On the dependence of the static friction force between a rigid,randomly rough fractal surface and a viscoelastic body on the normal force

The present 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. We numerically investigate the contact between a rigid, randomly rough surface and an elastic half-space and determine the dependence of the rms slope in the contact region on the normal force. For fractal surfaces with a Hurst exponent of H ≈ 1, the rms slope can be approximated very well by a logarithmic function of the normal force. Parameters of the approximation have been determined as functions of the Hurst exponent. The rms value of the slope always increases with the normal force, which indicates that the coefficient of friction should be an increasing function of the normal force.