Remarks on homogenization and $3D$-$2D$ dimension reduction of unbounded energies on thin films

Abstract

We study periodic homogenization and $3D$-$2D$ dimension reduction by $\Gamma (\pi )$-con-vergence of heterogeneous thin films whose the stored-energy densities have no polynomial growth. In particular, our results are consistent with one of the basic facts of nonlinear elasticity, namely the necessity of an infinite amount of energy to compress a finite volume of matter into zero volume. However, our results are not consistent with the noninterpenetration of the matter.