Calculating rotational motion in discrete element modelling of arbitrary shaped model objects

Application of the discrete element method (DEM) to real scale engineering problems involving three-dimensional modelling of large, non-spherical particles must consider the inertia tensor and temporal change in the orientation of the particles when calculating the rotational motion. This factor has commonly been neglected in discrete element modelling although it will significantly influence the dynamic behaviour of non-spherical particles. In this paper two methods, vector transformation and tensor transformation, for calculation of the rotational motion of particles in response to applied moments are presented. The methods consider the inertia tensor and the local object frame of arbitrary shaped particles and suggest solutions for the non-linear Euler equations for calculation of their rotational motion. They are discussed with respect to implementation into a discrete element code and assessed in terms of their accuracy and computational efficiency.