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 and the friction coefficient . 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 and the reduced bulk modulus 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 and the average reduced overlap and give the analysis on how and are affected by the variation of Z and . For frictionless disk packings, we find that the affine assumption causes large deviation on Z and relative to those of non-affine compression and therefore fails to predict the quantitative results of . For packings with a fixed , due to the non-affine deformation, varies approximately linear with the increasing and Z increases sharply near the jamming point and then approaches a saturation value. With a fixed and the increasing , changes by a small amount while Z presents obvious decrease. The decrease of Z causes the decrease of the slope of function and the value of at a fixed .