Models of dynamic damage and phase-field fracture, and their various time discretisations
Analysis of PDEs
2024-09-23 v1 Numerical Analysis
Numerical Analysis
Abstract
Several variants of models of damage in viscoelastic continua under small strains in the Kelvin-Voigt rheology are presented and analyzed by using the Galerkin method. The particular case, known as a phase-field fracture approximation of cracks, is discussed in detail. All these models are dynamic (i.e. involve inertia to model vibrations or waves possibly emitted during fast damage/fracture or induced by fast varying forcing) and consider viscosity which is also damageable. Then various options for time discretisation are devised. Eventually, extensions to more complex rheologies or a modification for large strains are briefly exposed, too.
Keywords
Cite
@article{arxiv.1906.04110,
title = {Models of dynamic damage and phase-field fracture, and their various time discretisations},
author = {Tomáš Roubíček},
journal= {arXiv preprint arXiv:1906.04110},
year = {2024}
}