Internal states of model isotropic granular packings. I. Assembling process, geometry and contact networks

TL;DR

This paper investigates the geometric and mechanical properties of static spherical bead packings under isotropic pressure, revealing how assembly methods influence structure, coordination, and force networks, with implications for understanding granular materials.

Contribution

It introduces detailed numerical simulations of frictionless and frictional granular packings, highlighting how assembly processes affect packing density, contact networks, and force indeterminacy.

Findings

Frictionless packings reach RCP with z*≈6 under fast assembly.

Different assembly methods produce packings with distinct contact structures.

Frictional packings retain force indeterminacy except at infinite friction.

Abstract

This is the first paper of a series of three, reporting on numerical simulation studies of geometric and mechanical properties of static assemblies of spherical beads under an isotropic pressure. Frictionless systems assemble in the unique random close packing (RCP) state in the low pressure limit if the compression process is fast enough, slower processes inducing traces of crystallization, and exhibit specific properties directly related to isostaticity of the force-carrying structure. The different structures of frictional packings assembled by various methods cannot be classified by the sole density. While lubricated systems approach RCP densities and coordination number z^*~=6 on the backbone in the rigid limit, an idealized "vibration" procedure results in equally dense configurations with z^*~=4.5. Near neighbor correlations on various scales are computed and compared to available laboratory data, although z^* values remain experimentally inaccessible. Low coordination packings have many rattlers (more than 10% of the grains carry no force), which should be accounted for on studying position correlations, and a small proportion of harmless "floppy modes" associated with divalent grains. Frictional packings, however slowly assembled under low pressure, retain a finite level of force indeterminacy, except in the limit of infinite friction.