| Issue |
ESAIM: COCV
Volume 11, Number 1, January 2005
|
|
|---|---|---|
| Page(s) | 139 - 160 | |
| DOI | https://doi.org/10.1051/cocv:2004031 | |
| Published online | 15 December 2004 | |
Spatial heterogeneity in 3D-2D dimensional reduction
LPMTM, Institut Galilée, Université Paris-Nord,
93430 Villetaneuse, France; jfb@galilee.univ-paris13.fr; francfor@galilee.univ-paris13.fr
Received:
15
October
2003
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.
Mathematics Subject Classification: 49J45 / 74B20 / 74G65 / 74K15 / 74K35
Key words: Dimension reduction / Γ-convergence / equi-integrability / quasiconvexity / relaxation.
© EDP Sciences, SMAI, 2005
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