Models of crack propagation

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Abstract
Three simple models of steady-state crack propagation are examined in a search for clues about the nature of dynamic velocity-selection mechanisms in these systems. The first is a one-dimensional model with stick-slip friction which includes, as a special case, a model of an earthquake fault. The conclusion here is that velocity-weakening slipping friction generally causes the crack to accelerate to the limiting wave speed independent of loading strength. The second model is also one dimensional, but the dissipation mechanism is the analog of a Kelvin viscosity. In this case, steady-state solutions at large applied stresses exhibit oscillating crack-opening displacements and propagate at speeds comparable to or higher than the nominal wave speed. The third model is the two-dimensional analog of the second. Its qualitative behavior turns out to be essentially the same as in the one-dimensional version.

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