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

摘要

We consider a cylindrical three-dimensional nonlinearly hyperelastic body and we let ill thickness go to zero. We show, under appropriate hypotheses on the applied toads, that the deformations that minimize the total energy weakly converge in a Sobolev space toward deformations that minimize a nonlinear membrane energy. The nonlinear membrane energy is obtained by computing the f-limit of the sequence of three-dimensional energies.