Spatial heterogeneity in 3D-2D dimensional reduction
LPMTM, Institut Galilée, Université Paris-Nord,
93430 Villetaneuse, France; email@example.com; firstname.lastname@example.org
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