I submitted the manuscript "An Archard-type multiscale theory of hysteretic friction on viscoelastic half-planes, built on exact per-scale viscoelastic contact solutions" for consideration as a Regular Article.
Hysteretic friction of soft solids on rough surfaces is a multiscale problem, and its standard description is Persson's mean-field theory, which computes the dissipation at each scale from the full-contact linear response at the frequency qV, weighted by the contact-area fraction. Physical Review E has published key exact numerical studies of this problem (e.g. G. Carbone and C. Putignano, Phys. Rev. E 89, 032408 (2014)). What has been missing is a multiscale theory in which every scale is a genuine viscoelastic contact problem, tested against exact solutions of the same multiscale geometry.
Summary of key findings
- Each scale of an Archard-type hierarchy is solved with the exact steady-state periodic viscoelastic contact solution; the mean pressure of a scale loads the next, friction coefficients add and contact fractions multiply. The solver is validated against Menga et al., Proc. R. Soc. A 470, 20140392 (2014).
- At a single scale, the strong asymmetry of the viscoelastic contact changes friction by less than about 10%, whereas the contact size, through the frequency V/a, controls the speed of the friction peak.
- Against full boundary-element solutions of multiscale profiles, the cascade places the friction peak at the correct speed (Persson's theory places it 1.8 to 7.5 times higher) and has 0.5 to 0.7 times the error of Persson's theory, for one relaxation time and for a broad relaxation spectrum; the advantage is lost when scales are not well separated.
- Both theories share the dependence of friction on the short-wavelength roughness cutoff, scaling as k_N^(1-H); improving the contact mechanics does not remove the cutoff problem.
See preprint at