Phase-field model of mode III dynamic fracture

We introduce a phenomenological continuum model for the mode III dynamic fracture that is based on the phase-field methodology used extensively to model interfacial pattern formation. We couple a scalar field, which distinguishes between broken and unbroken states of the system, to the displacement field in a way that consistently includes both macroscopic elasticity and a simple rotationally invariant short-scale description of breaking. We report two-dimensional simulations that yield steady-state crack motion in a strip geometry above the Griffith threshold.