Asymptotic Analysis of a Linear Isotropic Elastic Composite Reinforced by a Thin Layer of Periodically Distributed Isotropic Parallel Stiff Fibres

We present some mathematical convergence results using a two-scale method for a linear elastic isotropic medium containing one layer of parallel periodically distributed heterogeneities located in the interior of the whole domain around a plane surface Σ. The aim of this paper is to study the situation when the rigidity of the linearly isotropic elastic fibres is 1/εm the rigidity of the surrounding linearly isotropic elastic material. We use a two-scale convergence method adapted to the geometry of the problem (layer of fibres). In the models obtained Σ behaves for m=1 as a “material surface” without membrane 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.

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