Contact mechanics: relation between interfacial separation and load

TL;DR

This paper derives a mathematical relation between interfacial separation and applied load for a rough surface contact, confirming experimental observations and enhancing understanding of contact mechanics.

Contribution

It provides a theoretical derivation of the relation between interfacial separation and load for rough surface contact, aligning with experimental data.

Findings

p is proportional to exp(-u/u_0) at small pressures

The relation agrees with recent experimental results

Enhances understanding of elastic contact mechanics

Abstract

I study the contact between a rigid solid with a randomly rough surface and an elastic block with a flat surface. I derive a relation between the (average) interfacial separation $u$ and the applied normal squeezing pressure $p$. I show that for non-adhesive inte raction and small applied pressure, p is proportional to exp (-u/u_0), in good agreement with recent experimental observation.