A Model for Force Fluctuations in Bead Packs

TL;DR

This paper presents a theoretical model explaining force fluctuations in granular bead packs, aligning well with experimental and simulation data by considering contact angle variations and force balance constraints.

Contribution

It introduces a detailed force fluctuation model based on contact angles and force balance, matching observed force distributions in granular materials.

Findings

Model reproduces experimental force distribution features

Exact solutions for specific contact angle distributions

Good agreement with numerical simulations

Abstract

We study theoretically the complex network of forces that is responsible for the static structure and properties of granular materials. We present detailed calculations for a model in which the fluctuations in the force distribution arise because of variations in the contact angles and the constraints imposed by the force balance on each bead of the pile. We compare our results for force distribution function for this model, including exact results for certain contact angle probability distributions, with numerical simulations of force distributions in random sphere packings. This model reproduces many aspects of the force distribution observed both in experiment and in numerical simulations of sphere packings.