# Geometrical properties of rigid frictionless granular packings as a function of particle size and shape

## TL;DR

This study uses 3D simulations to explore how particle size and shape affect the packing density and microstructure of frictionless granular assemblies, revealing shape and polydispersity influences on solid fraction and order.

## Contribution

It provides new insights into the effects of particle shape and polydispersity on granular packing properties, confirming the isostatic conjecture and the impact of particle reorientation.

## Key findings

- Disordered packings of pinacoids achieve higher solid fractions than spherical packings.
- Solid fraction increases with bidispersity, peaking at 30% small particles.
- Particle shape has a minor effect compared to polydispersity on packing density.

## Abstract

Three-dimensional discrete numerical simulation is used to investigate the properties of close-packed frictionless granular assemblies as a function of particle polydispersity and shape. Unlike some experimental results, simulations show that disordered packings of pinacoids (eight-face convex polyhedron) achieve higher solid fraction values than amorphous packings of spherical or rounded particles, thus fulfilling the analogue of Ulam's conjecture stated by Jiao and co-workers for random packings [Y. Jiao and S. Torquato, Phys. Rev. E $\textbf{84}$, $041309$ ($2011$)]. This seeming discrepancy between experimental and numerical results is believed to lie with difficulties in overcoming interparticle friction through experimental densification processes. Moreover, solid fraction is shown to increase further with bidispersity and peak when the volume proportion of small particles reaches $30\%$. Contrarywise, substituting up to $50\%$ of flat pinacoids for isometric ones yields solid fraction decrease, especially when flat particles are also elongated. Nevertheless, particle shape seems to play a minor role on packing solid fraction compared to polydispersity. Additional investigations focused on the packing microstructure confirm that pinacoid packings fulfill the isostatic conjecture and that they are free of order except beyond $30$ to $50\%$ of flat or flat \& elongated polyhedra in the packing. This order increase progressively takes the form of a nematic phase caused by the reorientation of flat or flat \& elongated particles to minimize the packing potential energy. Simultaneously, this reorientation seems to increase the solid fraction value slightly above the maximum achieved by monodisperse isometric pinacoids, as well as the coordination number. Finally, partial substitution of elongated pinacoids for isometric ones has limited effect on packing solid fraction or order.