On the local character of $Γ$-closure for the simultaneous homogenization and dimensional reduction in elasticity

Mario Bukal, Igor Velcic

Published 2015-08-24Version 1

Starting from the three-dimensional linearized elasticity framework for composite materials we derive, by means of variational convergence, homogenized linear plate model. The main contribution is the proof of the locality property of Gamma-closure, i.e, every energy density obtained by the homogenization process can be in almost every point be obtained as the limit of in-plane periodic energy densities. The result also applies in the nonlinear elasticity for the cases of bending rod and von Karman plate.