Force distribution in granular media studied by an energy method based on statistical mechanics

TL;DR

This paper introduces a statistical mechanics-based method to determine force distribution in static granular media, revealing that elastic energy distribution follows a Bose-Einstein law, enabling new analytical approaches.

Contribution

It proposes a novel energy-based statistical mechanics method to analyze force distributions in granular materials, linking elastic energy division to Bose-Einstein statistics.

Findings

Elastic potential energy distribution follows Bose-Einstein law

Force distribution can be derived from energy distribution

Method validated with DEM simulations

Abstract

In the present letter a method to find a proper expression for the force distribution inside a granular sample in static equilibrium is proposed. The method is based in statistical mechanics and the force distribution is obtained by studying how the potential elastic energy is divided among the different contacts between grains. It is found with DEM simulations with spheres that the elastic potential energy distribution follows a Bose Einstein law from which the force distribution is deduced. The present letter open a way in which granular materials can be studied with the tools provided by statistical mechanics.