Calculus of Variations and Geometric Measure Theory
home | mail | papers | authors | news | seminars | events | open positions | login

G. Lazzaroni - R. Rossi - M. Thomas - R. Toader

Rate-independent damage in thermo-viscoelastic materials with inertia

created by lazzaroni on 14 Oct 2014
modified on 22 Oct 2014

[BibTeX]

Preprint

Inserted: 14 oct 2014
Last Updated: 22 oct 2014

Year: 2014
Notes:

Preprint SISSA 52$/$2014$/$MATE

WIAS-Preprint 2025


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.

Keywords: elastodynamics, Heat equation, rate-independent systems, energetic solutions, Partial damage, Phase-field models, Local solutions


Download:

Credits | Cookie policy | HTML 4.0.1 strict | CSS 2.1