Bending back stress chains and unique behaviour of granular matter in cylindrical geometries

TL;DR

This paper explores complex stress behaviors in granular materials within cylindrical geometries, revealing phenomena like curved, broadened, and back-bending stress chains, which enhance understanding of experimental observations in Couette cell studies.

Contribution

It provides a comprehensive analysis of stress fields in cylindrical geometries, uncovering novel phenomena such as back-bending stress chains and stress leakage, extending prior rectangular symmetry models.

Findings

Stress chains curve, broaden, and leak stress into a cone of influence.

Stress chains can bend back and transmit forces oppositely.

Non-uniform media exhibit chain branching and stress leakage.

Abstract

We analyse the general solutions for the stress field in planar annuli of isostatic media, a model often used for marginally rigid granular materials in Couette cells. We demonstrate that these solutions are much richer than in rectangular symmetries. Even for uniform media, stress chains are found to curve, broaden away from the stress source, attenuate and leak stress into a cone of influence. Most spectacularly, stress chains may bend back and transmit forces oppositely to the original direction. None of these phenomena arises in solutions for uniform media in Cartesian coordinates. We further analyse non-uniform media, which exhibit chain branching and stress leakage from the chains. These results are directly relevant to the many experiments on granular materials, carried out in Couette cells. They also shed light on, and are supported by, hitherto unexplained experimental observations of curved and back-bending chains, which we point out. In particular, we use our results to provide a new interpretation for the pattern of slip lines observed experimentally.