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Journal Articles ESAIM: Control, Optimisation and Calculus of Variations Year : 2005

Spatial heterogeneity in 3D-2D dimensional reduction

Abstract

A justification of heterogeneous membrane models as zero-thickness limits of a cylindral three-dimensional heterogeneous nonlinear hyperelastic body is proposed in the spirit of Le Dret & Raoult. Specific characterizations of the 2D elastic energy are produced. As a generalization of Bouchitté, Fonseca & Mascarenhas, the case where external loads induce a density of bending moment that produces a Cosserat vector field is also investigated. Throughout, the 3D-2D dimensional reduction is viewed as a problem of $\Gamma$-convergence of the elastic energy, as the thickness tends to zero.

Dates and versions

hal-00265686 , version 1 (19-03-2008)

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Jean-François Babadjian, Gilles A. Francfort. Spatial heterogeneity in 3D-2D dimensional reduction. ESAIM: Control, Optimisation and Calculus of Variations, 2005, 11 (1), pp.139-160. ⟨10.1051/cocv:2004031⟩. ⟨hal-00265686⟩
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