# On the accurate computation of the true contact-area in mechanical contact of random rough surfaces

## TL;DR

This paper presents a correction method for accurately computing the true contact area in rough surface contact problems, even with coarse meshes, by using geometrical insights and interface length measurements.

## Contribution

A novel correction function is introduced that improves contact area calculations on coarse meshes, validated across various surface types and spectral contents.

## Key findings

- Accurate contact area estimation with coarse meshes achieved.
- Correction method validated for different fractal dimensions.
- Topology smoothing enhances contact cluster analysis.

## Abstract

We introduce a corrective function to compensate errors in contact area computations coming from mesh discretization. The correction is based on geometrical arguments and requires only one additional quantity to be computed: the length of contact/non-contact interfaces. The new technique enables us to evaluate accurately the true contact area using a coarse mesh for which the shortest wavelength in the surface spectrum reaches the grid size. The validity of the approach is demonstrated for surfaces with different fractal dimensions and different spectral content using a properly designed mesh convergence test. In addition, we use a topology preserving smoothing technique to adjust the morphology of contact clusters obtained with a coarse grid.