Loss of polyconvexity by homogenization: a new example
Marco Barchiesi
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≥2 can be fixed arbitrarily.
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