Derivation of a homogenized nonlinear plate theory from 3d elasticity

Peter Hornung, Stefan Neukamm, Igor Velcic

Published 2012-10-19, updated 2012-10-22Version 2

We derive, via simultaneous homogenization and dimension reduction, the Gamma-limit for thin elastic plates whose energy density oscillates on a scale that is either comparable to, or much smaller than, the film thickness. We consider the energy scaling that corresponds to Kirchhoff's nonlinear bending theory of plates.