Computational homogenization of nonlinear elastic materials using neural networks

Summary In this work, a decoupled computational homogenization method for nonlinear elastic materials is proposed using neural networks. In this method, the effective potential is represented as a response surface parameterized by the macroscopic strains and some microstructural parameters. The disc...

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Vydáno v:International journal for numerical methods in engineering Ročník 104; číslo 12; s. 1061 - 1084
Hlavní autoři: Le, B. A., Yvonnet, J., He, Q.-C.
Médium: Journal Article
Jazyk:angličtina
Vydáno: Bognor Regis Blackwell Publishing Ltd 21.12.2015
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Témata:
Computation
computational homogenization
high-dimensional approximation
Homogenization
Homogenizing
Mathematical analysis
Mathematical models
Microstructure
multiscale methods
Neural networks
nonlinear homogenization
Nonlinearity
ISSN:0029-5981, 1097-0207
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Shrnutí:Summary In this work, a decoupled computational homogenization method for nonlinear elastic materials is proposed using neural networks. In this method, the effective potential is represented as a response surface parameterized by the macroscopic strains and some microstructural parameters. The discrete values of the effective potential are computed by finite element method through random sampling in the parameter space, and neural networks are used to approximate the surface response and to derive the macroscopic stress and tangent tensor components. We show through several numerical convergence analyses that smooth functions can be efficiently evaluated in parameter spaces with dimension up to 10, allowing to consider three‐dimensional representative volume elements and an explicit dependence of the effective behavior on microstructural parameters like volume fraction. We present several applications of this technique to the homogenization of nonlinear elastic composites, involving a two‐scale example of heterogeneous structure with graded nonlinear properties. Copyright © 2015 John Wiley & Sons, Ltd.
Bibliografie:Institut Universitaire de France (IUF)
istex:58AFE0E33105FC574380143043389CA3800422C9
ark:/67375/WNG-24T0JNKH-D
ArticleID:NME4953
Publishing Arts Research Council
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ISSN:0029-5981
1097-0207
DOI:10.1002/nme.4953