Systematic analysis of Persson's contact mechanics theory of randomly rough elastic surfaces

摘要

We systematically check explicit and implicit assumptions of Persson'scontact mechanics theory. It casts the evolution of the pressure distribution${\rm Pr}(p)$ with increasing resolution of surface roughness as a diffusiveprocess, in which resolution plays the role of time. The tested key assumptionsof the theory are: (a) the diffusion coefficient is independent of pressure$p$, (b) the diffusion process is drift-free at any value of $p$, (c) the point$p=0$ acts as an absorbing barrier, i.e., once a point falls out of contact, itnever reenters again, (d) the Fourier component of the elastic energy is onlypopulated if the appropriate wave vector is resolved, and (e) it no longerchanges when even smaller wavelengths are resolved. Using high-resolutionnumerical simulations, we quantify deviations from these approximations andfind quite significant discrepancies in some cases. For example, the driftbecomes substantial for small values of $p$, which typically represent pointsin real space close to a contact line. On the other hand, there is asignificant flux of points reentering contact. These and other identifieddeviations cancel each other to a large degree, resulting in an overallexcellent description for contact area, contact geometry, and gap distributionfunctions. Similar fortuitous error cancellations cannot be guaranteed underdifferent circumstances, for instance when investigating rubber friction. Theresults of the simulations may provide guidelines for a systematic improvementof the theory.