Rigorous Field-Theoretical Approach to the Contact Mechanics of Rough Elastic Solids

A statistical field theory is formulated, which allows one to calculate the pressure distribution Pr(p) in a contact formed by an elastic body and a rigid counter face of arbitrary topography. It is a cumulant expansion, which contains Persson's contact mechanics theory as the leading-order term. Our approach provides a framework with which corrections can now be derived systematically. As an example, Pr(p) is calculated to high accuracy for exponentially repulsive solids. Non-Gaussian tails in Pr(p) can be rationalized for surfaces whose height spectra differ from colored noise.