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Spatial heterogeneity in 3D-2D dimensional reduction

Published online by Cambridge University Press:  15 December 2004

Jean-François Babadjian  and
Gilles A. Francfort
Jean-François Babadjian
Affiliation:
LPMTM, Institut Galilée, Université Paris-Nord, 93430 Villetaneuse, France; jfb@galilee.univ-paris13.fr; francfor@galilee.univ-paris13.fr
Gilles A. Francfort
Affiliation:
LPMTM, Institut Galilée, Université Paris-Nord, 93430 Villetaneuse, France; jfb@galilee.univ-paris13.fr; francfor@galilee.univ-paris13.fr
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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 (1995). Specific characterizations of the 2D elastic energy are produced. As a generalization of Bouchitté et al. (2002), 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 Γ-convergence of the elastic energy, as the thickness tends to zero.

Keywords

Dimension reductionΓ-convergenceequi-integrabilityquasiconvexityrelaxation.
Type
Research Article
Information
ESAIM: Control, Optimisation and Calculus of Variations , Volume 11 , Issue 1 , January 2005 , pp. 139 - 160
Copyright
© EDP Sciences, SMAI, 2005

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