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...
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 (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 -convergence...
Homogenization of integral functionals is studied
under the constraint that admissible maps have to take their values
into a given smooth manifold. The notion of tangential
homogenization is defined by analogy with the tangential
quasiconvexity introduced by Dacorogna [ (1999) 185–206]. For energies with superlinear or linear growth, a
-convergence result is established in Sobolev spaces, the
homogenization problem in the space of functions of bounded
variation being the object of [Babadjian...
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