996

  • Coker, David A.; Torquato, Salvatore; Dunsmuir, John H.
  • Journal of Geophysical Research: Solid Earth, Vol. 101, Issue B8
  • DOI: 10.1029/96JB00811

Computational homogenization of rubber friction on rough rigid surfaces
journal, September 2013

Representation and computational structure-property relations of random media
journal, March 2011

Simulation of the deformation of polycrystalline nanostructured Ti by computational homogenization
journal, August 2013

A two-scale approach for trabecular bone microstructure modeling based on computational homogenization procedure
journal, February 2014

  • Wierszycki, Marcin; Szajek, Krzysztof; Łodygowski, Tomasz
  • Computational Mechanics, Vol. 54, Issue 2
  • DOI: 10.1007/s00466-014-0984-6

Incorporation of microstructural information into models of two-phase materials
journal, August 1995

Computational homogenization analysis in finite plasticity Simulation of texture development in polycrystalline materials
journal, April 1999

  • Miehe, Christian; Schröder, Jörg; Schotte, Jan
  • Computer Methods in Applied Mechanics and Engineering, Vol. 171, Issue 3-4
  • DOI: 10.1016/S0045-7825(98)00218-7

Computational micromechanics
journal, September 1996

Mean field variations in a statistical sample of heterogeneous linearly elastic solids
journal, August 1970

Multi-scale modeling of heterogeneous adhesives: Effect of particle decohesion
journal, May 2009

Applying genetic algorithms to selected topics commonly encountered in engineering practice
journal, December 2000

  • Matouš, K.; Lepš, M.; Zeman, J.
  • Computer Methods in Applied Mechanics and Engineering, Vol. 190, Issue 13-14
  • DOI: 10.1016/S0045-7825(00)00192-4

Three-dimensional image correlation from X-ray computed tomography of solid foam
journal, August 2008

A variational approach to the theory of the elastic behaviour of multiphase materials
journal, March 1963

High performance computing in biology: Multimillion atom simulations of nanoscale systems
journal, March 2007

On micro-to-macro transitions for multi-scale analysis of non-linear heterogeneous materials: unified variational basis and finite element implementation
journal, September 2010

  • Perić, D.; de Souza Neto, E. A.; Feijóo, R. A.
  • International Journal for Numerical Methods in Engineering, Vol. 87, Issue 1-5
  • DOI: 10.1002/nme.3014

Certification of projection-based reduced order modelling in computational homogenisation by the constitutive relation error: CERTIFIED GALERKIN-POD IN COMPUTATIONAL HOMOGENISATION
journal, October 2013

  • Kerfriden, P.; Ródenas, J. J.; Bordas, S. P. -A.
  • International Journal for Numerical Methods in Engineering, Vol. 97, Issue 6
  • DOI: 10.1002/nme.4588

PPM – A highly efficient parallel particle–mesh library for the simulation of continuum systems
journal, July 2006

  • Sbalzarini, I. F.; Walther, J. H.; Bergdorf, M.
  • Journal of Computational Physics, Vol. 215, Issue 2
  • DOI: 10.1016/j.jcp.2005.11.017

MOLECULAR DYNAMICS COMES OF AGE: 320 BILLION ATOM SIMULATION ON BlueGene/L
journal, December 2006

  • Kadau, Kai; Germann, Timothy C.; Lomdahl, Peter S.
  • International Journal of Modern Physics C, Vol. 17, Issue 12
  • DOI: 10.1142/S0129183106010182

Reduced-Order Multiscale-Multiphysics Model for Heterogeneous Materials
journal, January 2014

Mixed Atomistic and Continuum Models of Deformation in Solids †
journal, January 1996

  • Tadmor, E. B.; Phillips, Rob; Ortiz, M.
  • Langmuir, Vol. 12, Issue 19
  • DOI: 10.1021/la9508912

Computational homogenization for heterogeneous thin sheets
journal, August 2010

  • Coenen, E. W. C.; Kouznetsova, V. G.; Geers, M. G. D.
  • International Journal for Numerical Methods in Engineering, Vol. 83, Issue 8-9
  • DOI: 10.1002/nme.2833

Computational homogenisation of composite plates: Consideration of the thickness change with a modified projection strategy
journal, March 2014

Patient-Specific Modeling of Cardiovascular Mechanics
journal, August 2009

Energy‐Based Coupled Elastoplastic Damage Models at Finite Strains
journal, November 1989

Reduced-Basis Approach for Homogenization beyond the Periodic Setting
journal, January 2008

  • Boyaval, Sébastien
  • Multiscale Modeling & Simulation, Vol. 7, Issue 1
  • DOI: 10.1137/070688791

