Geodesic
The Cosserat Vector in Membrane Theory: a Variational Approach
Journal of convex analysis, Tome 16 (2009) no. 2, pp. 351-365.

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In a previous article of the authors [J. Elasticity 73 (2004) 75--99] a model of nonlinear membrane was studied, where the external surface loading induces a density of bending moment. Due to the special form of the applied surface forces, the emerging Cosserat vector, resulting from the 3D-2D dimension reduction, was restricted to a class of two dimensional functions. In this paper the full 3D dependence of the Cosserat vector is analyzed via Γ-convergence techniques.
Classification : 35E99, 35M10, 49J45, 74B20, 74K15, 74K20, 74K35
Mots-clés : Dimension reduction, Gamma-convergence, relaxation, quasiconvexity, bending effect 
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G. Bouchitté; I. Fonseca; M. L. Mascarenhas. The Cosserat Vector in Membrane Theory: a Variational Approach. Journal of convex analysis, Tome 16 (2009) no. 2, pp. 351-365. http://geodesic.mathdoc.fr/item/JCA_2009_16_2_JCA_2009_16_2_a1/