Statistical Voronoi Model for Monodisperse Disk Packings

doi:10.12141/j.issn.1000-565X.220340

Abstract

Abstract:

It is of great significance to study the geometric structure and characteristics of random packings for understanding the macroscopic physical properties of disordered systems such as granular matter, foam, colloid, etc. Combining with experiments and computer simulations, researchers have explored the random packings of particles with different shapes and dimensions. In theory, some models based on statistical geometry, mean field approximation or stochastic process were proposed to investigate the volume fraction and average coordination number of random packings. However, due to the complex constraints of packing structure, the difficulty of setting a criterion for the disorder, etc., it is difficult to perform rigorous analysis and calculation even for monodisperse disk packings. For the volume fraction of the random closed packing, different studies provided different results. In this paper，a statistical Voronoi model was proposed for the theoretical research of the geometric properties of the monodisperse disk packings. The Voronoi network was used to describe the configuration of a packing and an area formula of the Voronoi network was deduced for general case. Based on the concepts of excluded circle and Voronoi circle, several theorems were given for determining the Voronoi nearest neighbor relationship between rigid disks. For balanced and stable disk packings, based on the relationships between the features of a Voronoi cell and the contact structure of nearest neighbor disks, this paper derived several formulae such as the volume fraction of a symmetric Voronoi cell varying with the contact number, the area of a Voronoi cell and the geometric coordination number varying with angles of neighbor contact lines. Finally, this paper derived the integral formulae for the average geometric coordination number and the average reduced free volume with respect to the probability distribution of the contact line angle by using the statistical analysis of Voronoi network. Theoretical calculation results show that the volume fraction of a Voronoi cell increases both with the increase of its symmetry and its contact number, the average contact number is 4 and the average volume fraction is π²/12 for the random closed packing. These results can be used to understand the geometric structure and feature of the frictionless disk packing.

Key words: granular matter, disordered packing, volume fraction, Voronoi cell

CLC Number:

O414.2

ZHANG Xinggang, DAI Dan, TANG Yan . Statistical Voronoi Model for Monodisperse Disk Packings[J]. Journal of South China University of Technology(Natural Science Edition), 2023, 51(2): 122-130.

Figures/Tables 6

References 26

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