Spatial Heterogeneity in 3d-2d Dimensional Reduction

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. Received October 15, 2003.