A Variational Integrator for the Discrete Element Method

TL;DR

This paper introduces a new implicit variational integrator for the Discrete Element Method that offers comparable accuracy to traditional methods while providing a fully dynamical and energy-minimizing approach, especially useful in quasi-static regimes.

Contribution

The paper develops and tests a novel variational integrator for DEM, bridging dynamic simulation and energy minimization in a unified framework.

Findings

Equivalent accuracy to velocity-Verlet method

Demonstrates long-term stability in simulations

Provides a fully dynamical and energy-consistent scheme

Abstract

A novel implicit integration scheme for the Discrete Element Method (DEM) based on the variational integrator approach is presented. The numerical solver provides a fully dynamical description that, notably, reduces to an energy minimisation scheme in the quasi-static limit. A detailed derivation of the numerical method is presented for the Hookean contact model and tested against an established open source DEM package that uses the velocity-Verlet integration scheme. These tests compare results for a single collision, long-term stability and statistical quantities of ensembles of particles. Numerically, the proposed integration method demonstrates equivalent accuracy to the velocity-Verlet method.