Numerical simulations of granular assemblies with three-dimensional ellipsoid-shaped particles

Abstract

A numerical model to simulate the behaviour of idealized rounded granular materials in conditions of static equilibrium using assemblies of ellipsoid-shaped particles is developed. The model is based on the discrete element method (DEM) which simulates the state of an assembly of particles through tracing the motion of constitutive particles and their interactions at contact points.

The development of the model for ellipsoids consisted mainly of implementing an inter-ellipsoid contact detection algorithm to detect and calculate characteristics of contacts between ellipsoids. The algorithm was implemented in an existing discrete element program for spheres (TRUBAL).

A modified program TRUBAL was utilized to perform constant pressure deviatoric compression tests on a 1000 ellipsoids' assembly. The results of these tests showed that the characterization of anisotropy by symmetric and deviatoric second-order tensors applies to assemblies of ellipsoids. However, the provision for an additional fourth-order anisotropy tensor can become necessary in some cases (for example, to describe anisotropy in average tangential contact forces).

A Stress-Force-Fabric relationship between the macroscopic stress tensor and anisotropies in contact forces and in fabric was derived for ellipsoids. Particle shape has an increasingly higher effect on the relationship as deformation progresses. A form of force-fabric joint anisotropy contribution, usually negligibly small in two dimension, was found to play an important role in shaping the stress behaviour.

Rotations of ellipsoids were analyzed from a statistico-geometrical perspective and found to influence the (contact formation/disintegration)-related anisotropy. Ellipsoids have a tendency to create more contacts around their flat areas than any other areas. They use their rotational ability to maintain a near-constant distribution of contacts around their surfaces irrespective of the stress and deformation levels.