# Existence of solutions to a phase-field model of dynamic fracture with a crack-dependent dissipation

created by caponi on 05 Mar 2018
modified on 22 Dec 2018

[BibTeX]

Submitted Paper

Inserted: 5 mar 2018
Last Updated: 22 dec 2018

Year: 2018
Notes:

Preprint SISSA 06$/$2018$/$MATE

Abstract:

We propose a phase-field model of dynamic crack propagation based on the Ambrosio-Tortorelli approximation, which takes in account dissipative effects due to the speed of the crack tips. In particular, adapting the time discretization scheme contained in Bourdin et al., Int. J. Fracture 168 (2011), 133-143 and Larsen et al., Math. Models Methods Appl. Sci. 20 (2010), 1021-1048, we show the existence of a dynamic crack evolution satisfying an energy dissipation balance, according to Griffith's criterion.