A variational integrator for the discrete element method

de Klerk, D. N., Shire, T. , Gao, Z. , McBride, A. T. , Pearce, C. J. and Steinmann, P. (2022) A variational integrator for the discrete element method. Journal of Computational Physics, 462, 111253. (doi: 10.1016/j.jcp.2022.111253)

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.

• Item Type: Articles
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Steinmann, Professor Paul and McBride, Professor Andrew and Gao, Dr Zhiwei and de Klerk, Dr David and Shire, Dr Thomas and Pearce, Professor Chris
• Authors: de Klerk, D. N., Shire, T., Gao, Z., McBride, A. T., Pearce, C. J., and Steinmann, P.
• College/School: College of Science and Engineering > School of Engineering > Infrastructure and Environment
• Journal Name: Journal of Computational Physics
• Publisher: Elsevier
• ISSN: 0021-9991
• ISSN (Online): 1090-2716
• Published Online: 27 April 2022
• Copyright Holders: Copyright © 2022 The Author(s).
• First Published: First published in Journal of Computational Physics 462:111253
• Publisher Policy: Reproduced under a Creative Commons licence

Project Code	Award No	Project Name	Principal Investigator	Funder's Name	Funder Ref	Lead Dept
300129		Strategic Support Package: Engineering of Active Materials by Multiscale/Multiphysics Computational Mechanics	Christopher Pearce	Engineering and Physical Sciences Research Council (EPSRC)	EP/R008531/1	ENG - Infrastructure & Environment