A linear viscoelastic relaxation-contact model of a flat fractal surface: a Maxwell-type medium

This paper presents a continuous relaxation model for the contact of a viscoelastic material with a nominally flat surface. In this model a load-deflection relationship of the viscoelastic punch surface is obtained. The proposed model assumes that the surface material behaves as a linear Maxwell viscoelastic material. The roughness of the punch surface is assumed to be fractal, where the Cantor set theory is utilized to model the roughness. An asymptotic power law is obtained, reflecting the relaxed force with the applied displacement. This law is valid only when the approach is about the same size as the surface roughness. The model provides an analytical solution for the case when the deformation is linear viscoelastic. The modified analytical model shows good agreement when compared with the experimental results obtained by (Handzel-Powierza et al. in Wear 154:115-124, 1992).