In this paper, we prove a new existence result for a variational model of crack growth in brittle materials in the case of n-dimensional nonlinear elasticity, with a quasiconvex bulk energy and with prescribed boundary deformations and applied loads, both depending on time
We present a model for rate-independent, unidirectional, partial damage in visco-elastic materials with inertia and thermal effects. The damage process is modeled by means of an internal variable, governed by a rate-independent flow rule. The heat equation and the momentum balance for the displacements are coupled in a highly nonlinear way. Our assumptions on the corresponding energy functional also comprise the case of the Ambrosio-Tortorelli phase-field model (without passage to the brittle limit). We discuss a suitable weak formulation and prove an existence theorem obtained with the aid of a (partially) decoupled time-discrete scheme and variational convergence methods. We also carry out the asymptotic analysis for vanishing viscosity and inertia and obtain a fully rate-independent limit model for displacements and damage, which is independent of temperature.2010 MSC: 35Q74, 74H20, 74R05, 74C05, 74F05,
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