Crack propagation as a free boundary problem
  A newly developed sharp interface model describes crack propagation by a phase transition process. We solve this free boundary problem numerically and obtain steady state solutions with a self-consistently selected propagation velocity and shape of the crack, provided that elastodynamic effects are taken into account. Also, we find a saturation of the steady state crack velocity below the Rayleigh speed, tip blunting with increasing driving force and a tip splitting instability above a critical driving force. 
D. Pilipenko, R. Spatschek, E. A. Brener, H. M\"uller-Krumbhaar