On the application of quaternionbased approaches in discrete element methods

Purpose Though the problem of resolving translational motion in particle methods is a relatively straightforward task, the complications of resolving rotational motion are nontrivial. Many molecular dynamics and nondeformable discrete element applications employ an explicit integration for resolving...

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Bibliographic Details
Published in:Engineering computations 2009-08, Vol.26 (6), p.610-620
Main Authors: Johnson, Scott M., Williams, John R., Cook, Benjamin K.
Format: Article
Language:English
Subjects:
Dynamics
Integration
Rotation measurement
Rotational motion
Online Access:Get full text
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Summary:Purpose Though the problem of resolving translational motion in particle methods is a relatively straightforward task, the complications of resolving rotational motion are nontrivial. Many molecular dynamics and nondeformable discrete element applications employ an explicit integration for resolving orientation, often involving products of matrices, which have wellknown drawbacks. The purpose of this paper is to investigate commonly used algorithms for resolving rotational motion and describe the application of quaternionbased approaches to discrete element method simulations. Designmethodologyapproach Existing algorithms are compared against a quaternionbased reparameterization of both the central difference algorithm and the approach of Munjiza et al. for finitediscrete element modeling FEMDEM applications for the case of torquefree precession. Findings The resultant algorithms provide not only guaranteed orthonormality of the resulting rotation but also allow assumptions of smallangle rotation to be relaxed and the use of a more accurate Taylor expansion instead. Originalityvalue The approaches described in this paper balance ease of implementation within existing explicit codes with computational efficiency and accuracy appropriate to the order of error in many discrete element method simulations.
ISSN:0264-4401
DOI:10.1108/02644400910975414