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

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 $θ_R$ (finite slopes). Furthermore, these piles are stable under tilting by an angle smaller than a non-zero tilting angle $θ_T$, showing that $θ_R$ is different from the angle of marginal stability $θ_{MS}$, which is the maximum angle of stable piles. These measured angles are compared to a theoretical approximation. We also measure $θ_{MS}$ by continuously adding particles on the top of a stable pile.