A Simplified Version of Persson's Multiscale Theory for Rubber Friction Due to Viscoelastic Losses

Abstract

We show that the full multiscale Persson's theory for rubber friction due to viscoelastic losses can be approximated extremely closely to simpler models, like that suggested by Persson in 1998 and similarly by Popov in his 2010 book (but notice that we do not make any use of the so-called “Method of Dimensionality Reduction” (MDR)), so it is essentially a single scale model at the so-called large wavevector cutoff. The dependence on the entire spectrum of roughness is therefore only confusing, at least for range of fractal dimensions of interest D≃2.2, and we confirm this with actual exact calculations and reference to recent data of Lorenz et al. Moreover, we discuss the critical assumption of the choice of the “free parameter” best fit truncation cutoff.