Journal ArticleDOI
On the Size of RVE in Finite Elasticity of Random Composites
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In this article, a quantitative study of the size of representative volume element (RVE) of random matrix-inclusion composites based on a scale-dependent homogenization method is presented.Abstract:
This paper presents a quantitative study of the size of representative volume element (RVE) of random matrix-inclusion composites based on a scale-dependent homogenization method. In particular, mesoscale bounds defined under essential or natural boundary conditions are computed for several nonlinear elastic, planar composites, in which the matrix and inclusions differ not only in their material parameters but also in their strain energy function representations. Various combinations of matrix and inclusion phases described by either neo-Hookean or Ogden function are examined, and these are compared to those of linear elastic types.read more
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Mechanical behavior of unidirectional fiber-reinforced polymers under transverse compression: Microscopic mechanisms and modeling
Carlos González,Javier LLorca +1 more
TL;DR: In this paper, the mechanical behavior of polymer-matrix composites unidirectionally reinforced with carbon or glass fibers subjected to compression perpendicular to the fibers was studied using computational micromechanics using finite element analysis of a representative volume element of the microstructure idealized as a random dispersion of parallel fibers embedded in the polymeric matrix.
Journal ArticleDOI
A review of predictive nonlinear theories for multiscale modeling of heterogeneous materials
TL;DR: 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 is discussed that can be the basis of Virtual Materials Testing standards and aids in the development of new material formulations.
Journal ArticleDOI
Generation of 3D representative volume elements for heterogeneous materials: a review
Swantje Bargmann,Benjamin Klusemann,Benjamin Klusemann,Jürgen Markmann,Jürgen Markmann,Jan Eike Schnabel,Konrad Schneider,Celal Soyarslan,Jana Wilmers +8 more
TL;DR: In this paper, the authors present a systematic classification of representative volume element (RVE) generation techniques for heterogeneous materials, and divide heterogeneous solids into porous and non-porous media.
Journal ArticleDOI
Aspects of Computational Homogenization at Finite Deformations: A Unifying Review From Reuss' to Voigt's Bound
TL;DR: This contribution is to present a unifying review on strain-driven computational homogenization at finite strains, thereby elaborating on computational aspects of the finite element method.
Reference EntryDOI
Homogenization methods and multiscale modeling : Nonlinear problems
TL;DR: The two‐scale nonlinear computational homogenization (CH) scheme for mechanics is presented, along with details on representative unit cell aspects and statistics, and model performance is advocated through a decoupled implementation and multiscale schemes based on the nonuniform transformation field analysis.
References
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Journal ArticleDOI
A variational approach to the theory of the elastic behaviour of multiphase materials
Zvi Hashin,S. Shtrikman +1 more
TL;DR: In this paper, the authors derived upper and lower bounds for the effective elastic moduli of quasi-isotropic and quasi-homogeneous multiphase materials of arbitrary phase geometry.
Book
Non-Linear Elastic Deformations
TL;DR: In this paper, the influence of non-linear elastic systems on a simple geometric model for elastic deformations is discussed, and the authors propose a planar and spatial euler introduction to nonlinear analysis.
Book
Random Heterogeneous Materials: Microstructure and Macroscopic Properties
Salvatore Torquato,HW Haslach +1 more
TL;DR: In this article, a unified approach for the characterization of 2-dimensional (2-3D) moduli is presented. But the approach is not suitable for 3-dimensional moduli.
Journal ArticleDOI
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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