  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.
