Statistical Mechanics of Stress Transmission in Disordered Granular Arrays

TL;DR

This paper develops a statistical-mechanical framework to understand how stress propagates in disordered granular materials, providing fundamental equations and validating with isotropic array solutions.

Contribution

It introduces a novel statistical-mechanical theory for stress transmission in disordered granular arrays, deriving fundamental stress equilibrium equations from microscopic force and torque balances.

Findings

Derived fundamental stress equilibrium equations from microscopic principles.

Validated the theory by solving stress distribution in isotropic arrays.

Provided a new approach to analyze stress in disordered granular systems.

Abstract

We give a statistical-mechanical theory of stress transmission in disordered arrays of rigid grains with perfect friction. Starting from the equations of microscopic force and torque balance we derive the fundamental equations of stress equilibrium. We illustrate the validity of our approach by solving the stress distribution of a homogeneous and isotropic array.