title: History-dependent friction and slow slip from time-dependent microscopic junction laws studied in a statistical framework.
abstract: 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 microjunctions forming a macroscopic frictional interface. Each microjunction 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 microjunction 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 microjunction 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 effects 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 nonmonotonic (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 nontrivial history dependence of the macroscopic static friction force. In particular, the static friction coefficient at the onset of sliding is shown to increase with increasing deceleration during the final 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 effect is expected to be experimentally observable.
authors.affiliation: Department of Physics, University of Oslo, Sem Sælands vei 24, NO-0316 Oslo, Norway.
authors.forename: Kjetil
authors.initials: K
authors.lastname: Thøgersen
authors.affiliation: Department of Physics, University of Oslo, Sem Sælands vei 24, NO-0316 Oslo, Norway.
authors.forename: Jørgen Kjoshagen
authors.initials: JK
authors.lastname: Trømborg
authors.affiliation: Department of Physics, University of Oslo, Sem Sælands vei 24, NO-0316 Oslo, Norway.
authors.forename: Henrik Andersen
authors.initials: HA
authors.lastname: Sveinsson
authors.affiliation: Department of Physics, University of Oslo, Sem Sælands vei 24, NO-0316 Oslo, Norway.
authors.forename: Anders
authors.initials: A
authors.lastname: Malthe-Sørenssen
authors.affiliation: Laboratoire de Tribologie et Dynamique des Systèmes, CNRS, Ecole Centrale de Lyon, 36, Avenue Guy de Collongue, 69134 Ecully Cedex, France.
authors.forename: Julien
authors.initials: J
authors.lastname: Scheibert
mesh_terms: D003198:Computer Simulation; D017276:Friction; D015233:Models, Statistical; D009038:Motion; D053758:Nanoparticles / Q000737:chemistry* / Q000648:ultrastructure*; D013499:Surface Properties