Special Session 126: Defects, Microstructures, and Failure: Multiscale Variational Models

Dimension reduction in dynamical continuum mechanics
Riccardo Voso
UTIA, Czech Academy of Sciences
Czech Rep
Co-Author(s):    Martin Kruzik
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.