A linear viscoelastic creep-contact model of a flat fractal surface: Kelvin-Voigt medium

The objective of this paper is to construct a continuous model for the viscoelastic contact of a nominal flat punch and a smooth surface of a rigid half-space. The considered model aims at studying the normal approach as a function of the applied load. The proposed model assumes the punch surface material to behave according to Kelvin-Voigt viscoelastic material. The punch surface, which is known to be fractal in nature, is modelled in this work using a deterministic Cantor structure. An asymptotic power law, deduced using iterative relations, is used to express the punch surface approach as a function of the remote force when the approach of the punch surface and the half space is in the order of the size of the surface roughness. The results obtained using this model, which admits closed form solution, are displayed graphically for selected values of the system parameters; the fractal surface roughness and various material properties. The obtained results showed good agreement with published experimental results.