Multi-sphere shape generator for DEM simulations of complex-shaped particles

TL;DR

It is shown that, for a given number of spheres, MSS provides a closer approximation to the target shape at lower computational costs than other DEM multi-sphere particle generators reported in the literature.

Abstract

MSS is an algorithm to determine the radii and positions of spheres that fill a given volume. In the context of granular materials, MSS is a particle generator for DEM simulations of complex-shaped particles. Here, each particle of a given shape is represented by a set of spheres that collectively approximate the particle. This technique of particle shape representation is often referred to as the multi-sphere approach. We show that, for a given number of spheres, MSS provides a closer approximation to the target shape at lower computational costs than other DEM multi-sphere particle generators reported in the literature.

Figures (11)

• Figure 1: Flowchart of the MSS algorithm
• Figure 2: 3D target shape (a), a 2D voxelized and binarized array through a section along the blue plane (b), and the corresponding 2D Euclidean Distance Transform (c). The crosses indicate the local maxima of $E$ in pixel resolution. Comparison with the 3D target shape suggests that these maxima approximate the optimal location for three of the spheres to be determined.
• Figure 3: Computation of the location $i^\varoast$ of a local maximum of E at sub-voxel resolution. (a) specifies the considered data points. (b) and (c) illustrate the pairs of straight lines $(g_{-2,-1};g_{0,1})$ and $(g_{-1,0};g_{1,2})$, defining $i^\varoast_a$ and $i^\varoast_b$ respectively.
• Figure 4: Section of $E$ along the $i-j$ plane. Black curves show iso-lines of constant E. Black dot: center of the grey shaded voxel $i^\ast,j^\ast,k^\ast$ (location of a local $E$ maximum in voxel resolution). Red dot: $\hat{E}$ maximum in sub-voxel resolution $(i^\varoast,j^\varoast,k^\varoast)$; green dot: true yet unknown location of the $E$ maximum.
• Figure 5: Sub-voxel precision versus voxel precision. (a) voxelized and binarized 2D section through a target shape. (b) Location of the maximum of $E$ in voxel precision, $\left(h i^\ast, h j^\ast, h k^\ast\right)$ and a circle of radius $h E_{i^\ast j^\ast k^\ast}$. (c) Location of the maximum of $E$ in sub-voxel precision, $\vec{r}^{\,\varoast}$, and the red circle of radius $E^\varoast$