Finite-size scaling in the interfacial stiffness of rough elastic contacts

TL;DR

This paper investigates how the interfacial elastic stiffness of rough contact surfaces scales with applied pressure, revealing finite-size effects and providing analytical models that match numerical simulations.

Contribution

It extends Persson's contact mechanics theory to finite systems, deriving analytical expressions for the low-pressure scaling of interfacial stiffness.

Findings

K scales linearly with pressure at high p

Finite-size effects cause sublinear scaling at low p

Analytical expressions match simulation results

Abstract

The total elastic stiffness of two contacting bodies with a microscopically rough interface has an interfacial contribution K that is entirely attributable to surface roughness. A quantitative understanding of K is important because it can dominate the total mechanical response and because it is proportional to the interfacial contributions to electrical and thermal conductivity in continuum theory. Numerical simulations of the dependence of K on the applied squeezing pressure p are presented for nominally flat elastic solids with a range of surface roughnesses. Over a wide range of p, K rises linearly with p. Sublinear power-law scaling is observed at small p, but the simulations reveal that this is a finite-size effect. We derive accurate, analytical expressions for the exponents and prefactors of this low-pressure scaling of K by extending the contact mechanics theory of Persson to systems of finite size. In agreement with our simulations, these expressions show that the onset of the low-pressure scaling regime moves to lower pressure as the system size increases.