Contact stiffness of randomly rough surfaces

We investigate the contact stiffness of an elastic half-space and a rigid indenter with randomly rough surface having a power spectrum [Image: see text], where q is the wave vector. The range of [Image: see text] is studied covering a wide range of roughness types from white noise to smooth single asperities. At low forces, the contact stiffness is in all cases a power law function of the normal force with an exponent α. For H > 2, the simple Hertzian behavior is observed [Image: see text]. In the range of 0 < H < 2, the Pohrt-Popov behavior is valid ([Image: see text]). For H < 0, a power law with a constant power of approximately 0.9 is observed, while the exact value depends on the number of modes used to produce the rough surface. Interpretation of the three regions is given both in the frame of the three dimensional contact mechanics and the method of dimensionality reduction (MDR). The influence of the long wavelength roll-off is investigated and discussed.