Geodesic
Spatial heterogeneity in 3D-2D dimensional reduction
ESAIM: Control, Optimisation and Calculus of Variations, Tome 11 (2005) no. 1, pp. 139-160

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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.

DOI : 10.1051/cocv:2004031
Classification : 49J45, 74B20, 74G65, 74K15, 74K35
Keywords: dimension reduction, $\Gamma $-convergence, equi-integrability, quasiconvexity, relaxation 
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     title = {Spatial heterogeneity in {3D-2D} dimensional reduction},
     journal = {ESAIM: Control, Optimisation and Calculus of Variations},
     pages = {139--160},
     publisher = {EDP-Sciences},
     volume = {11},
     number = {1},
     year = {2005},
     doi = {10.1051/cocv:2004031},
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     zbl = {1085.49015},
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Babadjian, Jean-François; Francfort, Gilles A. Spatial heterogeneity in 3D-2D dimensional reduction. ESAIM: Control, Optimisation and Calculus of Variations, Tome 11 (2005) no. 1, pp. 139-160. doi: 10.1051/cocv:2004031

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