| Abstract: |
| In this talk, we discuss the derivation of a membrane model for hyper viscoelastic materials with inertia, starting from the full three-dimensional theory. At first, the hyperbolic minimizing movements scheme is introduced. This is a two time scale variational approximation which accounts for the reformulation of the problem in terms of incremental minimization of a energy-dissipation functional, where inertia is discretized in time. Within this framework, the asymptotic analysis as the thickness of the body vanishes is carried out via a $\Gamma$ convergence argument at the level of the functional and, subsequently, the continuous in time dynamics is recovered. |
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