In this work, a numerical simulation was completed using Matlab. The goal was to determine the dependence of the static friction force between a rigid, randomly rough fractal surface and a viscoelastic body on the normal force.

This investigation is based on the assumption that the static coefficient of friction can be characterized roughly by the rms value of the surface gradient in the contact region.

A relation between the rms slope and the normal force was found and parameters of the approximation have been determined as functions of the Hurst exponent.

The simulation was realized using the method of reduction of dimensionality which has been proposed for contact problems in [1] and was extended to contact of rough surfaces in [2,3].

Link to publication:

J. Benad - On the dependence of the static friction force between a rigid, randomly rough fractal surface and a viscoelastic body on the normal force, (Physical Mesomechanics, Springer, September 2012, Volume 15, Issue 5-6, pp 300-302).

​[1] - V.L. Popov, S.G. Psakhie. Numerical simulation methods in tribology - Tribology International, v. 40, 916-923. (2007)

[2] - T. Geike, V.L. Popov, Mapping of three-dimensional contact problems into one dimension. - Phys. Rev. E., v. 76, 036710, 5 pp. (2007)

[3] - T. Geike, V.L. Popov. Reduction of three-dimensional contact problems to one-dimensional ones. - Tribology International, v. 40, 924-929. (2007)