An efficient algorithm for granular dynamics simulation with complex-shaped objects

TL;DR

This paper introduces a novel, efficient algorithm for simulating granular materials with complex-shaped particles using Minkowski sums, enabling more realistic modeling of particle shapes and interactions.

Contribution

The paper presents a new simulation method that accurately models complex-shaped particles with improved efficiency and simplicity over existing models.

Findings

The algorithm reduces force calculation complexity to O(N).

Simulation results align with classical statistical mechanics for non-dissipative systems.

The model captures the critical state behavior of dissipative granular materials.

Abstract

The most difficult aspect of the realistic modeling of granular materials is how to capture the real shape of the particles. Here we present a method to simulate granular materials with complex-shaped particles. The particle shape is represented by the classical concept of a Minkowski sum, which permits the representation of complex shapes without the need to define the object as a composite of spherical or convex particles. A well defined interaction force between these bodies is derived. The algorithm for identification of neighbor particles reduces force calculations to O(N), where $N$ is the number of particles. The algorithm is much more efficient, accurate and easier to implement than other models. We investigate the existence of a statistical equilibrium in granular systems with circular non-spherical particles in the collisional. regime. We also investigate the limit state of dissipative granular materials using biaxial test simulations. The results are consistent with the classical assumption of the statistical mechanics for non-dissipative systems, and the critical state theory of soils mechanics for dissipative granular materials.