Loss of polyconvexity by homogenization: a new example
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.
Calc. Var. Partial Differential Equations 30 (2007) 215-230