The 4-parameter Compressible Packing Model (CPM) including a critical cavity size ratio

Gerard Roquier,F Radjai,S Luding,J.Y Delenne,S Nezamabadi

doi:10.1051/epjconf/201714002009

Abstract

The 4-parameter Compressible Packing Model (CPM) has been developed to predict the packing density of mixtures constituted by bidisperse spherical particles. The four parameters are: the wall effect and the loosening effect coefficients, the compaction index and a critical cavity size ratio. The two geometrical interactions have been studied theoretically on the basis of a spherical cell centered on a secondary class bead. For the loosening effect, a critical cavity size ratio, below which a fine particle can be inserted into a small cavity created by touching coarser particles, is introduced. This is the only parameter which requires adaptation to extend the model to other types of particles. The 4-parameter CPM demonstrates its efficiency on frictionless glass beads (300 values), spherical particles numerically simulated (20 values), round natural particles (125 values) and crushed particles (335 values) with correlation coefficients equal to respectively 99.0%, 98.7%, 97.8%, 96.4% and mean deviations equal to respectively 0.007, 0.006, 0.007, 0.010.

Highlights

The packing density is often an optimized physical value for high performing and sustainable materials
The 4-parameter Compressible Packing Model (CPM) offers a new theory on the wall effect and on the loosening effect studied by considering elementary juxtaposed cells
The effect of a coarse or a fine particle is examined on the basis of a foreign sphere surrounded by dominant class neighbours

Summary

Introduction

The packing density is often an optimized physical value for high performing and sustainable materials. The first strategy [2,3, 5] consists in taking that into account in the mathematical expressions used for the interaction coefficients It means that an adjustment by regression analysis is each time necessary to find the best functions of these parameters. The second strategy [4, 7] consists in taking into account of the packing process efficiency by a compaction index K and of the particle shape and of the surface texture through a critical cavity size ratio x0. This value, a small particle can be inserted into a small cavity created by touching coarser particles without disturbed their arrangement. The more global interference effect is materialized by the AKJI section

The 4-parameter CPM

Wall effect theory for spheres

Loosening effect and interference effect theory for spheres

Compaction index K and critical cavity size ratio x0

Conclusion