On Phase Transition and Self-Organized Critical State in Granular Packings

TL;DR

This paper models two-dimensional granular systems and finds a critical volume fraction where an abrupt transition from fluid-like to solid-like behavior occurs, exhibiting self-organized criticality.

Contribution

It demonstrates the existence of a critical volume fraction in granular packings where a rigidity transition occurs and shows self-organized criticality under certain boundary conditions.

Findings

Rigidity transition at a critical volume fraction $ u_c$

$ u_c$ decreases with increasing grain friction

System spontaneously evolves to $ u_c$ under constant normal stress

Abstract

We model two-dimensional systems of granular aggregates confined between two planes and demonstrate that at a critical grain volume fraction an abrupt rigidity transition occurs. This transition is observed both in static and shear tests. The grain volume fraction at which the transition occurs, $\nu_c$, decreases with increasing friction between the grains. Densely packed grains, with a volume fraction $\nu> \nu_c$, display an elastic-plastic rheology. Dilute packings, with $\nu<\nu_c$, display gas-like characteristics. Packings with $\nu=\nu_c$ display phase coexistance. It is shown that when volume fraction is allowed to change freely (using constant normal stress boundary condition), it evolves spontaneously to $\nu_c$ under a wide range of boundary conditions, exhibiting 'self-organized criticality'.