Criticality and Scaling Relations in a Sheared Granular Material

TL;DR

This paper explores the critical behavior and scaling laws of dense granular materials under shear, revealing power-law relationships in stress and pressure near a critical volume fraction through numerical experiments and scaling analysis.

Contribution

It introduces a new numerical investigation of shear rheology in granular materials and provides a simple scaling argument to explain observed power-law behaviors.

Findings

Identification of a critical volume fraction where stress and pressure follow power laws

Derivation of scaling exponents through a simple theoretical argument

Interpretation of power-law behavior under constant pressure conditions

Abstract

We investigate a rheological property of a dense granular material under shear. By a numerical experiment of the system with constant volume, we find a critical volume fraction at which the shear stress and the pressure behave as power-law functions of the shear strain rate. We also present a simple scaling argument that determines the power-law exponents. Using these results, we interpret a power-law behavior observed in the system under constant pressure.