Smooth Convex Three-Dimensional Particle for the Discrete-Element Method

Abstract

Stable and efficient algorithms are presented for a three-dimensional particle for discrete-element simulations. The particle, termed an “ovoid,” approximates an axisymmetric ellipsoid but is composed of two spherical caps and a middle torus section. The particle is smooth and strictly convex, and both prolate and oblate shapes are possible. Contact inquiry between two ovoids involves finding the minimum distance between two circles in three-dimensional space, and an efficient iterative algorithm is applied to this purpose. Computer trials show that the algorithms are stable and that runtimes are only modestly longer than for assemblies of spheres.