Self-affine roughness effects on the contact area between elastic bodies

We have calculated the real contact area between elastic bodies with self-affine rough surfaces, which are described in terms of analytical correlation models in Fourier space. It is found that the roughness has a strong influence on the real contact area A(lambda) at lateral length scales lambda which are comparable with the in-plane roughness correlation length xi, and for significant applied loads sigma(o) beyond the linear regime (or Aproportional tosigma(o)). The effect of the roughness exponent H can be rather complex, depending on the relative magnitude of the roughness correlation length xi with respect to the lateral length scale lambda where the contact area is considered. Finally, we also show that descriptions of the influence of the roughness that is only based on power law approximations of the self-affine roughness spectrum are rather insufficient, especially for large roughness exponents H (>0.5).