Steady state of tapped granular polygons

TL;DR

This study investigates how the packing density of tapped granular polygons varies with tapping intensity, revealing shape-dependent packing efficiencies and a sharp transition for polygons with more than 13 vertices.

Contribution

It introduces a discrete element method analysis of tapped granular polygons, highlighting shape effects and a novel transition in packing behavior for polygons with many vertices.

Findings

Polygon shapes tessellate and pack more densely.

A sharp transition occurs for polygons with >13 vertices.

Density fluctuations align with recent experimental results.

Abstract

The steady state packing fraction of a tapped granular bed is studied for different grain shapes via a discrete element method. Grains are monosized regular polygons, from triangles to icosagons. Comparisons with disk packings show that the steady state packing fraction as a function of the tapping intensity presents the same general trends in polygon packings. However, better packing fractions are obtained, as expected, for shapes that can tessellate the plane (triangles, squares and hexagons). In addition, we find a sharp transition for packings of polygons with more than 13 vertices signaled by a discontinuity in the packing fraction at a particular tapping intensity. Density fluctuations for most shapes are consistent with recent experimental findings in disk packing; however, a peculiar behavior is found for triangles and squares.