Molecular dynamics simulations of complex shaped particles using Minkowski operators

TL;DR

This paper introduces a novel method combining Minkowski operators with molecular dynamics to simulate complex-shaped particles efficiently, enabling accurate energy-conserving simulations of granular materials.

Contribution

It extends molecular dynamics with Minkowski operators and Voronoi-Minkowski diagrams, providing a new approach for simulating complex-shaped particles with improved efficiency.

Findings

Efficient simulation of complex-shaped particles using extended Verlet lists.

Generation of random packings with tunable particle roundness.

Validation of energy conservation in dissipative granular material simulations.

Abstract

The Minkowski operators (addition and substraction of sets in vectorial spaces) has been extensively used for Computer Graphics and Image Processing to represent complex shapes. Here we propose to apply those mathematical concepts to extend the Molecular Dynamics (MD) Methods for simulations with complex-shaped particles. A new concept of Voronoi-Minkowski diagrams is introduced to generate random packings of complex-shaped particles with tunable particle roundness. By extending the classical concept of Verlet list we achieve numerical efficiencies that do not grow quadratically with the body number of sides. Simulations of dissipative granular materials under shear demonstrate that the method complies with the first law of thermodynamics for energy balance.