A REMARK ON THE HOMOGENIZATION OF A MICROFIBERED LINEARLY ELASTIC MATERIAL

摘要

We consider the homogenization of a linearly elliptic boundary value problem of elasticity. The isotropic elastic material is reinforced by a periodic distribution of very thin parallel fibers in which the Lame coeffi-cients 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 con-vergence of the energy functional.