The strength and stability of frictional interfaces, ranging from tribological systems to earthquake faults, are intimately related to the underlying spatially extended dynamics. Here we provide a comprehensive theoretical account, both analytic and numeric, of spatiotemporal interfacial dynamics in a realistic rate-and-state friction model, featuring both velocity-weakening and velocity-strengthening behaviors. Slowly extending, loading-rate-dependent creep patches undergo a linear instability at a critical nucleation size, which is nearly independent of interfacial history, initial stress conditions, and velocity-strengthening friction. Nonlinear propagating rupture fronts—the outcome of instability—depend sensitively on the stress state and velocity-strengthening friction. Rupture fronts span a wide range of propagation velocities and are related to steady-state-front solutions.

• Received 16 June 2013
• Corrected 20 December 2013

DOI:https://doi.org/10.1103/PhysRevE.88.060403