Field-theoretical approach to estimate mean gap and gap distribution in randomly rough surface contact mechanics

TL;DR

This paper develops a field-theoretical model to analytically predict the mean gap and gap distribution in rough surface contact mechanics, validated by simulations, advancing understanding of interfacial behavior under pressure.

Contribution

It introduces a second-order cumulant expansion within a field-theoretical framework to derive explicit relations for gap statistics in rough surface contact, extending prior models.

Findings

Analytical expressions for mean gap and gap distribution derived.

Model predictions agree well with GFMD simulations.

Framework enables quantitative predictions of contact stresses and gaps.

Abstract

We extend the statistical field-theoretical framework of rough surface contact mechanics to characterize the interfacial gap between an elastic half-space and a randomly rough surface incorporating exponential repulsion. Building upon a cumulant expansion to second-order, we derive an explicit analytical relation between the mean gap and the applied normal pressure. This result provides a closed-form expression for the drift and diffusion coefficients in a convection-diffusion equation governing the scale-dependent evolution of the gap distribution. Solving this equation with appropriate initial and boundary conditions yields the gap distribution under varying external pressures. Both the mean gap and the gap distribution are found to be in good agreement with Green's function molecular dynamics (GFMD) simulations. Our results demonstrate that the field-theoretical approach enables quantitative predictions not only for contact stresses but also for interfacial gap in rough surface contacts.