Fundamental structural characteristics of planar granular assemblies: self-organisation and scaling away friction and initial state

TL;DR

This study investigates the microstructural statistics of 2D granular assemblies, revealing universal behaviors, analytical relations, and the scaling effects of friction and initial conditions, suggesting that packing procedures primarily govern microstructure.

Contribution

It provides analytical formulas and demonstrates the universal-like distribution of structural elements, showing that microstructural characteristics can be scaled away from friction and initial state effects.

Findings

Q volume distributions collapse onto a single exponential tail curve

Mean Q volume decreases with higher friction coefficients

Derived analytical relations linking coordination number, packing fraction, and rattlers

Abstract

We identify the fundamental factors determining the microstructural (MS) statistics of granular systems, using numerical experiments on 2D assemblies of polydisperse frictional discs and studying the emergent properties of quadrons (Qs), the basic structural elements of granular solids, whose statistics are universal-like[1]. The dependence of the structures and of the packing fraction on friction and initial state are analysed and we report the following. 1. Derivation of an analytical formula for the mean Q volume in terms of: the mean coordination number, the packing fraction and the rattlers fraction. 2. Derivation of a unique, initial-state-independent, relation between the mean coordination number and the rattler-free packing fraction. We support the relation with data for a range of different systems. 3. Collapse of the Q volume distributions of all systems onto one curve, having an exponential tail. 4. Decomposition of the Q volumes distribution into conditional distributions, each of these also collapsing onto a single curve. 5. The mean Q volume decreases with increasing inter-granular friction coefficients, an effect prominent in high order cells. We argue that this phenomenon is due to an increased probability of stable irregularly-shaped cells and test this by a herewith developed free cell analytical model. We conclude that, in principle, the MS characteristics are governed mainly by the packing procedure, while effects of friction and initial states can be scaled away. Yet, mechanical constraints limit slightly occurrence of small Q volumes in large cells, which does depend on friction. We quantify this deviation from exact collapse for these cells. 6. We argue that our results support the view that ensemble granular statistical mechanics does not satisfy the uniform measure assumption of conventional statistical mechanics.