# The role of the roughness spectral breadth in elastic contact of rough surfaces

## TL;DR

This paper investigates how the spectral breadth of surface roughness influences the true contact area in elastic contact, revealing a logarithmic decrease with the Nayak parameter and proposing a phenomenological model linking contact area and pressure.

## Contribution

It introduces a highly accurate computational method to analyze the effect of spectral breadth on contact area evolution and proposes a new phenomenological equation incorporating the Nayak parameter.

## Key findings

- Contact area decreases logarithmically with the Nayak parameter at constant pressure.
- The effect of spectral breadth is significant for surfaces with rich spectra.
- A phenomenological model for contact area growth is proposed, depending on the Nayak parameter.

## Abstract

We study frictionless and non-adhesive contact between elastic half-spaces with self-affine surfaces. Using a recently suggested corrective technique, we ensure an unprecedented accuracy in computation of the true contact area evolution under increasing pressure. This accuracy enables us to draw conclusions on the role of the surface's spectrum breadth (Nayak parameter) in the contact area evolution. We show that for a given normalized pressure, the contact area decreases logarithmically with the Nayak parameter. By linking the Nayak parameter with the Hurst exponent (or fractal dimension), we show the effect of the latter on the true contact area. This effect, undetectable for surfaces with poor spectral content, is quite strong for surfaces with rich spectra. Numerical results are compared with analytical models and other available numerical results. A phenomenological equation for the contact area growth is suggested with coefficients depending on the Nayak parameter. Using this equation, the pressure-dependent friction coefficient is deduced based on the adhesive theory of friction. Some observations on Persson's model of rough contact, whose prediction does not depend on Nayak parameter, are reported. Overall, the paper provides a unifying picture of rough elastic contact and clarifies discrepancies between preceding results.