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To study the microscopic origins of friction, we build a framework todescribe the collective behaviour of a large number of individualmicro-junctions forming a macroscopic frictional interface. Each micro-junctioncan switch in time between two states: A pinned state characterized by adisplacement-dependent force, and a slipping state characterized by atime-dependent force. Instead of tracking each micro-junction individually, thestate of the interface is described by two coupled distributions for (i) thestretching of pinned junctions and (ii) the time spent in the slipping state.We show how this framework represents an overarching structure for importantmodels existing in the friction literature. We then use it to studysystematically the effect of the time-scale that controls the duration of theslipping state. We first find the steady-state friction force as a function ofthe sliding velocity. As the framework allows for a whole family ofmicro-junction behaviour laws, we show how these laws can be chosen to obtainmonotonic (strengthening or weakening) or non-monotonic velocity dependence atthe macroscale. By then considering transient situations, we predict that themacroscopic static friction coefficient is strongly influenced by the way theinterface was prepared, in particular by the slip dynamics of the previoussliding event. We also show that slow slip spontaneously occurs in theframework for a wide range of behaviour laws.

History-dependent friction and slow slip from time-dependent microscopic junction laws studied in a statistical framework