Numerical approximation for a non-linear membrane problem

We present a numerical study of large deformations of non-linearly elastic membranes. We consider the non-linear membrane model obtained by Le Dret and Raoult using ΓΓ-convergence, in the case of a Saint Venant-Kirchhoff bulk material. We consider conforming P1P1 and Q1Q1 finite element approximations of the membrane problem and use a non-linear conjugate gradient algorithm to minimize the discrete energy. We present numerical tests including membranes subjected to live pressure loads.