Alignment and anisotropy of stresses in disordered granular media

TL;DR

This paper introduces a minimal force-balance model to analyze stress states in disordered granular media, successfully predicting stress alignment and anisotropy that match simulation data, advancing understanding of the statistical mechanics of such systems.

Contribution

The paper presents a novel minimal force-balance model that captures stress structure and anisotropy in disordered granular packings, validated against simulation data.

Findings

Model accurately predicts stress alignment in granular packings.

Quantitative agreement with hopper and shear flow simulations.

Highlights the role of geometric motifs in disordered systems.

Abstract

Characterizing the degeneracy of local stress states is a central challenge in obtaining the complete statistical mechanics of disordered media. Here, we introduce a minimal force-balance model for isolated granular clusters to probe the structure of the stress space through principal stress orientation and stress anisotropy. We further show that when complemented by physically motivated pairwise constraints, the model produces predictions for the stress alignment in packings of repulsive hard spheres. We compare these predictions against simulation data for grains in hopper and simple shear flows, finding quantitative agreement. This demonstrates the promise of modeling bulk athermal disordered systems through the combinatorics of few primitive geometric motifs.