Asymptotic analysis of a linear isotropic elastic composite reinforced by a thin layer of periodically distributed isotropic parallel stiff fibres.
Résumé
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 \Sigma. The aim of this paper is to study the
situation when the rigidity of the linearly isotropic elastic fibres is 1/ \epsilon ^ m 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 \Sigma 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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