# Multi-sphere approximation of realistic particles with a combined 3D thinning and greedy algorithm

## TL;DR

This paper presents a novel method combining 3D thinning and greedy algorithms to efficiently approximate realistic particles with minimal spheres, ensuring accurate mechanical properties for DEM simulations.

## Contribution

It introduces a combined 3D thinning and greedy set-covering algorithm for optimal sphere approximation of particles, with density correction for accurate mass and inertia properties.

## Key findings

- Successfully approximates complex particle shapes with minimal spheres.
- Demonstrates improved accuracy in particle-wall contact, settling, and granular flow simulations.
- Uses Rigid3D DEM code for validation, enhancing simulation reliability.

## Abstract

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.