Calculus of Variations and Geometric Measure Theory

M. Barchiesi

Loss of polyconvexity by homogenization: a new example

created by barchiesi on 15 Mar 2006
modified on 12 Jan 2012


Published Paper

Inserted: 15 mar 2006
Last Updated: 12 jan 2012

Journal: Calc. Var. Partial Differential Equations
Volume: 30
Number: 2
Pages: 215-230
Year: 2007


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.

Keywords: Homogenization, Polyconvexity, Gamma-convergence, quasiconvexity, composite materials, rank-one laminates, two-scale Young measures