Rheology of Granular Materials: Dynamics in a Stress Landscape

TL;DR

This paper introduces a stress landscape framework for the rheology of dense granular materials, utilizing a stress-based ensemble and angoricity to model slow driving and stress fluctuations, aligning with experimental observations.

Contribution

It develops a novel stress landscape model for granular rheology based on the stress ensemble and angoricity, extending the Soft Glassy Rheology approach to granular systems.

Findings

Derived constitutive equations for granular flow.

Predicted yield stress consistent with experiments.

Modeled stress dissipation distribution during shearing.

Abstract

We present a framework for analyzing the rheology of dense driven granular materials, based on a recent proposal of a stress-based ensemble. In this ensemble fluctuations in a granular system near jamming are controlled by a temperature-like parameter, the angoricity, which is conjugate to the stress of the system. In this paper, we develop a model for slowly driven granular materials based on the stress ensemble and the idea of a landscape in stress space. The idea of an activated process driven by the angoricity has been shown by Behringer et al (2008) to describe the logarithmic strengthening of granular materials. Just as in the Soft Glassy Rheology (SGR) picture, our model represents the evolution of a small patch of granular material (a mesoscopic region) in a stress-based trap landscape. The angoricity plays the role of the fluctuation temperature in SGR. We determine (a) the constitutive equation, (b) the yield stress, and (c) the distribution of stress dissipated during granular shearing experiments, and compare these predictions to experiments of Hartley & Behringer (2003).