# Existence of solutions to a phase-field model of dynamic fracture with a crack-dependent dissipation

## TL;DR

This paper introduces a phase-field model for dynamic fracture that incorporates crack-speed dependent dissipation, proving the existence of solutions satisfying energy balance and extending previous models without dissipation.

## Contribution

It develops a new dynamic fracture model with dissipative effects and proves the existence of solutions fulfilling Griffith's energy criterion.

## Key findings

- Existence of solutions with crack-speed dependent dissipation.
- Energy-dissipation balance is satisfied in the model.
- Extension of previous models without dissipation.

## Abstract

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.