Angle of Repose and Angle of Marginal Stability: Molecular Dyanmics of Granular Particles

TL;DR

This paper introduces a realistic static friction model in molecular dynamics simulations of granular particles, revealing that piles have a finite angle of repose and are stable below a certain tilt, distinguishing it from the maximum stable angle.

Contribution

The study implements a Coulomb-based static friction model in MD simulations and distinguishes between the angle of repose and the angle of marginal stability in granular piles.

Findings

Piles have a finite angle of repose $ heta_R$.

Piles are stable under tilting below $ heta_T$.

Measured angles compare well with theoretical predictions.

Abstract

We present an implementation of realistic static friction in molecular dynamics (MD) simulations of granular particles. In our model, to break contacts between two particles, one has to apply a finite amount of force, determined by the Coulomb criterion. Using a two dimensional model, we show that piles generated by avalanches have a {\it finite} angle of repose $\theta_R$ (finite slopes). Furthermore, these piles are stable under tilting by an angle smaller than a non-zero tilting angle $\theta_T$, showing that $\theta_R$ is different from the angle of marginal stability $\theta_{MS}$, which is the maximum angle of stable piles. These measured angles are compared to a theoretical approximation. We also measure $\theta_{MS}$ by continuously adding particles on the top of a stable pile.