Critical time-step for DEM simulations of dynamic systems using a Hertzian contact model

Shane J. Burns, Petri T. Piiroinen, Kevin J. Hanley

Research output: Contribution to journalArticlepeer-review

Abstract / Description of output

The discrete element method typically uses an explicit numerical integration scheme to solve the equations of motion. However, like all explicit schemes, the scheme is only conditionally stable, with the stability determined by the size of the time-step. Currently, there are no comprehensive techniques for estimating appropriate DEM time-steps when a nonlinear contact interaction is used. It is common practice to apply a large factor of safety to these estimates to ensure stability which unnecessarily increases the computational cost of these simulations. This work introduces an alternative framework for selecting a stable time-step for nonlinear contact laws, specifically for the Hertz–Mindlin contact law. This approach uses the fact that the discretised equations of motion take the form of a nonlinear map and can be analysed as such. Using this framework, we analyse the effects of both system damping and the initial relative velocity of collision on the critical time-step for a Hertz–Mindlin contact event between spherical particles.
Original languageEnglish
JournalInternational Journal for Numerical Methods in Engineering
Early online date7 Mar 2019
Publication statusE-pub ahead of print - 7 Mar 2019

Keywords / Materials (for Non-textual outputs)

  • DEM
  • Time-step
  • Stability
  • Hertzian contact
  • Damping


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