Elastic contact between self-affine surfaces: Comparison of numerical stress and contact correlation functions with analytic predictions

TL;DR

This study investigates elastic contact between self-affine surfaces using Green's function molecular dynamics, revealing algebraic decay in stress and contact autocorrelation functions and comparing results with analytic theories.

Contribution

It provides new numerical insights into stress and contact correlations on self-affine surfaces and evaluates the accuracy of recent contact mechanics theories.

Findings

Stress and contact autocorrelation functions decay algebraically.

Exponents differ from analytic predictions across studied roughness exponents.

Exponential interaction results align with recent contact mechanics corrections.

Abstract

Contact between an elastic manifold and a rigid substrate with a self-affine fractal surface is reinvestigated with Green's function molecular dynamics. Stress and contact autocorrelation functions (ACFs) are found to decrease algebraically. A rationale is provided for the observed similarity in the exponents for stress and contact ACFs. Both exponents differ substantially from analytic predictions over the range of Hurst roughness exponents studied. The effect of increasing the range of interactions from a hard sphere repulsion to exponential decay is analyzed. Results for exponential interactions are accurately described by recent systematic corrections to Persson's contact mechanics theory. The relation between the area of simply connected contact patches and the normal force is also studied. Below a threshold size the contact area and force are consistent with Hertzian contact mechanics, while area and force are linearly related in larger contact patches.