The Cosserat Vector in Membrane Theory: a Variational Approach

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.