Abstract
We present some mathematical convergence results using a two-scale method for a linearelastic isotropic medium containing one layer of parallel periodically distributed heterogeneities locatedin the interior of the whole domain around a plane surface \Sigma. The aim of this paper is to study thesituation when the rigidity of the linearly isotropic elastic fibres is 1/ \epsilon ^ m the rigidity of the surroundinglinearly isotropic elastic material. We use a two-scale convergence method adapted to the geometry of theproblem (layer of fibres). In the models obtained \Sigma behaves for m = 1 as a "material surface" withoutmembrane energy in the direction of the plane orthogonal to the direction of the fibres. For m = 3 the"material surface" has no bending energy in the direction orthogonal to the fibres.