Finite-element analysis of contact between elastic self-affine surfaces

TL;DR

This study uses finite element methods to analyze contact mechanics between elastic self-affine surfaces, revealing linear contact area growth with load, pressure independence, and fractal contact morphology, with results aligning with some experimental and theoretical predictions.

Contribution

It provides a detailed finite element analysis of contact between elastic self-affine surfaces, highlighting new insights into contact area, pressure distribution, and morphology.

Findings

Contact area increases linearly with load at small loads

Mean pressure in contact regions is load-independent and proportional to rms slope

Contact regions exhibit fractal geometry and pressure distribution has an exponential tail

Abstract

Finite element methods are used to study non-adhesive, frictionless contact between elastic solids with self-affine surfaces. We find that the total contact area rises linearly with load at small loads. The mean pressure in the contact regions is independent of load and proportional to the rms slope of the surface. The constant of proportionality is nearly independent of Poisson ratio and roughness exponent and lies between previous analytic predictions. The contact morphology is also analyzed. Connected contact regions have a fractal area and perimeter. The probability of finding a cluster of area $a_c$ drops as $a_c^{-\tau}$ where $\tau $ increases with decreasing roughness exponent. The distribution of pressures shows an exponential tail that is also found in many jammed systems. These results are contrasted to simpler models and experiment.