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Spatial heterogeneity in 3D-2D dimensional reduction

Jean-Francois Babadjian·Gilles A. Francfort
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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 & 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 $Γ$-convergence of the elastic energy, as the thickness tends to zero.

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Jean-Francois Babadjian, Gilles A. Francfort. 2006-04-26. Spatial heterogeneity in 3D-2D dimensional reduction. https://arxiv.org/abs/math/0604556

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