Elastic Contacts of Randomly Rough Indenters with Thin Sheets, Membranes Under Tension, Half Spaces, and Beyond

Abstract

We consider the adhesion-less contact between a two-dimensional, randomly rough, rigid indenter, and various linearly elastic counterfaces, which can be said to differ in their spatial dimension D. They include thin sheets, which are either free or under equi-biaxial tension, and semi-infinite elastomers, which are either isotropic or graded. Our Green’s function molecular dynamics simulation identifies an approximately linear relation between the relative contact area ar and pressure p at small p only above a critical dimension. The pressure dependence of the mean gap ug obeys identical trends in each studied case: quasi-logarithmic at small p and exponentially decaying at large p. Using a correction factor with a smooth dependence on D, all obtained ug(p) relations can be reproduced accurately over several decades in pressure with Persson’s theory, even when it fails to properly predict the interfacial stress distribution function.