Nucleation and propagation of fracture at a fricitonal interface*

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 level,

            beyond which cracks can propagate.

            Here we will 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 both objects,

            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  test these predictions in a minimal model of frictional interfaces. We will then discuss a path to use these ideas

for the intialization of flow in bulk granular materials.