Stiffness of Contacts Between Rough Surfaces

TL;DR

This study investigates how self-affine roughness influences contact mechanics between solids, revealing linear load-stiffness relationships and the applicability of Persson's theory across various conditions, with atomic-scale effects mainly impacting lateral stiffness.

Contribution

It demonstrates that Persson's contact theory effectively collapses data for different roughnesses and system sizes, and highlights atomic-scale effects on lateral stiffness.

Findings

Contact area and normal stiffness increase linearly with load

Load increases exponentially as surfaces approach

Atomic-scale effects significantly reduce lateral stiffness

Abstract

The effect of self-affine roughness on solid contact is examined with molecular dynamics and continuum calculations. The contact area and normal and lateral stiffnesses rise linearly with the applied load, and the load rises exponentially with decreasing separation between surfaces. Results for a wide range of roughnesses, system sizes and Poisson ratios can be collapsed using Persson's contact theory for continuous elastic media. The atomic scale response at the interface between solids has little affect on the area or normal stiffness, but can greatly reduce the lateral stiffness. The scaling of this effect with system size and roughness is discussed.