Modeling friction on a mesoscale: Master equation for the earthquake-like model

TL;DR

This paper develops an analytical master equation for an earthquake-like model with a distribution of static thresholds, providing insights into solid friction and regimes of stick-slip and smooth sliding.

Contribution

It introduces a solvable master equation framework that separates friction force calculation from contact property analysis in mesoscale models.

Findings

Analytical solution for the master equation describing friction.

Clear distinction between stick-slip and smooth sliding regimes.

Framework applicable to tribological systems with distributed static thresholds.

Abstract

The earthquake-like model with a continuous distribution of static thresholds is used to describe the properties of solid friction. The evolution of the model is reduced to a master equation which can be solved analytically. This approach naturally describes stick-slip and smooth sliding regimes of tribological systems within a framework which separates the calculation of the friction force from the studies of the properties of the contacts.