Homogenization of two-dimensional elasticity problems with very stiff coefficients

International audienceIn this paper we study the asymptotic behaviour of a sequence of two-dimensional linear elasticity problems with equicoercive elasticity tensors. Assuming the sequence of tensors is bounded in L^1, we obtain a compactness result extending to the elasticity the div-curl approach of [12] for the conduction. In the periodic case this compactness result is refined replacing the L^1-boundedness by a less restrictive condition involving the oscillations period. We also build a sequence of isotropic elasticity problems with L^1-unbounded Lamé's coefficients, which converges to a second gradient limit problem. This loss of compactness shows a gap in the limit behaviour between the very stiff problems of elasticity and those of conduction. Indeed, in the conduction case a compactness result was proved in [13] without assuming any bound from above for the conductivities