Phase Field Modeling of Fast Crack Propagation
  We present a continuum theory which predicts the steady state propagation of cracks. The theory overcomes the usual problem of a finite time cusp singularity of the Grinfeld instability by the inclusion of elastodynamic effects which restore selection of the steady state tip radius and velocity. We developed a phase field model for elastically induced phase transitions; in the limit of small or vanishing elastic coefficients in the new phase, fracture can be studied. The simulations confirm analytical predictions for fast crack propagation. 
Robert Spatschek, Miks Hartmann, Efim Brener, Heiner   Mueller-Krumbhaar, Klaus Kassner