# Friction law and hysteresis in granular materials

## TL;DR

This paper investigates the velocity-weakening friction law and hysteresis in granular materials, revealing the role of acoustic noise and soft spots, and provides a microscopic theory with experimentally testable predictions.

## Contribution

It introduces a microscopic theory explaining the non-monotonic friction law and hysteresis in granular materials, highlighting the role of acoustic noise and soft spots.

## Key findings

- Velocity-weakening friction law exists even with identical microscopic friction coefficients.
- Soft particles eliminate the velocity-weakening behavior.
- Predicted scaling laws for acoustic noise and sliding contacts are confirmed numerically.

## Abstract

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 non-monotonic behavior in the friction law $\mu(I)$, 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 $\theta_s$. We build a microscopic theory for the non-monotonicity of $\mu(I)$, which also predicts the scaling behavior of acoustic noise, the fraction of sliding contacts $\chi$ and the sliding velocity, in terms of $\theta_s$. Surprisingly, these quantities have no limit when particles become infinitely hard, as confirmed numerically. Our analysis rationalizes previously unexplained observations and makes new experimentally testable predictions.