The effective equilibrium law for a highly heterogeneous elastic periodic medium

Abstract

We study the homogenization of the linearized system of elasticity standing for the equilibrium equation of a highly periodic heterogeneous elastic medium submitted to small deformations and made of two different materials: a very rigid material located in a set Fε (ε being the size of the period of the medium) of vertical fibres surrounded by a soft elastic material localized in the set Mε. The ratio between the coefficients of the elasticity tensor of the two materials is assumed to be 1/ε4. We deal with the general case without any special assumption, such as isotropy, on the material.