Force propagation in isostatic granular packs

TL;DR

This study examines force propagation in frictionless, isostatic granular packs at the jamming transition, revealing that such packs do not necessarily follow the null stress law and are highly sensitive to boundary conditions.

Contribution

The paper demonstrates that isotropic isostatic granular packs can exhibit irregular responses and do not always obey the null stress law, challenging previous assumptions.

Findings

Isotropic packs show divergent responses to point forces.

Adding a boundary stabilizes the response, making it more regular.

Null stress rays are not observed in stabilized, isostatic packs.

Abstract

We investigate how forces spread through frictionless granular packs at the jamming transition. Previous work has indicated that such packs are isostatic, and thus obey a null stress law which, independent of the packing history, causes rays of stress to propagate away from a point force at oblique angles. Prior verifications of the null stress law have used a sequential packing method which yields packs with anisotropic packing histories. We create packs without this anisotropy, and then later break the symmetry by adding a boundary. Our isotropic packs are very sensitive, and their responses to point forces diverge wildly, indicating that they cannot be described by any continuum stress model. We stabilize the packs by supplying an additional boundary, which makes the response much more regular. The response of the stabilized packs resembles what one would expect in a hyperstatic pack, despite the isostatic bulk. The expected stress rays characteristic of null stress behavior are not present. This suggests that isostatic packs do not need to obey a null stress condition. We argue that the rays may arise instead from more simple geometric considerations, such as preferred contact angles between beads.