Optimal shapes of disk assembly in saturated random packings

Area of Science:

• Physics
• Materials Science
• Computational Science

Background:

• Particle morphology significantly impacts granular material packing structures.
• Inverse packing problems are crucial for material design, seeking optimal particle shapes for targeted properties.
• Determining the densest or loosest random packing for specific particle shapes remains a challenge.

Purpose of the Study:

• To identify particle shapes that yield the densest and loosest random packings in a 2D disk assembly model.
• To explore shape optimization within defined species of disk assemblies.
• To provide insights for designing granular materials with specific packing properties.

Main Methods:

• Utilized a genetic algorithm with a unique shape representation method to optimize particle shapes in a continuous shape space.
• Simulated particle packing using the random sequential adsorption process to prevent crystallization.
• Investigated three disk assembly species: congruent tangent disks, incongruent tangent disks, and congruent overlapping disks.

Main Results:

• Identified an isosceles circulo-triangle shape for maximal packing density and an unclosed ring for minimal packing density in saturated random packings.
• Achieved high packing densities of approximately 0.6 with the perfect sno-cone and isosceles circulo-triangle shapes.
• Demonstrated that optimized shapes yield significantly denser packings compared to ellipses.

Conclusions:

• The study successfully identified optimal particle shapes for maximizing and minimizing random packing densities in 2D disk assemblies.
• The findings offer a pathway for the inverse design of granular materials by tailoring particle morphology.
• Optimized shapes like the isosceles circulo-triangle provide a significant improvement over traditional shapes such as ellipses.