  This article is the updated version of the paper: "Combined 3D thinning and
greedy algorithm to approximate realistic particles with corrected mechanical
properties, Granular Matter (2019)" by the first author [58]. The main changes
here are (1) a recently developed DEM code Rigid3D is used for the DEM
simulations, instead of the open-source software LIGGGHTS in the original work;
(2) three new validation tests were carried out.
  The main idea of this work is to combine the 3D thinning and greedy
set-covering algorithms for the approximation of realistic particles with
multiple spheres. First, the particle's medial surface (or surface skeleton),
from which all candidate (maximal inscribed) spheres can be generated, is
computed by the topological 3D thinning algorithm. Then, the clump generation
procedure is converted into a greedy set-covering problem. The advantage of
this approach over previous studies is that, with a given particle media
surface and a grid resolution for the discretized particle, a minimum number of
component (or primary) spheres for an MS particle is guaranteed for a maximum
volume coverage, thanks to the combined algorithm. To correct the mass
distribution of an MS particle due to the highly overlapped component spheres,
linear programming (LP) is used to adjust the density of each component sphere,
such that the aggregate properties such as mass, center of mass, and inertia
tensor are identical or close enough to the prototypical particle. We then
demonstrate the capability of the combined algorithm to approximate simple to
complex particle shapes in three test cases: (1) particle-wall contact; (2)
particle settling; and (3) granular flow in a rotating drum.
