On the Justification of the Nonlinear Inextensional Plate Model

We consider a cylindrical three-dimensional body, made of a Saint Venant-Kirchhoff material, and we let its thickness go to zero. For a specific order of magnitude for the applied loads and under appropriate restrictions on the set of admissible deformations, we show that the almost-minimizers of the total energy converge toward deformations that minimize the nonlinear bending energy obtained by Fox, Raoult and Simo using formal asymptotic expansions. Our result is obtained by Γ-convergence arguments.