Phenomenological theory of friction in the quasistatic limit : collective pinning and memory effects

TL;DR

This paper develops a phenomenological theory linking hysteretic friction behavior in quasistatic elastic body movements to collective elastic instabilities and substrate properties, with numerical confirmation of predicted scalings.

Contribution

It introduces a new theoretical framework connecting hysteresis in friction to collective elastic instabilities and substrate characteristics.

Findings

Hysteresis approaches exponential asymptotically.

The exponential length scale depends on surface elasticity and substrate roughness.

Numerical simulations confirm the predicted scalings.

Abstract

When a elastic body is moved quasistatically back and forth over a surface, the friction of the interface is experimentally observed to circulate through a hysteretic loop. The asymptotic behaviour of the hysteresis loop is approached exponentially. We describe how this behaviour is connected to the collective properties of the elastic instabilities suffered by the elastic body as it is displaced quasistatically. We express the length scale of the exponential in terms of the elasticity of the surface and the properties of the rough substrate. The predicted scalings are confirmed numerically.