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's function molecular dynamics. The indenter's 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* ḡ) ≪ 1, sufficiently large systems are consistent with a linear ac=κp* relation. Here p is the pressure, E* is the contact modulus, ḡ the root-mean-square height gradient, and κ a unitless proportionality coefficient. However, the parameter ḡ 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 κ.