Asymptotic analysis of a linear isotropic elastic composite reinforced by a thin layer of periodically distributed isotropic parallel stiff fibres. - Archive ouverte HAL
Article Dans Une Revue Journal of Elasticity Année : 2016

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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Dates et versions

hal-01121260 , version 1 (27-02-2015)

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Michel Bellieud, Giuseppe Geymonat, Françoise Krasucki. Asymptotic analysis of a linear isotropic elastic composite reinforced by a thin layer of periodically distributed isotropic parallel stiff fibres.. Journal of Elasticity, 2016, 122, pp.43-74. ⟨10.1007/s10659-015-9532-7⟩. ⟨hal-01121260⟩
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