The Membrane Shell Model in Nonlinear Elasticity

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

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