Response of a Hexagonal Granular Packing under a Localized External Force

TL;DR

This study investigates how a two-dimensional hexagonal granular packing responds to a localized force, revealing characteristic peak patterns and self-similarity in force transmission.

Contribution

It introduces a statistical approach linking the granular response to a correlated q-model, providing new insights into force distribution in frictionless granular packings.

Findings

Response shows two peaks along lattice directions.

Peak magnitudes decrease with depth, central peak develops.

Self-similarity observed across different system sizes.

Abstract

We study the response of a two-dimensional hexagonal packing of rigid, frictionless spherical grains due to a vertically downward point force on a single grain at the top layer. We use a statistical approach, where each configuration of the contact forces is equally likely. We show that this problem is equivalent to a correlated $q$-model. We find that the response displays two peaks which lie precisely on the downward lattice directions emanating from the point of application of the force. With increasing depth, the magnitude of the peaks decreases, and a central peak develops. On the bottom of the pile, only the middle peak persists. The response of different system sizes exhibits self-similarity.