Materials by numbers: Computations as tools of discovery
journal, May 2005

Nonlocal Integral Formulations of Plasticity and Damage: Survey of Progress
journal, November 2002

A reduced basis localized orthogonal decomposition
journal, August 2015

A Global Geometric Framework for Nonlinear Dimensionality Reduction
journal, December 2000

Computational homogenization analysis in finite elasticity: material and structural instabilities on the micro- and macro-scales of periodic composites and their interaction
journal, October 2002

  • Miehe, Christian; Schröder, Jörg; Becker, Martin
  • Computer Methods in Applied Mechanics and Engineering, Vol. 191, Issue 44
  • DOI: 10.1016/S0045-7825(02)00391-2

Multiscale aggregating discontinuities: A method for circumventing loss of material stability
journal, February 2008

  • Belytschko, Ted; Loehnert, Stefan; Song, Jeong-Hoon
  • International Journal for Numerical Methods in Engineering, Vol. 73, Issue 6
  • DOI: 10.1002/nme.2156

Nonuniform transformation field analysis of elastic–viscoplastic composites
journal, January 2009

Verification tests in solid mechanics
journal, November 2013

Computational Homogenization Method and Reduced Database Model for Hyperelastic Heterogeneous Structures
journal, January 2013

Quasicontinuum analysis of defects in solids
journal, June 1996

Reconstruction of random microstructures––a stochastic optimization problem
journal, September 2004

Ballistic performance of hybrid 3D woven composites: Experiments and simulations
journal, September 2015

Mature HIV-1 capsid structure by cryo-electron microscopy and all-atom molecular dynamics
journal, May 2013

  • Zhao, Gongpu; Perilla, Juan R.; Yufenyuy, Ernest L.
  • Nature, Vol. 497, Issue 7451
  • DOI: 10.1038/nature12162

Multiscale cohesive failure modeling of heterogeneous adhesives
journal, April 2008

  • Matous, K.; Kulkarni, M.; Geubelle, P.
  • Journal of the Mechanics and Physics of Solids, Vol. 56, Issue 4
  • DOI: 10.1016/j.jmps.2007.08.005

Solution of Interface Problems by Homogenization. III
journal, November 1977

  • Babuška, Ivo
  • SIAM Journal on Mathematical Analysis, Vol. 8, Issue 6
  • DOI: 10.1137/0508071

Asynchronous multi-domain variational integrators for nonlinear hyperelastic solids
journal, June 2010

  • Beneš, Michal; Matouš, Karel
  • Computer Methods in Applied Mechanics and Engineering, Vol. 199, Issue 29-32
  • DOI: 10.1016/j.cma.2010.02.017

Asymptotic homogenization analysis for damage amplification due to singular interaction of micro-cracks
journal, August 2012

  • Markenscoff, Xanthippi; Dascalu, Cristian
  • Journal of the Mechanics and Physics of Solids, Vol. 60, Issue 8
  • DOI: 10.1016/j.jmps.2012.04.004

Two-scale computational homogenization of electro-elasticity at finite strains
journal, August 2014

  • Keip, Marc-André; Steinmann, Paul; Schröder, Jörg
  • Computer Methods in Applied Mechanics and Engineering, Vol. 278
  • DOI: 10.1016/j.cma.2014.04.020

Computational homogenization of cellular materials
journal, June 2014

Multi-scale continuous–discontinuous framework for computational-homogenization–localization
journal, August 2012

  • Coenen, E. W. C.; Kouznetsova, V. G.; Geers, M. G. D.
  • Journal of the Mechanics and Physics of Solids, Vol. 60, Issue 8
  • DOI: 10.1016/j.jmps.2012.04.002

Micromechanics-based modeling of plastic polycrystals: an affine formulation
journal, June 2000

Multiscale modeling of elasto-viscoplastic polycrystals subjected to finite deformations
journal, December 2009

  • Matous, Karel; Maniatty, Antoinette M.
  • Interaction and multiscale mechanics, Vol. 2, Issue 4
  • DOI: 10.12989/imm.2009.2.4.375

Uncertainty Quantification in Multiscale Simulation of Materials: A Prospective
journal, July 2013

Nanoscale tomography in materials science
journal, December 2007

On multiscale FE analyses of heterogeneous structures: from homogenization to multigrid solvers
journal, January 2007

  • Miehe, C.; Bayreuther, C. G.
  • International Journal for Numerical Methods in Engineering, Vol. 71, Issue 10
  • DOI: 10.1002/nme.1972

Reconstruction of periodic unit cells of multimodal random particulate composites using genetic algorithms
journal, April 2008

