A microscopic model of rate and state friction evolution

Whether rate- and state-dependent friction evolution is primarily slip dependent or time dependent is not well resolved. Although slide-hold-slide experiments are traditionally interpreted as supporting the aging law, implying time-dependent evolution, recent studies show that this evidence is equivocal. In contrast, the slip law yields extremely good fits to velocity step experiments, although a clear physical picture for slip-dependent friction evolution is lacking. We propose a new microscopic model for rate and state friction evolution in which each asperity has a heterogeneous strength, with individual portions recording the velocity at which they became part of the contact. Assuming an exponential distribution of asperity sizes on the surface, the model produces results essentially similar to the slip law, yielding very good fits to velocity step experiments but not improving much the fits to slide-hold-slide experiments. A numerical kernel for the model is developed, and an analytical expression is obtained for perfect velocity steps, which differs from the slip law expression by a slow-decaying factor. By changing the quantity that determines the intrinsic strength, we use the same model structure to investigate aging-law-like time-dependent evolution. Assuming strength to increase logarithmically with contact age, for two different definitions of age we obtain results for velocity step increases significantly different from the aging law. Interestingly, a solution very close to the aging law is obtained if we apply a third definition of age that we consider to be nonphysical. This suggests that under the current aging law, the state variable is not synonymous with contact age.