On the application of quaternion‐based approaches in discrete element methods

Abstract

Purpose

Though the problem of resolving translational motion in particle methods is a relatively straightforward task, the complications of resolving rotational motion are non‐trivial. Many molecular dynamics and non‐deformable discrete element applications employ an explicit integration for resolving orientation, often involving products of matrices, which have well‐known drawbacks. The purpose of this paper is to investigate commonly used algorithms for resolving rotational motion and describe the application of quaternion‐based approaches to discrete element method simulations.

Design/methodology/approach

Existing algorithms are compared against a quaternion‐based reparameterization of both the central difference algorithm and the approach of Munjiza et al. for finite/discrete element modeling (FEM/DEM) applications for the case of torque‐free precession.

Findings

The resultant algorithms provide not only guaranteed orthonormality of the resulting rotation but also allow assumptions of small‐angle rotation to be relaxed and the use of a more accurate Taylor expansion instead.

Originality/value

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.

Citation

Johnson, S.M., Williams, J.R. and Cook, B.K. (2009), "On the application of quaternion‐based approaches in discrete element methods", Engineering Computations, Vol. 26 No. 6, pp. 610-620. https://doi.org/10.1108/02644400910975414