Authors: Lucas Frérot, Lars Pastewka

Surface roughness emerges naturally during mechanical removal of material, fracture, chemical deposition, plastic deformation, indentation, and other processes. Here, we use continuum simulations to show how roughness which is neither Gaussian nor self-affine emerges from repeated elastic-plastic contact of a rough and rigid surface on a flat elastic-plastic substrate. Roughness profiles change with each contact cycle, but appear to approach a steady-state long before true elastic shakedown of the substrate. We propose a simple dynamic collapse for the emerging power-spectral density, which shows that the multi-scale nature of the roughness is encoded in the first few indentations. In contrast to macroscopic roughness parameters, roughness at small scales and the skewness of the height distribution of the resulting roughness do not show a steady-state, with the latter vanishing asymptotically.

Cover art: made with Blender, computed with Tamaas, HDRI from Polyhaven.