Coordinated Stress-Structure Self-Organization in Granular Packing

TL;DR

This paper introduces a quantitative method to analyze stress-structure correlations in granular packings, revealing how local stress and structure self-organize during quasi-static compression, challenging existing stress transmission theories.

Contribution

The paper presents a novel method for quantifying stress-structure correlations in planar granular systems and demonstrates its application across different packing protocols and friction coefficients.

Findings

Cells align with local stress principal axes.

Stress ratios depend on cell order and friction.

Stress ratio distributions collapse onto a single curve.

Abstract

During quasi-static dynamics of granular systems, the stress and structure self-organise, but there is currently no quantitative measure or understanding of this phenomenon. Such an understanding is essential because local structural properties of the settled material are then correlated with the local stress, which calls into question existing linear theories of stress transmission in granular media. A method to quantify the local stress-structure correlations is necessary for addressing this issue and we present here such a method for planar systems. We then use it to analyze numerically several different systems, compressed quasi-statically by two different procedures. We define cells, cell orders, cell orientations, and cell stresses and report the following results. 1. Cells orient along the local stress major principal axes. 2. The mean ratio of cell principal stresses decreases with cell order and increases with friction. 3. The ratio distributions collapse onto a single curve under a simple scaling, for all packing protocols and friction coefficients. 4. A constructed model explains the correlations between the local cell and stress principal axis orientations. 5. The collapse of the stress ratios onto a Weibull distribution is explained theoretically. Our results quantify the cooperative stress-structure self-organization and provide a way to relate quantitatively the stress-structure coupling to different process parameters and particle characteristics. Significantly, the strong stress-structure correlation, driven by structural re-organization upon application of external stress, suggests that current stress theories of granular matter need to be revisited.