Eur. Phys. J. E (2021) 44: 140
https://doi.org/10.1140/epje/s10189-021-00145-3

Regular Article - Flowing Matter

Aspects of bulk properties of amorphous jammed disks under isotopic compression

¹ Institute of Physics, Guizhou University, 550025, Guiyang, Guizhou, China
² College of Computer Science and Technology, Guizhou University, 550025, Guiyang, China

^a xgzhang@gzu.edu.cn

Received: 14 September 2021
Accepted: 1 November 2021
Published online: 18 November 2021

Abstract

By investigating the bidisperse disks under isotropic compression, we show the importance of non-affine deformation on the bulk properties of jammed disordered matter and how the mechanical properties are affected by the variation of microscopic quantities with the excess volume density $\mathrm{\Delta }{\rho }_V$ and the friction coefficient $\mu$. In theory, we derive a simple formula for the pressure of disk packings which sets up a bridge between the pressure and other statistical quantities like the contact number density and the average normal force. This pressure formula is used to derive the reduced pressure $P^{\ast }$ and the reduced bulk modulus $K^{\ast }$ for disk packings with linear interactions and under affine compression without new contacts. Combining theoretical formulae with Discrete Element Method (DEM) simulations, we investigate the average contact number $Z(\mathrm{\Delta }{\rho }_V,\mu )$ and the average reduced overlap $\overline{U}(\mathrm{\Delta }{\rho }_V,\mu )$ and give the analysis on how $P^{\ast }$ and $K^{\ast }$ are affected by the variation of Z and $\overline{U}$. For frictionless disk packings, we find that the affine assumption causes large deviation on Z and $\overline{U}$ relative to those of non-affine compression and therefore fails to predict the quantitative results of $K^{\ast }$. For packings with a fixed $\mu$, due to the non-affine deformation, $\overline{U}$ varies approximately linear with the increasing $\mathrm{\Delta }{\rho }_V$ and Z increases sharply near the jamming point and then approaches a saturation value. With a fixed $\mathrm{\Delta }{\rho }_V$ and the increasing $\mu$, $\overline{U}$ changes by a small amount while Z presents obvious decrease. The decrease of Z causes the decrease of the slope of function $P^{\ast }(\mathrm{\Delta }{\rho }_V)$ and the value of $K^{\ast }$ at a fixed $\mathrm{\Delta }{\rho }_V$.