Spatial heterogeneity in 3D-2D dimensional reduction

Details Spatial heterogeneity in 3D-2D dimensional reduction Spatial heterogeneity in 3D-2D dimensional reduction

2006-04-26

arxiv.org/abs/math/0604556v1

ESAIM: Cont. Opt. Calc. Var., 11 (2005) No. 1, 139-160

Mathematics

Analysis of PDEs

22 pages

Scientific paper

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 Bouchitt\'e, 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.

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