Statistical mechanics of granular materials: stress propagation and distribution of contact forces

Abstract

 In a static granular material all particles are touching their neighbours and given a sufficiently high density a jammed state results. A new approach which employs statistical-mechanical concepts is offered for the description of such states. We investigate the simplest statically determinate problem and derive equations of stress propagation. The simplest Boltzmann type equation for the probability of contact force distribution is formulated and solved for model packings. The theory predicts a distribution for the probability of finding a contact force of magnitude f as e ^{− f / ¯f} which is in a good agreement with experimental data. We also propose a pathway to calculating the macroscopic stress tensor as a function of compactivity in a static and slowly sheared granular media.