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 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 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 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 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.

Connecting the grain-shearing mechanism of wave propagation in marine sediments to fractional order wave equations

“…In the latter case it manifests itself as a result of the microscopic junctions formed due to the sliding of micro-asperities against each other. 39,40 Such situations might arise in partially saturated sediments as well as where the grains could come into direct contact with each other, and still exhibit time-dependent behavior.…”

Connecting the Viscous Grain-shearing Mechanism of Wave Propagation in Marine Sediments to Fractional Calculus

“…These micro-junctions have an inherent property of being time-dependent. 47 One of the goals achieved through this work is that we have shown that the equations derived from the fundamental physical process of grain-shearing could lead to fractional-order wave equations. This may be the first result which directly connects the fractional framework to a process deeply rooted in physics.…”

Propagation Length of Self-healing Slip Pulses at the Onset of Sliding: A Toy Model

“…We have assumed that broken contacts are immediately restored with zero stretching. Instead, one may assume that the contacts repin after some delay time τ d [10,14,15,21,9]. Assuming a constant τ d , the width of the self-healing crack will increase from λ c to vτ d , with v the (minimal) propagation velocity of the front (see Refs.…”