Collective effects at frictional interfaces

TL;DR

This paper explores how long-range elastic interactions in frictional interfaces influence the collective behavior of contacts, leading to phenomena like elastic instabilities and propagating frictional cracks.

Contribution

It introduces a characteristic elastic correlation length and analyzes how interactions below and above this scale affect interface dynamics and stability.

Findings

Elastic correlation length $bb_c$ determines rigid body behavior.

Strong interactions narrow contact threshold distribution.

Above $bb_c$, interactions screen perturbations and enable collective modes.

Abstract

We discuss the role of the long-range elastic interaction between the contacts inside an inhomogeneous frictional interface. The interaction produces a characteristic elastic correlation length $\lambda_c = a^2 E / k_c$ (where $a$ is the distance between the contacts, $k_c$ is the elastic constant of a contact, and $E$ is the Young modulus of the sliding body), below which the slider may be considered as a rigid body. The strong inter-contact interaction leads to a narrowing of the effective threshold distribution for contact breaking and enhances the chances for an elastic instability to appear. Above the correlation length, $r > \lambda_c$, the interaction leads to screening of local perturbations in the interface, or to appearance of collective modes --- frictional cracks propagating as solitary waves.