Effect of Structural Parameters on the Relative Contact Area for Ideal, Anisotropic, and Correlated Random Roughness

The relative contact area between an initially flat, adhesion- and frictionless, linearly elastic body and a variety of rough, rigid counterbodies is studied using Green\u0027s function molecular dynamics. The indenter\u0027s height profiles range from ideal random roughness through roughness with a moderate amount of correlation to periodically repeated, single-asperity indenters having perfect phase coherence. At small reduced pressures, p* := p/(E*/g) \u003c\u003c 1, sufficiently large systems are consistent with a linear aC = kappa p* relation. Here, p is the pressure, E* is the contact modulus, g the root-mean-square height gradient, and kappa a unitless proportionality coefficient. However, the parameter g must be evaluated over the real contact area for the linear relation to hold if the random roughness is correlated or the interfacial dimension reduced. No single unitless structural parameter--- including the Nayak parameter--- correlates in a significant fashion with kappa.