A rigorous approach to the contact mechanics of rough, elastic solids*

The basic ideas of a statistical field theory is presented, which allows one to calculate the displacement field and the pressure distribution $\Pr(p)$ in a contact formed by an elastic body and a rigid counter face of arbitrary topography. The theory is a cumulant expansion, which contains Persson's contact mechanics theory as the leading-order term. The cumulant approach provides a framework with which corrections can now be systematically derived. Comparison is made to numerical data for surfaces that interact via exponentially repulsive forces.