Variational Convergences of Dual Energy Functionals for Elastic Materials with a ε-Thin Strong Inclusion

Abstract

We give a new derivation, based on the complementary energy formulation, of a simplified model for a multi-structure made up of two anisotropic hyper-elastic bodies connected by a thin strong material layer. The model is obtained by identifying the Mosco-limit of the stored complementary energy functional when the thickness is of order e and the stiffness of order 1/e where e is a positive real adimensional parameter. In order to prove the existence of the displacement associated with the stress we use a suitable weak version of the Saint-Venant compatibility condition also known as Donati’s theorem.