Shear flow of angular grains: acoustic effects and non-monotonic rate dependence of volume

TL;DR

This paper develops a theoretical model explaining the non-monotonic shear volume behavior in angular granular materials, incorporating acoustic effects, grain shape, and friction, with quantitative agreement to experiments.

Contribution

It introduces an Ising-like internal variable and acoustic noise modeling within the STZ framework to account for shape and friction effects in granular flow.

Findings

Quantitative agreement with experimental data

Non-monotonic shear volume dependence on shear rate

Role of acoustic noise and grain interlocking in flow behavior

Abstract

Naturally-occurring granular materials often consist of angular particles whose shape and frictional characteristics may have important implications on macroscopic flow rheology. In this paper, we provide a theoretical account for the peculiar phenomenon of auto-acoustic compaction -- non-monotonic variation of shear band volume with shear rate in angular particles -- recently observed in experiments. Our approach is based on the notion that the volume of a granular material is determined by an effective-disorder temperature known as the compactivity. Noise sources in a driven granular material couple its various degrees of freedom and the environment, causing the flow of entropy between them. The grain-scale dynamics is described by the shear-transformation-zone (STZ) theory of granular flow, which accounts for irreversible plastic deformation in terms of localized flow defects whose density is governed by the state of configurational disorder. To model the effects of grain shape and frictional characteristics, we propose an Ising-like internal variable to account for nearest-neighbor grain interlocking and geometric frustration, and interpret the effect of friction as an acoustic noise strength. We show quantitative agreement between experimental measurements and theoretical predictions, and propose additional experiments that provide stringent tests on the new theoretical elements.