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Loss of polyconvexity by homogenization: a new example

Marco Barchiesi
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Abstract

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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Marco Barchiesi. 2006-03-30. Loss of polyconvexity by homogenization: a new example. https://arxiv.org/abs/math/0603711

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