Non-monotonic dependence of the friction coefficient on heterogeneous stiffness

TL;DR

This study uses numerical simulations to reveal that the macroscopic friction coefficient exhibits a non-monotonic relationship with the system's bulk elasticity, influenced by rupture front geometries during stick-slip dynamics.

Contribution

It demonstrates, through a 2D Burridge-Knopoff model, that the macroscopic friction coefficient non-monotonically depends on elastic properties, linking rupture front orientations to elasticity.

Findings

Friction coefficient varies non-monotonically with bulk elasticity.

Four regimes of rupture front orientations identified.

Energetic balance explains the non-monotonic behavior.

Abstract

The complexity of the frictional dynamics at the microscopic scale makes difficult to identify all of its controlling parameters. Indeed, experiments on sheared elastic bodies have shown that the static friction coefficient depends on loading conditions, the real area of contact along the interfaces and the confining pressure. Here we show, by means of numerical simulations of a 2D Burridge-Knopoff model with a simple local friction law, that the macroscopic friction coefficient depends non-monotonically on the bulk elasticity of the system. This occurs because elastic constants control the geometrical features of the rupture fronts during the stick-slip dynamics, leading to four different ordering regimes characterized by different orientations of the rupture fronts with respect to the external shear direction. We rationalize these results by means of an energetic balance argument.