Continuum Theory of Fracture

We present a continuum theory of fracture which describes the fast 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 the selection of the steady state tip radius and velocity. Two different numerical approaches are presented to solve this problem. A sharp interface approach allows to study the steady state regime by the means of a series expansion technique. Also, 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, and the results of both numerical approaches are in excellent agreement with each other.