  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.
