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.
CITATION STYLE
Lazzaroni, G., Rossi, R., Thomas, M., & Toader, R. (2018). Rate-Independent Damage in Thermo-Viscoelastic Materials with Inertia. Journal of Dynamics and Differential Equations, 30(3), 1311–1364. https://doi.org/10.1007/s10884-018-9666-y
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