Relation between Interfacial Separation and Load: A General Theory of Contact Mechanics

I study the contact between a rigid solid with a randomly rough surface and an elastic block with a flat surface. I derive a relation between the (average) interfacial separation u and the applied normal squeezing pressure p. I show that, for nonadhesive interaction and small applied pressure, p approximately exp(-u/u(0)), in good agreement with recent experimental observations.