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A multilevel finite element method (FE2) to describe the response of highly non-linear structures using generalized continua
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This article is published in Computer Methods in Applied Mechanics and Engineering.The article was published on 2003-07-18. It has received 480 citations till now. The article focuses on the topics: Mixed finite element method & Extended finite element method.read more
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Multiscale Methods for Composites: A Review
TL;DR: In this article, a review of multiscale methods for modeling mechanical and thermomechanical responses of composites is presented, both at the material level and at the structural analysis level.
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A framework for data-driven analysis of materials under uncertainty: Countering the curse of dimensionality
Miguel A. Bessa,Miguel A. Bessa,Ramin Bostanabad,Zeliang Liu,A. Hu,Daniel W. Apley,Catherine Brinson,Wei Chen,Wing Kam Liu +8 more
TL;DR: A new data-driven computational framework is developed to assist in the design and modeling of new material systems and structures and includes the recently developed “self-consistent clustering analysis” method in order to build large databases suitable for machine learning.
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Self-consistent clustering analysis: An efficient multi-scale scheme for inelastic heterogeneous materials
TL;DR: A mechanistic, data-driven, two-scale approach is developed for predicting the behavior of general heterogeneous materials under irreversible processes such as inelastic deformation and is believed to open new avenues in parameter-free multi-scale modeling of complex materials, and perhaps in other fields that require homogenization of irreversible processes.
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Computational microstructure characterization and reconstruction: Review of the state-of-the-art techniques
Ramin Bostanabad,Yichi Zhang,Xiaolin Li,Tucker Kearney,L. Catherine Brinson,Daniel W. Apley,Wing Kam Liu,Wei Chen +7 more
TL;DR: A comprehensive review of representative approaches for MCR and elaborate on their algorithmic details, computational costs, and how they fit into the PSP mapping problems is provided.
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The reduced model multiscale method (R3M) for the non-linear homogenization of hyperelastic media at finite strains
Julien Yvonnet,Qi-Chang He +1 more
TL;DR: A new multi-scale method for the homogenization analysis of hyperelastic solids undergoing finite strains, coined as reduced model multiscale method (R3M), allows reducing significantly the computation times, as no large matrix needs to be inverted and as the convergence of both macro and micro problems is enhanced.
References
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Elastic materials with couple-stresses
TL;DR: HAL as discussed by the authors is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not, which may come from teaching and research institutions in France or abroad, or from public or private research centers.
Théorie des corps déformables
TL;DR: Cosserat and Hermann as mentioned in this paper discussed the kinematical and dynamical theories of the flexible line, the flexible surface, and the deformable three-dimensional medium in great detail.
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On first strain-gradient theories in linear elasticity
Raymond D. Mindlin,N.N. Eshel +1 more
TL;DR: In this paper, a study of the linear theory of elasticity in which the potential energy-density depends on the gradient of the strain in addition to the strain was performed, and the relations connecting the stresses in the three forms and the boundary conditions in three forms were derived.
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A numerical method for computing the overall response of nonlinear composites with complex microstructure
Hervé Moulinec,Pierre Suquet +1 more
TL;DR: An alternate method based on Fourier series which avoids meshing and which makes direct use of microstructure images is proposed, based on the exact expression of the Green function of a linear elastic and homogeneous comparison material.
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Preprocessing and postprocessing for materials based on the homogenization method with adaptive finite element methods
José M. Guedes,Noboru Kikuchi +1 more
TL;DR: In this paper, the effective average elastic constants of linear elasticity of general composite materials by considering their microstructure were determined using the homogenization method, and a finite element approximation was introduced with convergence study and corresponding error estimate.