Scaling theory for the statistics of slip at frictional interfaces

Abstract

Slip at a frictional interface occurs via intermittent events. Understanding how these events are nucleated, can propagate, or stop spontaneously remains a challenge, central to earthquake science and tribology. In the absence of disorder, rate-and-state approaches predict a diverging nucleation length at some stress σ * , beyond which cracks can propagate. Here we argue that disorder is a relevant perturbation to this description. We justify why the distribution of slip contains two parts: a power-law corresponding to 'avalanches', and a 'narrow' distribution of system-spanning 'fracture' events. We derive novel scaling relations for avalanches, including a relation between the stress drop and the spatial extension of a slip event. We compute the cut-off length beyond which avalanches cannot be stopped by disorder, leading to a system-spanning fracture, and successfully test these predictions in a minimal model of frictional interfaces.

Nucleation of frictional slip: A yielding or a fracture process?

“…In particular, the fully-dynamic formulation of these equations accounts for all dynamic effects, including the wave-mediated stress transfers. These are computed through a convolution integral over the causality cone of distant points [44] and introduce long-range interactions into the system, which may have an important effect on stability, as observed for the dynamics of elastic depinning [2,45,46]. This formulation is given as follows:…”