Contact area of rough spheres: Large scale simulations and simple scaling laws

TL;DR

This study uses large-scale molecular simulations to analyze the contact mechanics of rough spheres across a wide size and load range, deriving simple scaling laws and analytical expressions that unify different contact regimes.

Contribution

It introduces parameter-free analytical models for contact area of rough spheres, bridging atomic to macroscopic scales, and validates common approximations in contact mechanics.

Findings

Contact area scales linearly with load at intermediate forces.

Hertzian contact behavior dominates at large loads.

Derived simple scaling laws applicable across scales.

Abstract

We use molecular simulations to study the nonadhesive and adhesive atomic-scale contact of rough spheres with radii ranging from nanometers to micrometers over more than ten orders of magnitude in applied normal load. At the lowest loads, the interfacial mechanics is governed by the contact mechanics of the first asperity that touches. The dependence of contact area on normal force becomes linear at intermediate loads and crosses over to Hertzian at the largest loads. By combining theories for the limiting cases of nominally flat rough surfaces and smooth spheres, we provide parameter-free analytical expressions for contact area over the whole range of loads. Our results establish a range of validity for common approximations that neglect curvature or roughness in modeling objects on scales from atomic force microscope tips to ball bearings.