Upper bounds for the homogenization problem in nonlinear elasticity : the incompressible case

Abstract

We consider periodic homogenization of hyperelastic models incorporating incompressible behavior via the constraint det(∇u) = 1. We show that the ’usual’ homogenized integral functional ´ Whom(∇u) dx, where Whom is the standard multicell-formula of non-convex homogenization restricted to volume preserving deformations, yields an upper bound for the -limit as the scale of periodicity tends to zero.