Instabilities at frictional interfaces: Creep patches, nucleation, and rupture fronts

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.