Force Distribution in a Granular Medium

TL;DR

This study systematically measures the normal force distribution in granular materials under compression, revealing a universal exponential decay for forces above the mean, unaffected by system history or boundary conditions.

Contribution

It provides the first comprehensive experimental characterization of force distributions in 3D granular packings, proposing an empirical model consistent with simulations.

Findings

Force distribution is nearly uniform below the mean force.

Distribution decays exponentially for forces above the mean.

Shape and decay constant are unaffected by system history or boundary conditions.

Abstract

We report on systematic measurements of the distribution of normal forces exerted by granular material under uniaxial compression onto the interior surfaces of a confining vessel. Our experiments on three-dimensional, random packings of monodisperse glass beads show that this distribution is nearly uniform for forces below the mean force and decays exponentially for forces greater than the mean. The shape of the distribution and the value of the exponential decay constant are unaffected by changes in the system preparation history or in the boundary conditions. An empirical functional form for the distribution is proposed that provides an excellent fit over the whole force range measured and is also consistent with recent computer simulation data.