  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 [C.J. Larsen, C. Ortner, and E. S\"uli, Math. Models
Methods Appl. Sci. (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 [B. Bourdin, C.J. Larsen,
and C.L. Richardson, Int. J. Fracture (2011)] and [C.J. Larsen, IUTAM Symposium
on Variational Concepts with Applications to the Mechanics of Materials (2010)]
with no dissipative terms.
