Stochastic process model for interfacial gap of purely normal elastic rough surface contact

TL;DR

This paper develops a stochastic process-based convection-diffusion model for the interfacial gap in elastic rough surface contact, providing a new approach to predict gap distribution and address adhesive contact problems.

Contribution

It introduces a convection-diffusion PDE for the interfacial gap PDF derived from stochastic process theory, complementing existing contact pressure models.

Findings

Model agrees with GFMD at high loads

Deviations at low loads due to model simplifications

Effective in solving adhesive contact under DMT limit

Abstract

In purely normal elastic rough surface contact problems, Persson's theory of contact shows that the evolution of the probability density function (PDF) of contact pressure with the magnification is governed by a diffusion equation. However, there is no partial differential equation describing the evolution of the PDF of the interfacial gap. In this study, we derive a convection--diffusion equation in terms of the PDF of the interfacial gap based on stochastic process theory, as well as the initial and boundary conditions. A finite difference method is developed to numerically solve the partial differential equation. The predicted PDF of the interfacial gap agrees well with that by Green's Function Molecular Dynamics (GFMD) and other variants of Persson's theory of contact at high load ranges. At low load ranges, the obvious deviation between the present work and GFMD is attributed to the overestimated mean interfacial gap and oversimplified magnification-dependent diffusion coefficient used in the present model. As one of its direct application, we show that the present work can effectively solve the adhesive contact problem under the DMT limit. The current study provides an alternative methodology for determining the PDF of the interfacial gap and a unified framework for solving the complementary problem of random contact pressure and random interfacial gap based on stochastic process theory.