  • Kumar, Natarajan Chennimalai; Matouš, Karel; Geubelle, Philippe H.
  • Computational Materials Science, Vol. 42, Issue 2
  • DOI: 10.1016/j.commatsci.2007.07.043

Multi-scale second-order computational homogenization of multi-phase materials: a nested finite element solution strategy
journal, December 2004

  • Kouznetsova, V. G.; Geers, M. G. D.; Brekelmans, W. A. M.
  • Computer Methods in Applied Mechanics and Engineering, Vol. 193, Issue 48-51
  • DOI: 10.1016/j.cma.2003.12.073

Computational homogenization for multiscale crack modeling. Implementational and computational aspects
journal, June 2011

  • Nguyen, Vinh Phu; Lloberas‐Valls, Oriol; Stroeven, Martijn
  • International Journal for Numerical Methods in Engineering, Vol. 89, Issue 2
  • DOI: 10.1002/nme.3237

A non-linear dimension reduction methodology for generating data-driven stochastic input models
journal, June 2008

  • Ganapathysubramanian, Baskar; Zabaras, Nicholas
  • Journal of Computational Physics, Vol. 227, Issue 13
  • DOI: 10.1016/j.jcp.2008.03.023

Computational Design of Hierarchically Structured Materials
journal, August 1997

Nonlinear Dimensionality Reduction by Locally Linear Embedding
journal, December 2000

Computational micro–macro transitions and overall moduli in the analysis of polycrystals at large strains
journal, December 1999

Studies of microstructural size effect and higher-order deformation in second-order computational homogenization
journal, December 2010

On the Size of RVE in Finite Elasticity of Random Composites
journal, August 2006

Integration of laboratory testing and constitutive modeling of soils
journal, September 2007

The determination of the elastic field of an ellipsoidal inclusion, and related problems
journal, August 1957

  • Eshelby, John Douglas
  • Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences, Vol. 241, Issue 1226, p. 376-396
  • DOI: 10.1098/rspa.1957.0133

Damage initiation and growth in metals. Comparison between modelling and tomography experiments
journal, November 2005

  • Maire, E.; Bordreuil, C.; Babout, L.
  • Journal of the Mechanics and Physics of Solids, Vol. 53, Issue 11
  • DOI: 10.1016/j.jmps.2005.06.005

Why GENERIC ?
journal, September 2010

On rigorous derivation of strain gradient effects in the overall behaviour of periodic heterogeneous media
journal, June 2000

Computational continua revisited
journal, October 2014

  • Fish, Jacob; Filonova, Vasilina; Fafalis, Dimitrios
  • International Journal for Numerical Methods in Engineering, Vol. 102, Issue 3-4
  • DOI: 10.1002/nme.4793

Size effects in indentation response of thin films at the nanoscale: A molecular dynamics study
journal, November 2008

Uncertainty Quantification and Polynomial Chaos Techniques in Computational Fluid Dynamics
journal, January 2009

Predicting Local Cell Deformations in Engineered Tissue Constructs: A Multilevel Finite Element Approach
journal, March 2002

  • Breuls, Roel G. M.; Sengers, Bram G.; Oomens, Cees W. J.
  • Journal of Biomechanical Engineering, Vol. 124, Issue 2
  • DOI: 10.1115/1.1449492

Conceptual Density Functional Theory
journal, May 2003

  • Geerlings, P.; De Proft, F.; Langenaeker, W.
  • Chemical Reviews, Vol. 103, Issue 5
  • DOI: 10.1021/cr990029p

Computational homogenization of coupled consolidation problems in micro‐heterogeneous porous media
journal, June 2011

  • Su, Fang; Larsson, Fredrik; Runesson, Kenneth
  • International Journal for Numerical Methods in Engineering, Vol. 88, Issue 11
  • DOI: 10.1002/nme.3221

Overall potentials and extremal surfaces of power law or ideally plastic composites
journal, June 1993

A multiscale framework for localizing microstructures towards the onset of macroscopic discontinuity
journal, February 2014

Laplacian Eigenmaps for Dimensionality Reduction and Data Representation
journal, June 2003

Computational homogenization of liquid-phase sintering with seamless transition from macroscopic compressibility to incompressibility
journal, November 2013

  • Öhman, Mikael; Larsson, Fredrik; Runesson, Kenneth
  • Computer Methods in Applied Mechanics and Engineering, Vol. 266
  • DOI: 10.1016/j.cma.2013.07.006

DFT in a nutshell
journal, July 2012

  • Burke, Kieron; Wagner, Lucas O.
  • International Journal of Quantum Chemistry, Vol. 113, Issue 2
  • DOI: 10.1002/qua.24259

Homogenization of locally resonant acoustic metamaterials towards an emergent enriched continuum
journal, February 2016

