Review and extension of normal force models for the Discrete Element Method

H. Kruggel-Emden, E. Simsek, S. Rickelt, S. Wirtz, V. Scherer
Department of Energy Plant Technology
Ruhr-Universitaet Bochum, Universitaetsstrasse 150,
D-44780 Bochum,
Germany
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Abstract

For the simulation of dense granular systems the Discrete Element Method based on a soft-sphere approach is commonly used. In such simulations collisions between particles take a finite time. The equations of motion are applied for each particle and solved numerically. Therefore models for the forces acting between particles in contact need to be specified. In this paper the focus is set on normal contacts. Based on macroscopic and microscopic accessible parameters like coefficient of restitution, collision time, force, displacement and displacement rate a wide range of commonly used force schemes are reviewed. Results obtained from these commonly used models are compared to experimental data on collisions of different metal alloys, ice and marble as reported in literature. Due to obvious limitations extensions are presented. The new extended models based on linear and non-linear models are compared to experimental data and their accuracy and applicability are discussed. © 2006 Elsevier B.V. All rights reserved

Introduction

Several phenomena in nature as well as many industrial applications involve static or dynamic granular assemblies. Depending on the physical background the number of particles being involved in these assemblies differs largely. Whereas laboratory scale experiments usually involve small numbers of particles, industrial applications like silos may contain several cubic meters of granular material in which the particle number may easily exceed the order of 109 per cubic meter. Phenomena related to nature like avalanches often incorporate hundreds of tons of granular material therefore involving even larger quantities of particles. In general, simulations provide a feasible alternative to experimental investigations. Their better reproducibility, less demand for time and reduced costs are advantageous. In recent years modeling and simulation of particle assemblies have been difficult due to their enormous demand of computer power. With advances in computer processing speed and due to parallel computing the field of industrial applications is nowadays accessible by numerical simulations [1–3]. A very promising approach for modeling particle systems is the Discrete Element Method. It provides a way of simulating systems of an arbitrary number of particles by modeling each particle and its interactions with the surrounding, individually. Depending on the density of the granular system two different approaches are applicable. In low density systems like granular gases the Event Driven (ED) Discrete Element Method [4] is most feasible. Here it can be assumed, that the collision time is of much lower magnitude than the mean free flight time and collisions higher than binary ones are excluded. In case that these assumptions are violated the Molecular Dynamics (MD) Discrete Element Approach [5] finds application. Originally this approach was designed for the simulation of particles on the atomic and molecular level. By definition of pairwise potentials information on the thermodynamics of fluids were accessible otherwise only available by statistical means [6,7]. To perform a MD simulation the initial conditions of the particle system need to be specified.



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