Properties of layer-by-layer vector stochastic models of force fluctuations in granular materials

TL;DR

This paper investigates stochastic lattice models for granular force distributions, revealing that while vertical forces align with existing models, horizontal forces exhibit asymmetry influenced by model specifics.

Contribution

It introduces a layer-by-layer stochastic modeling approach that incorporates force and torque balance constraints in granular materials.

Findings

Vertical force distribution matches scalar q model predictions

Horizontal force distribution is asymmetric and model-dependent

Vertical forces are robust across different implementations

Abstract

We attempt to describe the stress distributions of granular packings using lattice-based layer-by-layer stochastic models that satisfy the constraints of force and torque balance and non-tensile forces at each site. The inherent asymmetry in the layer-by-layer approach appears to lead to an asymmetric force distribution, in disagreement with both experiments and general symmetry considerations. The vertical force component probability distribution is robust and in agreement with predictions of the scalar q model while the distribution of horizontal force components is qualitatively different and depends on the details of implementation.