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

作者：Bellieud Michel; Geymonat Giuseppe; Krasucki Francoise^*

来源：Journal of Elasticity, 2016, 122(1): 43-74.

DOI：10.1007/s10659-015-9532-7

• Linear elasticity
• Fibres reinforced structures
• Two-scale convergence
• Homogenization

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 I pound. 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 I pound 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.

• 出版日期2016-1