Lattice models of failure: Sensitivity to the local dynamics

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Abstract
Quasistatic lattice models to explore scaling and other properties of failure events, including earthquakes, are characterized by the presence of two or more time scales. We show that there is a remarkable degree of variability in the qualitative behavior of these models: In one model with periodic boundary conditions, which simulates a moving dislocation or avalanche model of fracture, the trajectories are always periodic in both one and two dimensions. In another quasistatic model which simulates a growing coherent crack, the trajectories are either periodic or chaotic, depending on the initial conditions. Characteristic behaviors derived from analytic results are illustrated by numerical simulations.