Crack Propagation as a Free Boundary Problem
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 sharp interface method and a phase field approach to investigate the model. The simulations confirm analytical predictions for fast crack propagation.
S.W. Nam, Y.W. Chang, S.B. Lee and N.J. Kim
R. Spatschek et al., "Crack Propagation as a Free Boundary Problem", Key Engineering Materials, Vols. 345-346, pp. 429-432, 2007