Static Versus Dynamic Friction: The Role of Coherence

TL;DR

This paper presents a simple spring-based model for solid friction that explains the difference between static and dynamic friction through coherence loss among asperity springs, showing how their ratio varies with asperity distribution.

Contribution

It introduces a probabilistic spring model that captures the static-dynamic friction difference and quantifies how asperity distribution affects their ratio.

Findings

The static and dynamic friction ratio ranges between 1 and 2.

The ratio decreases as the asperity strain distribution widens.

Coherence loss among asperities explains static-dynamic friction differences.

Abstract

A simple model for solid friction is analyzed. It is based on tangential springs representing interlocked asperities of the surfaces in contact. Each spring is given a maximal strain according to a probability distribution. At their maximal strain the springs break irreversibly. Initially all springs are assumed to have zero strain, because at static contact local elastic stresses are expected to relax. Relative tangential motion of the two solids leads to a loss of coherence of the initial state: The springs get out of phase due to differences in their sizes. This mechanism alone is shown to lead to a difference between static and dynamic friction forces already. We find that in this case the ratio of the static and dynamic coefficients decreases with increasing relative width of the probability distribution, and has a lower bound of 1 and an upper bound of 2.