Calculus of Variations and Geometric Measure Theory

M. Caponi

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 11 Feb 2020


Accepted Paper

Inserted: 5 mar 2018
Last Updated: 11 feb 2020

Journal: NoDEA Nonlinear Differential Equations Appl.
Year: 2020
Doi: 10.1007/s00030-020-0617-z

ArXiv: 1908.01986 PDF
Links: Journal site


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.