Average stresses and force fluctuations in non-cohesive granular materials

TL;DR

This paper introduces a lattice model for analyzing stress fluctuations in non-cohesive granular materials, ensuring force and torque balance, and aligns with continuum theories for average stresses without assuming constitutive relations.

Contribution

The model extends previous scalar models by incorporating force and torque balance, enabling rapid generation of configurations that match continuum stress predictions.

Findings

Model produces average stress distributions consistent with continuum theories.

Generates force distributions similar to q-model with singular q-distributions.

Allows statistical analysis of large granular systems efficiently.

Abstract

A lattice model is presented for investigating the fluctuations in static granular materials under gravitationally induced stress. The model is similar in spirit to the scalar q-model of Coppersmith et al., but ensures balance of all components of forces and torques at each site. The geometric randomness in real granular materials is modeled by choosing random variables at each site, consistent with the assumption of cohesionless grains. Configurations of the model can be generated rapidly, allowing the statistical study of relatively large systems. For a 2D system with rough walls, the model generates configurations consistent with continuum theories for the average stresses (unlike the q-model) without requiring the assumption of a constitutive relation. For a 2D system with periodic boundary conditions, the model generates single-grain force distributions similar to those obtained from the q-model with a singular distribution of q's.