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Using the linear elastic Boundary Element Method, we calculated the normal con- tact stiffness of fractal rough surfaces by means of the differential quotient of normal force and indentation and found a power-law dependence on the applied load. Exponents vary from 0.5 to 0.85 depending on the fractal dimension in contrast to Persson's theory, which predicts a linear dependency. For very high forces, saturation is reached, corresponding to full mate- rial contact of an equivalent smooth indenter. Efficient algorithms allowed for statistical evaluation after just a few days of calculation with grid sizes of 2049x2049 on a standard PC. The fractal behavior of the surface roughness was applied all the way from the sample size down to the shortest wavelength that could be represented on the chosen grid. The same cases were investigated using a reduction method proposed by one of the authors, which maps the 3D-contact onto a 1D-rough line having the same mechanical properties. Results were obtained with dramatically less investments in CPU time. As this approach al- lows for a much higher resolution up to 2^23, we found the power law to be valid in the as- ymptotic behavior for small normal forces, given that the surface has fractal-like roughness in the corresponding small length scales.

CONTACT STIFFNESS OF BODIES WITH FRACTAL ROUGHNESS: COMPARISON OF 3D BEM RESULTS AND REDUCTION METHOD