Elastic contact between rough surfaces: Effect of roughness at large and small wavelengths

The area and pressure distribution in elastic contacts between frictionless, nonadhesive surfaces is studied as a function of load and surface geometry using finite element calculations. Surfaces that follow self-affine scaling on all resolved scales are compared to surfaces with cutoffs at small and large length scales, and experimental surfaces that are not self-affine. In all cases the true area of contact is proportional to load and inversely proportional to elastic modulus and the mean slope of the surface. The constant of proportionality κκ is nearly constant and lies between analytic predictions. Large wavelength cutoffs lead to a small increase in κκ, a homogeneous distribution of contacts at large scales, and limit the size of the largest connected regions. Small wavelength cutoffs lead to local redistributions in pressure that decrease the probability of low and high local pressures.