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.

Full text not available from this repository.

Official URL: https://doi.org/10.1007/s10884-018-9666-y

## Abstract

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 |

Repository Staff Only: item control page