The toy-model of the Boltzmann type equation for the contact force distribution in disordered packings of particles

TL;DR

This paper introduces a simplified Boltzmann-type model to analytically describe the distribution of contact forces in disordered particle packings, successfully deriving the experimentally observed exponential distribution.

Contribution

It presents a novel toy-model of a Boltzmann-type equation for contact force distribution in disordered packings, enabling analytical insights.

Findings

Derived the exponential distribution of contact forces

Formulated a statically determinate problem for contact force analysis

Provided an analytical approach matching experimental observations

Abstract

The packing of hard-core particles in contact with their neighbors is considered as the simplest model of disordered particulate media. We formulate the statically determinate problem which allows analytical investigation of the statistical distribution of contact force magnitude. The toy-model of the Boltzmann type equation for the probability of contact force distribution is formulated and studied. An experimentally observed exponential distribution is derived.