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Critical time step for DEM simulations of dynamic systems using a Hertzian contact model
Author(s) -
Burns Shane J.,
Piiroinen Petri T.,
Hanley Kevin J.
Publication year - 2019
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.6056
Subject(s) - nonlinear system , contact mechanics , stability (learning theory) , contact force , hertz , work (physics) , collision , discrete time and continuous time , mathematics , finite element method , computer science , control theory (sociology) , classical mechanics , engineering , physics , mechanical engineering , structural engineering , telecommunications , statistics , control (management) , quantum mechanics , machine learning , artificial intelligence , computer security
Summary The discrete element method (DEM) 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.