Repository: Freie Universität Berlin, Math Department

Rate-independent damage in thermoviscoelastic materials with inertia

Lazzaroni, Guiliano and Rossi, Riccarda and Thomas, Marita and Toader, Rodica (2018) Rate-independent damage in thermoviscoelastic materials with inertia. J Dyn Diff Equat, 30 . pp. 1311-1364.

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Abstract 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.

Item Type:Article
Additional Information:Published online 2018 J Dyn Diff Equat (2018) 30:1311–1364
Subjects:Mathematical and Computer Sciences > Mathematics > Applied Mathematics
Divisions:Department of Mathematics and Computer Science > Institute of Mathematics
ID Code:2722
Deposited By: Monika Drueck
Deposited On:15 Feb 2022 15:30
Last Modified:15 Feb 2022 15:30

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