A JKR/Griffith model transition to slip in frictional contact between layered surfaces with roughness

In a recent study, Liang et al. developed an analytical framework, termed the "Johnson-Kendall-Roberts (JKR)-Griffith model," to describe how an energetic model of friction between nominally flat rough surfaces leads to the onset of slip governed by elastic instability. In the present study, this approach is extended to the case of a layered solid. By combining Persson's contact mechanics theory, a JKR-type approximation, and the Cattaneo-Mindlin superposition principle, the model captures the transition from sticking to sliding under tangential loading. The analysis shows that the static friction can exceed the kinetic friction, with this enhancement depending on the ratio of elastic moduli, surface roughness, and normal load. The model further predicts that the maximum discrepancy between static and kinetic friction occurs at an intermediate layer thickness. This framework provides useful guidance for the design of layered surfaces to mitigate stick-slip phenomena, which are often responsible for undesirable machine vibrations and wear.