THE NONLINEAR MEMBRANE MODEL AS VARIATIONAL LIMIT OF NONLINEAR 3-DIMENSIONAL ELASTICITY

We consider a cylindrical three-dimensional nonlinearly hyperelastic b ody and we let its thickness go to zero. We show, under appropriate hy potheses on the applied loads, that the deformations that minimize the total energy weakly converge in a Sobolev space toward deformations t hat minimize a nonlinear membrane energy. The nonlinear membrane energ y is obtained by computing the Gamma-limit of the sequence of three-di mensional energies.