Discrete element method: Difference between revisions

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The term '''discrete element method''' (DEM) is a family of [[numerical analysis|numerical]] methods for computing the motion of a large number of particles like molecules or grains of sand. The method was originally applied by [[Peter A. Cundall | Cundall]] in [[1971]] to problems in rock mechanics. The theoretical basis of the method was detailed by [[John R. Williams | Williams]], [[Grant Hocking | Hocking]], and [[Graham Mustoe| Mustoe]] in [[1985]] who showed that DEM could be viewed as a generalized finite element method. Its applications to geomechanics problems is described in the book ''Numerical Modeling in Rock Mechanics'', by Pande, G., Beer, G. and Williams, J.R.. Good sources detailing research in the area are to be found in the 1st, 2nd and 3rd International ConferenceConferences on Discrete Element Methods. Journal articles reviewing the state of the art have been published by [[John R. Williams | Williams]], and [[Nenad Bicanic| Bicanic]] (see below). A comprehensive treatment of the combined Finite Element-Discrete Element Method is contained in the book ''The Combined Finite-Discrete Element Method'' by [[Ante Munjiza | Munjiza]]. The method is sometimes called ''[[molecular dynamics]]'' (MD), even when the particles are not molecules. However, in contrast to molecular dynamics the method can be used to model particles with non-spherical shape. The various branches of the DEM family are the [[distinct element method]] proposed by [[Peter A. Cundall | Cundall]] in [[1971]], the [[generalized modal finite element method]]proposed by [[Grant Hocking | Hocking]], [[John R. Williams | Williams]] and [[Graham Mustoe| Mustoe]] in [[1985]],the [[discontinuous deformation analysis]] (DDA) proposed by [[Gen-hua Shi | Shi]] in [[1988]] and the finite-discrete element method proposed by [[Ante Munjiza| Munjiza]] and [[Roger Owen| Owen]] in [[2004]].

Discrete element methods are processor intensive and this limits either the length of a simulation 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. An alternative to treating all particles separately is to treat the material as a continuum and use [[computational fluid dynamics]].

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* P.A. Cundall, O.D.L. Strack, A distinct element model for granular assemblies. ''Geotechnique,'' '''29''':47–65, 1979.

* Williams, J.R., Hocking, G., and Mustoe, G.G.W., “The Theoretical Basis of the Discrete Element Method,” NUMETA 1985, Numerical Methods of Engineering, Theory and Applications, A.A. Balkema, Rotterdam, January 1985

* Shi, G, Discontinuous deformation analysis - A new numerical model for the statics and dynamics of deformable block structures, 16pp. In ''1st U.S. Conf. on Discrete Element Methods'', Golden. CSM Press: Golden, CO, 1989.

* Williams, J.R. and Pentland, A.P., "Superquadric and Modal Dynamics for Discrete Elements in Concurrent Design," National Science Foundation Sponsored 1st U.S. Conference of Discrete Element Methods, Golden, CO, October 19-20, 1989.

* Pande, G., Beer, G. and Williams, J.R., ''Numerical Modeling in Rock Mechanics'', John Wiley and Sons, 1990.

* Kawaguchi, T., Tanaka, T. and Tsuji, Y., [http://www-mupf.mech.eng.osaka-u.ac.jp/paper_pdf/PT98,v96,129 "Numerical simulation of two-dimensional fluidized beds using the discrete element method (comparison between the two- and three-dimensional models)], ''Powder Technology,'' '''96'''(2):129–138, 1998.

* Griebel, Knapek, Zumbusch, Caglar: ''Numerische Simulation in der Molekulardynamik''. Springer, 2004. ISBN 3-540-41856-3.

* Bicanic, Ninad, ''Discrete Element Methods'' in Stein, de Borst, Hughes ''Encyclopedia of Computational Mechanics, Vol. 1''. Wiley, 2004. ISBN 0-470-84699-2.

* Shi, G, Discontinuous deformation analysis - A new numerical model for the statics and dynamics of deformable block structures, 16pp. In ''1st U.S. Conf. on Discrete Element Methods'', Golden. CSM Press: Golden, CO, 1989.

* Kawaguchi, T., Tanaka, T. and Tsuji, Y., [http://www-mupf.mech.eng.osaka-u.ac.jp/paper_pdf/PT98,v96,129 "Numerical simulation of two-dimensional fluidized beds using the discrete element method (comparison between the two- and three-dimensional models)], ''Powder Technology,'' '''96'''(2):129–138, 1998.

* Pande, G., Beer, G. and Williams, J.R., ''Numerical Modeling in Rock Mechanics'', John Wiley and Sons, 1990.

* 2nd International Conference on Discrete Element Methods, Editors Williams, J.R. and Mustoe, G.G.W., IESL Press, 1992 ISBN 0-918062-88-8

* Williams, J.R. and O’Connor, R., ''Discrete Element Simulation and the Contact Problem,'' Archives of Computational Methods in Engineering, Vol. 6, 4, 279-304, 1999