Résumé
We consider the homogenization of a linear elliptic boundary value problem of elasticity. The isotropic elastic material is reinforced by a periodic distribution of very thin parallel fibers in which the Lamé coefficients are assumed to have high values. Bellieud and Gruais proved that the macroscopic behavior is the one of a generalized continuum medium involving an additional state variable accounting for the microstructure. Here we propose a proof of this result by studying the variational convergence of the energy functional.