A polyellipsoid particle for nonspherical discrete element method

• Published in: Engineering computations 2009-08, Vol.26 (6), p.645-657
• Main Authors: Peters, John F., Hopkins, Mark A., Kala, Raju, Wahl, Ronald E.
• Format: Article
• Language: English
• Subjects: Geometric planes and solids; Particle size measurement; Programming languages
• ISSN: 0264-4401
• DOI: 10.1108/02644400910975441

Purpose The purpose of this paper is to present a simple nonsymmetric shape, the polyellipsoid, to describe particles in discrete element simulations that incur a computational cost similar to ellipsoidal particles. Designmethodologyapproach Particle shapes are derived from joining octants of eight ellipsoids, each having different aspect ratios, across their respective principal planes to produce a compound surface that is continuous in both surface coordinate and normal direction. Because each octant of the polyellipsoid is described as an ellipsoid, the mathematical representation of the particle shape can be in the form of either an implicit function or as parametric equations. Findings The particle surface is defined by six parameters vs the 24 parameters required to define the eight component ellipsoids owing to dependencies among parameters that must be imposed to create continuous intersections. Despite the complexity of the particle shapes, the particle mass, centroid and moment of inertia tensor can all be computed in closed form. Practical implications The particle can be implemented in any contact algorithm designed for ellipsoids with minor modifications to determine in which pair of octants the potential contact occurs. Originalityvalue The polyellipsoid particle is a computational device to represent nonspherical particles in DEM models.