Three-dimensional modelling of discrete particles by superellipsoids

Discrete Elements are used for the simulation of granular materials (sand, ballast) as well as for molecular assemblies. Circles (2D) and spheres (3D) are often used in literature on the Discrete Element Method (DEM) however they represent a strong idealisation of the real geometry. Superellipsoids provide the opportunity to generate a wide variety of three-dimensional geometrical shapes (e.g. sphere, cube, cylinder). The motion of each particle is described by means of rigid body dynamics. Suitable numerical integration methods are necessary which are able to conserve the essential physical quantities like momentum energy etc.. Possible choices are e.g. the explicit Verlet-Leapfrog method for the translation and the explicit fourth order Runge-Kutta method for the rotation. The implemented contact formulation takes damping as well as friction into account. Efficient implementation of the contact search is the main aim of this part of the work. It is subdivided into the neighbourhood search and the local search. A bisection algorithm is used to calculate the gap between two superellipsoids within the search. For the neighbourhood search two binning algorithms were implemented and compared for several packages of particles. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)