Inserted: 5 mar 2018
Last Updated: 11 feb 2020
Journal: NoDEA Nonlinear Differential Equations Appl.
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. Süli, 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.