Damage in Models of Fracture Nucleation and Propagation

Damage and healing are modeled as a generalized phase transitions including both scaling behaviors and nucleation processes. I examine several models of faults in the earth's crust that demonstrate aspects of scaling behavior similar to those seen in experiments and in nature. First, a composite model for earthquake rupture initiation and propagation is studied. System failure times and modes of rupture propagation are determined as a function of the hazard-rate exponent and the range of interaction. Second, I study a model for frictional sliding with long range interactions and recurrent damage and healing during sliding. I show there is a critical point transition and provide a mapping to the mean-field percolation transition (spinodal nucleation). Third, I propose a time-dependent slider-block model which incorporates a time-to-failure function dependent on stress. I associate this new time dependent failure mechanism with stress fatigue. The resulting behavior produces both the Gutenberg-Richter scaling law for event sizes and the Omori's scaling law for the rate of aftershocks. And last, I discuss a general model for fracture nucleation and growth. I have constructed a phase diagram and categorized growth modes numerically using a Metropolis algorithm. I also model repulsive interactions and compare the symmetry breaking transitions to the anti-ferromagnetic Ising model.