Velocity weakening friction: A renormalization approach

Abstract

The frictional response when a two‐dimensional elastic body, under a steady antiplane shearing, slides over a rigid frictional surface is solved using a real‐space renormalization technique. The model is mapped onto iterations of the classical Burridge‐Knopoff chain model. A velocity weakening friction law is assumed for the interactions between the rigid interface and the elastic slider. Through the renormalization approach, we specifically study the coupling between the bulk elastic response of the slider and the friction at the interface level. The frictional system is characterized by its mechanical response in terms of mean friction force opposed to a prescribed constant velocity. The response is shown to differ strongly from the interface friction law. Under renormalization, the response converges toward an apparent dynamical Coulomb's friction law, with distinct static and dynamic coefficients. This result provides some new insight in the “ubiquity” of Coulomb's friction law. On the base of this model, the experimental observability of velocity weakening friction laws and their scaling to seismically active system are discussed. The main result is that velocity weakening friction law is scale dependent. Within the assumptions of the model, the friction law at the scale of the system appears to be rather insensitive to the exact form of the friction at local scale on the interface.