Loss of polyconvexity by homogenization: a new example

Details Loss of polyconvexity by homogenization: a new example Loss of polyconvexity by homogenization: a new example

2006-03-30

arxiv.org/abs/math/0603711v1

Mathematics

Analysis of PDEs

12 pages, 1 figure

Scientific paper

This article is devoted to the study of the asymptotic behavior of the zero-energy deformations set of a periodic nonlinear composite material. We approach the problem using two-scale Young measures. We apply our analysis to show that polyconvex energies are not closed with respect to periodic homogenization. The counterexample is obtained through a rank-one laminated structure assembled by mixing two polyconvex functions with $p$-growth, where $p\geq2$ can be fixed arbitrarily.

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