Polyhedra faster than spheres?

Purpose – The purpose of this paper is to present a new and efficient technique for discrete element modelling using non-convex polyhedral grain shapes. Design/methodology/approach – The efficiency of the technique follows from the use of grains that are dilated versions of the basic polyhedral grain shapes. Dilation of an arbitrary polyhedral grain is accomplished by placing the center of a sphere of fixed radius at every point on the surface. The dilated vertices become sphere segments and the edges become cylinder segments. The sharpness of the vertices and edges can be adjusted by varying the dilation radius. Contacts between two dilated polyhedral grains can be grouped into three categories; vertex on surface, vertex on edge, and edge on edge, or in the grammar of the model, sphere on polygonal surface, sphere on cylinder, and cylinder on cylinder. Simple, closed-form solutions exist for each of these cases. Findings – The speed of the proposed polyhedral discrete element model is compared to similar models using spherical and ellipsoidal grains. The polyhedral code is found to run about 40 percent as fast as an equivalent code using spherical grains and about 80 percent as fast as an equivalent code using ellipsoidal grains. Finally, several applications of the polyhedral model are illustrated. Originality/value – Few examples of discrete element modeling studies in the literature use polyhedral grains. This dearth is because of the perceived complexity of the polyhedral coding challenges and the slow speed of the codes compared to codes for other grain shapes. This paper presents a much simpler approach to discrete element modeling using polyhedral grain shapes.