Friction law and hysteresis in granular materials [Physics]
The macroscopic friction of particulate materials often weakens as the flow rate is increased, leading to potentially disastrous
intermittent phenomena including earthquakes and landslides. We theoretically and numerically study this phenomenon in simple
granular materials. We show that velocity weakening, corresponding to a nonmonotonic behavior in the friction law,
μ(I), is present even if the dynamic and static microscopic friction coefficients are identical, but disappears for softer particles.
We argue that this instability is induced by endogenous acoustic noise, which tends to make contacts slide, leading to faster
flow and increased noise. We show that soft spots, or excitable regions in the materials, correspond to rolling contacts that
are about to slide, whose density is described by a nontrivial exponent
θs. We build a microscopic theory for the nonmonotonicity of
μ(I), which also predicts the scaling behavior of acoustic noise, the fraction of sliding contacts
χ, and the sliding velocity, in terms of
θs. Surprisingly, these quantities have no limit when particles become infinitely hard, as confirmed numerically. Our analysis
rationalizes previously unexplained observations and makes experimentally testable predictions.
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