Stress Correlations in Frictional Granular Media

TL;DR

This study shows that in frictional granular packings, stress autocorrelations are mainly determined by pressure and torque fluctuations, with pressure fluctuations decaying slower than expected, unlike in elastic solids.

Contribution

It proves that stress autocorrelation matrices in frictional granular media are constrained by isotropy and mechanical balance, revealing pressure fluctuations as the key factor.

Findings

Stress autocorrelation is determined by pressure and torque auto-correlations.

Torque fluctuations are hyper-uniform, pressure fluctuations decay slower.

Pressure fluctuations originate during initial compression before jamming.

Abstract

This paper investigates whether in frictional granular packings, like in Hamiltonian amorphous elastic solids, the stress autocorrelation matrix presents long range anisotropic contributions just as elastic Green's functions. We find that in a standard model of frictional granular packing this is not the case. We prove quite generally that mechanical balance and material isotropy constrain the stress auto-correlation matrix to be fully determined by two spatially isotropic functions: the pressure and torque auto-correlations. The pressure and torque fluctuations being respectively normal and hyperuniform force the stress autocorrelation to decay as the elastic Green's function. Since we find the torque fluctuations to be hyper-uniform, the culprit is the pressure whose fluctuations decay slower than normally as a function of the system's size. Investigating the reason for these abnormal pressure fluctuations we discover that anomalous correlations build up already during the compression of the dilute system before jamming. Once jammed these correlations remain frozen. Whether this is true for frictional matter in general or is it the consequence of the model properties is a question that must await experimental scrutiny and possible alternative models.