Instabilities at Frictional Interfaces: Creep Patches, Nucleation and Rupture Fronts

TL;DR

This paper provides a comprehensive theoretical analysis of the spatiotemporal dynamics at frictional interfaces, revealing how creep patches become unstable and lead to rupture fronts with diverse velocities, relevant to earthquakes and tribology.

Contribution

It offers the first combined analytic and numerical study of rate-and-state friction dynamics, identifying the critical nucleation size and the dependence of rupture fronts on stress and friction.

Findings

Creep patches become linearly unstable at a nearly history-independent critical size.

Rupture front velocities vary widely and are linked to steady state solutions.

The stability and propagation of rupture fronts depend on stress state and velocity-strengthening friction.

Abstract

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 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 fronts solutions.