Combined 3D thinning and greedy algorithm to approximate realistic particles with corrected mechanical properties

Abstract

The shape of irregular particles has significant influence on micro-and macro-scopic behaviour of granular systems. This paper presents a combined 3D thinning and greedy set-covering algorithm to approximate realistic particles with a clump of overlapping spheres for discrete element method (DEM) simulations. First, the particle medial surface (or surface skeleton), from which all candidate (maximal inscribed) spheres can be generated, is computed by the topological 3D thinning. Then, the clump generation procedure is converted into a greedy set-covering (SCP) problem.To correct the mass distribution due to highly overlapped spheres inside the clump, linear programming (LP) is used to adjust the density of each component sphere, such that the aggregate properties mass, center of mass and inertia tensor are identical or close enough to the prototypical particle. In order to find the optimal approximation accuracy (volume coverage: ratio of clump's volume to the original particle's volume), particle flow of 3 different shapes in a rotating drum are conducted. It was observed that the dynamic angle of repose starts to converge for all particle shapes at 85% volume coverage (spheres per clump < 30), which implies the possible optimal resolution to capture the mechanical behaviour of the system.

A novel procedure for medial axis reconstruction of vessels from Medical Imaging segmentation

“…A second category of algorithms relates to the possibility of extracting information on the central axis of a discrete figure, using the distance function directly. In fact, the latter contains information on the point distance of each element from the edge, which makes it possible to identify the axis through the identification of an area of symmetry in the distribution of distances [ [29] , [30] , [31] ]. This type of formulation appears extremely efficient from a computational point of view, being robust with respect to rotation.…”