Aspects of bulk properties of amorphous jammed disks under isotopic compression

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