Multi-scale experimental analysis of rate dependent metal–elastomer interface mechanics
journal, July 2015

  • Neggers, J.; Hoefnagels, J. P. M.; van der Sluis, O.
  • Journal of the Mechanics and Physics of Solids, Vol. 80
  • DOI: 10.1016/j.jmps.2015.04.005

A numerical investigation of the effect of particle clustering on the mechanical properties of composites
journal, May 2003

Elastic properties of reinforced solids: Some theoretical principles
journal, September 1963

Prediction of the mechanical behavior of nonlinear heterogeneous systems by multi-level finite element modeling
journal, March 1998

  • Smit, R. J. M.; Brekelmans, W. A. M.; Meijer, H. E. H.
  • Computer Methods in Applied Mechanics and Engineering, Vol. 155, Issue 1-2
  • DOI: 10.1016/S0045-7825(97)00139-4

Characterization and simulation of microstructure and properties of EPS lightweight concrete
journal, December 2007

A variational multiscale approach to strain localization – formulation for multidimensional problems
journal, July 2000

Study of efficient homogenization algorithms for nonlinear problems
journal, October 2009

Upper and lower bounds for non-linear composite behaviour
journal, February 1994

A multiscale projection method for macro/microcrack simulations
journal, January 2007

  • Loehnert, Stefan; Belytschko, Ted
  • International Journal for Numerical Methods in Engineering, Vol. 71, Issue 12
  • DOI: 10.1002/nme.2001

Boundary condition effects on multiscale analysis of damage localization
journal, June 2008

  • Inglis, Helen M.; Geubelle, Philippe H.; Matouš, Karel
  • Philosophical Magazine, Vol. 88, Issue 16
  • DOI: 10.1080/14786430802345645

A Theorem on the Conductivity of a Composite Medium
journal, April 1964

  • Keller, Joseph B.
  • Journal of Mathematical Physics, Vol. 5, Issue 4
  • DOI: 10.1063/1.1704146

On continuum damage-elastoplasticity at finite strains
journal, January 1989

Experimental study of the compression behaviour of syntactic foams by in situ X-ray tomography
journal, March 2007

Computational homogenization of diffusion in three-phase mesoscale concrete
journal, March 2014

  • Nilenius, Filip; Larsson, Fredrik; Lundgren, Karin
  • Computational Mechanics, Vol. 54, Issue 2
  • DOI: 10.1007/s00466-014-0998-0

Computational continua
journal, October 2010

  • Fish, Jacob; Kuznetsov, Sergey
  • International Journal for Numerical Methods in Engineering, Vol. 84, Issue 7
  • DOI: 10.1002/nme.2918

Zur plastischen verformung des vielkristalls
journal, February 1961

    Sort by:
    [ × clear filter / sort ]

    Works referencing / citing this record:

    Integration efficiency for model reduction in micro-mechanical analyses
    journal, November 2017

    • van Tuijl, Rody A.; Remmers, Joris J. C.; Geers, Marc G. D.
    • Computational Mechanics, Vol. 62, Issue 2
    • DOI: 10.1007/s00466-017-1490-4

    Computational Methods for Ductile Fracture Modeling at the Microscale
    journal, September 2018

    • Shakoor, Modesar; Trejo Navas, Victor Manuel; Pino Munõz, Daniel
    • Archives of Computational Methods in Engineering, Vol. 26, Issue 4
    • DOI: 10.1007/s11831-018-9276-1

    Predicting the mechanical response of oligocrystals with deep learning
    journal, November 2019

    Two-scale constitutive modeling of a lattice core sandwich beam
    journal, March 2019

    Wang tiling aided statistical determination of the Representative Volume Element size of random heterogeneous materials
    journal, July 2018

    Sharp volumetric billboard based characterization and modeling of complex 3D Ni/Al high energy ball milled composites
    journal, May 2017

    $${\text {FE}}^r$$ method with surrogate localization model for hyperelastic composite materials
    journal, October 2020

    • Hatano, Ryo; Matsubara, Seishiro; Moriguchi, Shuji
    • Advanced Modeling and Simulation in Engineering Sciences, Vol. 7, Issue 1
    • DOI: 10.1186/s40323-020-00175-0

    Level-set based design of Wang tiles for modelling complex microstructures
    text, January 2019

    Manifold embedding data-driven mechanics
    journal, May 2022

    • Bahmani, Bahador; Sun, Waicheng
    • Journal of the Mechanics and Physics Solids
    • DOI: 10.7916/a769-zw09
      Sort by:
      [ × clear filter / sort ]

      Similar Records in DOE PAGES and OSTI.GOV collections: