Homogenization of an elastic medium reinforced by anisotropic fibers

Abstract

We study the homogenization of an elastic medium periodically reinforced by thin anisotropic elastic fibers, the radius of the fibers being of the order of the size ε of the period, while 1/ε² is the ratio between the coefficients of the tensor inside the fibers with those of the tensor outside them. In this case, the sequence u^ε of the displacements is not apriori bounded in (L²(Ω))³. We prove that the homogenized problem is a strongly coupled nonlocal problem which involves variables due to the anisotropy of the fibers.