Isostaticity in two dimensional pile of rigid disks

TL;DR

This study investigates the static structure of two-dimensional rigid disk piles, demonstrating that frictionless piles are isostatic with a coordination number of 4, while frictional piles tend toward isostaticity with a coordination number near 3, depending on preparation.

Contribution

It provides the first detailed analysis of isostaticity in 2D rigid disk piles, highlighting the effects of friction and preparation procedures on structural properties.

Findings

Frictionless piles have a coordination number converging to 4, indicating isostaticity.

Frictional piles can approach isostaticity with a coordination number near 3.

Pile preparation influences the structural coordination in frictional cases.

Abstract

We study the static structure of piles made of polydisperse disks in the rigid limit with and without friction using molecular dynamic simulations for various elasticities of the disks and pile preparation procedures. The coordination numbers are calculated to examine the isostaticity of the pile structure. For the frictionless pile, it is demonstrated that the coordination number converges to 4 in the rigid limit, which implies that the structure of rigid disk pile is isostatic. On the other hand, for the frictional case with the infinite friction constant, the coordination number depends on the preparation procedure of the pile, but we find that the structure becomes very close to isostatic with the coordination number close to 3 in the rigid limit when the pile is formed through the process that tends to make a pile of random configuration.