Revisiting the diffusion equation derivation in Persson's theory of contact
arXiv:2509.02397 · doi:10.1115/1.4069634
Abstract
In Persson's seminal work on tire-road interaction (Persson, J. Chem. Phys. {\bf 115}(8), 2001), he ingeniously derived a diffusion equation in Appendix B to characterize the evolution of contact pressure between a rigid rough indenter and an elastic half-space with spatial magnification, which constitutes the foundation of Persson's theory of contact. Persson's theory has been extensively validated and applied to investigate nearly all critical aspects of tribological problems. In contrast to the well-known Greenwood-Williamson (GW) model, Persson's theory receives relatively less attention within the tribology community. One contributing factor to this discrepancy is that the original derivation of the diffusion equation in Appendix B is not easily understandable to non-physicists. In this technical note, the authors provide supplementary information for each step of the derivation, aiming to clarify the conceptual foundation for researchers who encounter difficulties in understanding Persson's theory, thereby encouraging its broader application within and beyond tribology.
References in corpus (5)
- Contact mechanics: relation between interfacial separation and load
- Theory of the leak-rate of seals
- On the elastic energy and stress correlation in the contact between elastic solids with randomly rough surfaces
- Persson's Theory of Purely Normal Elastic Rough Surface Contact: A Tutorial Based on Stochastic Process Theory
- Stochastic process model for interfacial gap of purely normal elastic rough surface contact