Inserted: 5 mar 2018
Last Updated: 1 aug 2018
Preprint SISSA 06$/$2018$/$MATE
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.