Scale separation in granular packings: stress plateaus and fluctuations

TL;DR

This study uses numerical simulations to identify a scale range where the stress field in granular packings remains nearly resolution independent, aiding in objective stress measurement and understanding fluctuations.

Contribution

It introduces the concept of a stress plateau in granular packings where the stress tensor is resolution independent, supported by numerical evidence and analysis of fluctuations.

Findings

Existence of a stress plateau over a range of coarse graining scales.

Ensemble averaging extends the plateau to sub-particle scales.

Stress response varies with external loading and gravity.

Abstract

It is demonstrated, by numerical simulations of a 2D assembly of polydisperse disks, that there exists a range (plateau) of coarse graining scales for which the stress tensor field in a granular solid is nearly resolution independent, thereby enabling an `objective' definition of this field. Expectedly, it is not the mere size of the the system but the (related) magnitudes of the gradients that determine the widths of the plateaus. Ensemble averaging (even over `small' ensembles) extends the widths of the plateaus to sub-particle scales. The fluctuations within the ensemble are studied as well. Both the response to homogeneous forcing and to an external compressive localized load (and gravity) are studied. Implications to small solid systems and constitutive relations are briefly discussed.