A self-similar model for shear flows in dense granular materials

TL;DR

This paper introduces a self-similar probabilistic model for quasistatic shear flows in dense granular materials, capturing velocity profiles and stress fluctuations observed in experiments.

Contribution

It presents a novel self-similar model based on fracture formation and cluster motion to explain shear flow behaviors in granular materials.

Findings

Predicts velocity profiles consistent with experimental data

Identifies large stress fluctuations at the moving wall

Provides a probabilistic framework for cluster formation and motion

Abstract

We propose a model to describe the quasistatic shearing of dry granular materials, which notably captures the differences in velocity profiles recently observed in 2 and 3-D Couette flow experiments. In our scheme, the steady-state flow is due to the intermittent motion of particle clusters moving together with the wall. The motion of a cluster is associated with the transient formation of a fracture inside the sheared pack. The model is based on the existence of a persistence length for the fractures, which imposes a self-similar structure on the clusters. Through a probabilistic approach, we can evaluate the rate of appearance of a cluster of a given size and obtain a prediction for the average velocity profiles. We also predict the existence of large stress fluctuations at the moving wall, which characteristics are in good agreement with experimental data.