The nonlinear membrane model as variational limit of nonlinear three-dimensional elasticity. (English) Zbl 0847.73025

Summary: We consider a cylindrical 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 membrane energy. The nonlinear membrane energy is obtained by computing the \(\Gamma\)-limit of the sequence of three-dimensional energies.


74K20 Plates
74B20 Nonlinear elasticity
74S30 Other numerical methods in solid mechanics (MSC2010)
74P10 Optimization of other properties in solid mechanics