A poly‐ellipsoid particle for non‐spherical discrete element method

The purpose of this paper is to present a simple non‐symmetric shape, the poly‐ellipsoid, to describe particles in discrete element simulations that incur a computational cost similar to ellipsoidal particles.

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 poly‐ellipsoid 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.

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.

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.

The poly‐ellipsoid particle is a computational device to represent non‐spherical particles in DEM models.