A minimal model for the onset of slip pulses in frictional rupture

Abstract: We present a minimal one-dimensional model for the transition from crack-like to pulse-like propagation of frictional rupture. In its non-dimensional form, the model depends on only two free parameters: the non-dimensional pre-stress and an elasticity ratio that accounts for the finite height of the system. The model contains stable slip pulse solutions for slip boundary conditions, and unstable slip pulse solutions for stress boundary conditions. Results demonstrate that the existence of pulse-like ruptures requires only elastic relaxation and redistribution of initial pre-stress. The novelty of our findings is that pulse-like propagation along frictional interfaces is a generic elastic feature, whose existence is not sensitive to particular rate- or slip-dependencies of dynamic friction.