General homogenization of bending theory for plates from 3D elasticity; the case of elastic laminates

Maroje Marohnic, Igor Velcic

Published 2014-09-30Version 1

In this paper we study the homogenization effects on the model of elastic plate in the bending regime, under the assumption that the energy density (material) oscillates in the thickness direction on the scale smaller than the thickness. We study two different cases. First we show, starting from 3D elasticity, by means of $\Gamma$-convergence and under general (not necessarily periodic) assumption that the effective behavior of the limit is not influenced by the fast oscillations in the thickness direction. In the second case we study the periodic in-plane oscillations of the energy density coupled with the periodic oscillations in the thickness direction. In contrast to the first case we show that there are homogenization effects coming also from the oscillations in the thickness direction.