History-dependent friction and slow slip from time-dependent microscopic junction laws studied in a statistical framework
Résumé
To study how macroscopic friction phenomena originate from microscopic junction laws, we introduce a general statistical framework describing the collective behavior of a large number of individual micro-junctions forming a macroscopic frictional interface. Each micro-junction can switch in time between two states: A pinned state characterized by a displacement-dependent force, and a slipping state characterized by a time-dependent force. Instead of tracking each micro-junction individually, the state of the interface is described by two coupled distributions for (i) the stretching of pinned junctions and (ii) the time spent in the slipping state. This framework allows for a whole family of micro-junction behavior laws, and we show how it represents an overarching structure for many existing models found in the friction literature. We then use this framework to pinpoint the e ects of the time-scale that controls the duration of the slipping state. First, we show that the model reproduces a series of friction phenomena already observed experimentally. The macroscopic steady-state friction force is velocity-dependent, either monotonic (strengthening or weakening) or non-monotonic (weakening-strengthening), depending on the microscopic behavior of individual junctions. In addition, slow slip, which has been reported in a wide variety of systems, spontaneously occurs in the model if the friction contribution from junctions in the slipping state is time-weakening. Next, we show that the model predicts a non-trivial history-dependence of the macroscopic static friction force. In particular, the static friction coe cient at the onset of sliding is shown to increase with increasing deceleration during the nal phases of the preceding sliding event. We suggest that this form of history-dependence of static friction should be investigated in experiments, and we provide the acceleration range in which this e ect is expected to be experimentally observable.
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