A fractal expansion of a three dimensional elastic–plastic multi-scale rough surface contact model

Abstract This work presents a fractal contact model for nominally flat rough surfaces and its analytical solution. Based on the non-statistical multi-scale model of Jackson and Streator, the model investigates the resolution-dependent contact area. A hierarchy of scales is constructed from a fractal surface description, based on the power spectral density of the surface roughness. In contrast to other fractal contact models, the concept of asperities is retained. Elasto-plastic deformation effects are included by virtue of an appropriate asperity model. The analytical solution yields a concise description of the resolution-dependent progression of fractal contact, decoupling the asperity physics from texture influence.