01243nas a2200145   4500008004100000020001400041245010900055210007100164260001500235300000700250490000700257520076800264100001901032856004601051       2020                        eng d  a1420-900400aExistence of solutions to a phase–field model of dynamic fracture with a crack–dependent dissipation0 aExistence of solutions to a phase–field model of dynamic fractur  c2020/02/11  a140 v273 a<p>We propose a phase–field model of dynamic fracture based on the Ambrosio–Tortorelli’s approximation, which takes into account dissipative effects due to the speed of the crack tips. By adapting the time discretization scheme contained in Larsen et al. (Math Models Methods Appl Sci 20:1021–1048, 2010), we show the existence of a dynamic crack evolution satisfying an energy–dissipation balance, according to Griffith’s criterion. Finally, we analyze the dynamic phase–field model of Bourdin et al. (Int J Fract 168:133–143, 2011) and Larsen (in: Hackl (ed) IUTAM symposium on variational concepts with applications to the mechanics of materials, IUTAM Bookseries, vol 21. Springer, Dordrecht, 2010, pp 131–140) with no dissipative terms.</p>1 aCaponi, Maicol  uhttps://doi.org/10.1007/s00030-020-0617-z