Optimizing Packing Fraction in Granular Media Composed of Overlapping Spheres

TL;DR

This study combines molecular dynamics simulations and artificial evolution to identify particle shapes, specifically planar triangular particles, that achieve high packing fractions in random packings, validated through experiments with 3D-printed models.

Contribution

It introduces a novel method for optimizing particle shape for packing density using overlapping spheres and evolutionary algorithms, discovering highly efficient packing shapes.

Findings

Triangular particles achieve packing fractions around 0.73.

Simulations are validated by experiments with 3D-printed particles.

Triangular particles outperform many known shapes in packing efficiency.

Abstract

What particle shape will generate the highest packing fraction when randomly poured into a container? In order to explore and navigate the enormous search space efficiently, we pair molecular dynamics simulations with artificial evolution. Arbitrary particle shape is represented by a set of overlapping spheres of varying diameter, enabling us to approximate smooth surfaces with a resolution proportional to the number of spheres included. We discover a family of planar triangular particles, whose packing fraction of $\phi \sim$ 0.73 outpaces almost all reported experimental results for random packings of frictionless particles. We investigate how $\phi$ depends on the arrangement of spheres comprising an individual particle and on the smoothness of the surface. We validate the simulations with experiments using 3D-printed copies of the simplest member of the family, a planar particle consisting of three overlapping spheres with identical radius. Direct experimental comparison with 3D-printed aspherical ellipsoids demonstrates that the triangular particles pack exceedingly well not only in the limit of large system size but also when confined to small containers.