Loss of polyconvexity by homogenization
type: Item
instance of: scholarly article
title: Loss of polyconvexity by homogenization
zbMATH Open document ID: 0811.73005
DOI: 10.1007/BF00377660
author: Andrea Braides
published in: Archive for Rational Mechanics and Analysis
publication date: 1994-11-14T00:00:00Z
review text: The study of the effective properties of composite or cellular elastic materials requires the description of the asymptotic behavior as \(n\) tends to \(+ \infty\) of variational integrals of the form \({\mathcal F}_ n(u) = \int_ \Omega W(nx, Du(x))dx\), where \(Du\) denotes the gradient matrix of the displacement \(u\), and \(W\) is an energy density characterizing the microscopic properties of the elastic body. In this paper we show with an explicit example that the variational limit of a sequence of oscillating functionals of the form \({\mathcal F}_ n\) as above, with \(W(x,\cdot)\) polyconvex for all \(x\), is in general a variational integral \({\mathcal F}_{\text{hom}} (u) = \int_ \Omega W_{\text{hom}}(Du(x)) dx\), with \(W_{\text{hom}}\) quasiconvex but not polyconvex.
Mathematics Subject Classification ID: 74E05
Mathematics Subject Classification ID: 74E30
Mathematics Subject Classification ID: 74S30
Mathematics Subject Classification ID: 74P10
zbMATH DE Number: 687669
zbMATH Keywords: effective properties
zbMATH Keywords: cellular elastic materials
zbMATH Keywords: asymptotic behavior
zbMATH Keywords: energy density
zbMATH Keywords: variational integral
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 687669