A JKR/Griffith Model for the Inception of Slip in the Contact Between Nominally Flat Rough Surfaces

Abstract We develop an analytical model to describe how an energetic model of friction (JKR-Griffith model) between nominally flat rough surfaces leads to an inception of slip which is governed by an elastic instability. By extending classical contact mechanics from Persson’s solution with a JKR approach, the model captures the transition from sticking to sliding under shear. The relation between mean shear and mean interfacial slip is derived. It reveals that static friction can exceed kinetic friction and that this enhancement depends on surface roughness and normal load. The model predicts a saturated enhancement in static friction at small pressure and diminishing value at high pressure. Such enhancement will be suppressed if the roughness amplitude of the surface is magnified. Comparisons with experimental data show good agreement, after considering that friction energy is time-dependent, offering insight into adhesion-driven friction in applications ranging from microscale to tectonic plate scales.