Some observations on Bar Sinai, Brener and Bouchbinder (BSBB) model for friction

Recently, the observation of “slow fronts” in Fineberg’s group beautiful experiments in the transition from stick to slip has motivated some interesting mesoscopic models for friction, introduced along the lines of rate-state dependent models, but with a key role played by a viscous strengthening term in the friction law. In particular two models, proposed by Bar Sinai, Brener and Bouchbinder (BSBB), are considered in this work which differ in the strengthening term: the first introduces a logarithmic strengthening, the second a linear strengthening. The models aim to show that the velocity of the slip propagating fronts can be related to the much smaller slip velocities in the friction steady state curve. With the logarithmic strengthening model the increase in the local friction coefficient remains negligible if compared with the experimental results. When a stronger-than-logarithmic strengthening friction model is considered an order of magnitude increase of friction coefficient is observed in steady state friction curves, nevertheless when the local shear/pressure ratio is related with the front velocity, the results are inconsistent with the experiments. Some closed form equations are obtained to show the main results of the BSBB models, not shown in the original papers. The results and the limitations of the present models are presented.