# How collective asperity detachments nucleate slip at frictional interfaces

## TL;DR

This paper presents a microscopic model of frictional interfaces showing how asperity detachments lead to slip nucleation, revealing a pseudo-gap distribution and finite size effects that influence stick-slip behavior.

## Contribution

It introduces a novel asperity-level disorder model with elastic interactions and inertia, linking frictional slip nucleation to amorphous plasticity concepts and finite size effects.

## Key findings

- Slip nucleation governed by a Griffith criterion for asperity avalanches.
- Presence of a pseudo-gap in asperity yield distances with a non-universal exponent.
- Stick-slip behavior is a slow finite size effect with a diverging nucleation radius.

## Abstract

Sliding at a quasi-statically loaded frictional interface can occur via macroscopic slip events, which nucleate locally before propagating as rupture fronts very similar to fracture. We introduce a novel microscopic model of a frictional interface that includes asperity-level disorder, elastic interaction between local slip events, and inertia. For a perfectly flat and homogeneously loaded interface, we find that slip is nucleated by avalanches of asperity detachments of extension larger than a critical radius $A_c$ governed by a Griffith criterion. We find that after slip, the density of asperities at a local distance to yielding $x_\sigma$ presents a pseudo-gap $P(x_\sigma) \sim (x_\sigma)^\theta$, where $\theta$ is a non-universal exponent that depends on the statistics of the disorder. This result makes a link between friction and the plasticity of amorphous materials where a pseudo-gap is also present. For friction, we find that a consequence is that stick-slip is an extremely slowly decaying finite size effect, while the slip nucleation radius $A_c$ diverges as a $\theta$-dependent power law of the system size. We discuss how these predictions can be tested experimentally.