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Journal Articles Annales de l'Institut Henri Poincaré C, Analyse non linéaire Year : 2009

A variational approach to the local character of G-closure: the convex case

Abstract

This article is devoted to characterize all possible effective behaviors of composite materials by means of periodic homogenization. This is known as a $G$-closure problem. Under convexity and $p$-growth conditions ($p>1$), it is proved that all such possible effective energy densities obtained by a $\Gamma$-convergence analysis, can be locally recovered by the pointwise limit of a sequence of periodic homogenized energy densities with prescribed volume fractions. A weaker locality result is also provided without any kind of convexity assumption and the zero level set of effective energy densities is characterized in terms of Young measures. A similar result is given for cell integrands which enables to propose new counter-examples to the validity of the cell formula in the nonconvex case and to the continuity of the determinant with respect to the two-scale convergence.

Dates and versions

hal-00265694 , version 1 (19-03-2008)

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Cite

Jean-François Babadjian, Marco Barchiesi. A variational approach to the local character of G-closure: the convex case. Annales de l'Institut Henri Poincaré C, Analyse non linéaire, 2009, 26 (2), pp.351-373. ⟨10.1016/j.anihpc.2007.08.002⟩. ⟨hal-00265694⟩

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