Discrete element method

Discrete element methods (DEM) comprise a family of related mathematical tools for determining the kinematic behavior of finite-sized particles. As defined by Cundall, discrete element methods allow:

1. finite displacement, rotation and separation of elements, and
   
2. new particle contacts are recognized algorithmically as the simulation proceeds.

Two prominent members of the DEM family are the distinct element method proposed by Cundall in 1971, and the discontinuous deformation analysis (DDA) proposed by Shi in 1988.

Discrete element modeling (also abbreviated to DEM) is a computational method for simulating the behaviour of a systems of discrete objects (particles). It tracks every individual particle (and any bounding geometry) subjecting them to contact and body forces, and updating the system incrementally in time. As opposed to CFD a much smaller time step is necessary to accurately simulate the contacts between objects, typically of the order ot 10^-5 - 10^-6. DEM software allows the user to understand existing behaviour and make predictions on new systems. Typical industries using DEM are:

1. Mining
2. Pharmaceutical
3. Oil and gas
4. Agriculture and food handling
5. Chemical

DEM is processor intensive and this limits either the length of a simulation (given the small timestep) or the number of particles. Advances in the software are beginning to take advantage of parallel processing capabilities (shared or distributed systems) to scale up the number of particles or length of the simulation.

Bibliography

• P.A. Cundall, O.D.L. Strack: A distinct element model for granular assemblies. Geotechnique, 29:47,65, 1979.
• Griebel, Knapek, Zumbusch, Caglar: Numerische Simulation in der Molekulardynamik. Springer, 2004. ISBN 3-540-41856-3
• Nenad Bicanic: Discrete Element Methods in Stein, de Borst, Hughes Encyclopedia of Computational Mechanics, Vol. 1. Wiley, 2004. ISBN 0-470-84699-2
• Shi, G (1989). Discontinuous deformation analysis - A new numerical model for the statics and dynamics of deformable block structures. In 1st U.S. Conf. on Discrete Element Methods, Golden. CSM Press: Golden, CO, 16pp.
• Kawaguchi, T., Tanaka, T. and Tsuji, Y., "Numerical simulation of two-dimensional fluidized beds using the discrete element method (comparison between the two- and three-dimensional models)," Powder Technology, Vol. 96, No. 2 (1998), pp. 129-138.
• itasca DEM pubs.html

Software

Open source and non-commercial software:

• BALL & TRUBAL (1979-1980) distinct element method (fortran code), authored by Colin Thornton.
• SDEC Spherical Discrete Element Code.
• YADE Yet Another Dynamic Engine, second incarnation of SDEC written from ground-up, GPL license.

Commercially available DEM software packages include PFC3D and EDEM:

• PFC2D and PFC3D (Particle Flow Code in 2 Dimensions; Particle Flow Code in 3 Dimensions)
• EDEM (DEM Solutions Ltd.)