Discrete element method: Difference between revisions

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==The DEM family==

The various branches of the DEM family are the [[distinct element method]] proposed by [[Peter A. Cundall]] and Otto D. L. Strack in 1979,<ref>{{Cite journal|last1=Cundall|first1=Peter. A.|last2=Strack|first2=Otto D. L.|date=1979|title=Discrete numerical model for granular assemblies|url=http://websrv.cs.umt.edu/classes/cs477/images/0/0e/Cundall_Strack.pdf|journal=Géotechnique|volume=29|issue=1|pages=47–65|doi=10.1680/geot.1979.29.1.47}}</ref> the [[generalized discrete element method]] {{harv|Williams|Hocking|Mustoe|1985}}<ref>https://docs.google.com/document/d/1ljujwjib2h2NwYksdh9wONZhEpNljGQdAmehXANFJw4/edit?usp=sharing</ref>, the [[Discontinuous Deformation Analysis|discontinuous deformation analysis]] (DDA) {{harv|Shi|1992}} and the finite-discrete element method concurrently developed by several groups (e.g., [[Ante Munjiza|Munjiza]] and [[Roger Owen (mathematician)|Owen]]). The general method was originally developed by Cundall in 1971 to problems in rock mechanics. {{harvtxt|Williams|Hocking|Mustoe|1985}}<ref>https://docs.google.com/document/d/1ljujwjib2h2NwYksdh9wONZhEpNljGQdAmehXANFJw4/edit?usp=sharing</ref> showed that DEM could be viewed as a generalized finite element method, allowing deformation and fracturing of particles. Its application to geomechanics problems is described in the book ''Numerical Methods in Rock Mechanics'' {{harv|Williams|Pande|Beer|1990}}. The 1st, 2nd and 3rd International Conferences on Discrete Element Methods have been a common point for researchers to publish advances in the method and its applications. Journal articles reviewing the state of the art have been published by Williams and O'Connnor,{{harv|Williams|O'Connor|1999}} [[Nenad Bicanic|Bicanic]], and [[Antonio Bobet|Bobet]] et al. (see below). A comprehensive treatment of the combined Finite Element-Discrete Element Method is contained in the book ''The Combined Finite-Discrete Element Method''.<ref name="Munjiza 2004">{{cite book |last1=Munjiza |first1=Ante |title=The Combined Finite-Discrete Element Method |date=2004 |publisher=Wiley |___location=Chichester |isbn=978-0-470-84199-0}}</ref>

[[File:Cundall DEM.gif|thumb|upright=1|Discrete-element simulation with particles arranged after a photo of [[Peter A. Cundall]]. As proposed in Cundall and Strack (1979), grains interact with linear-elastic forces and Coulomb friction. Grain kinematics evolve through time by temporal integration of their force and torque balance. The collective behavior is self-organizing with discrete shear zones and angles of repose, as characteristic to cohesionless granular materials.]]

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* {{cite book|last1=Griebel|first1=Michael|title=Numerische Simulation in der Moleküldynamik |date=2003 |publisher=Springer |___location=Berlin |isbn=978-3-540-41856-6|display-authors=etal}}

* {{cite journal |last1=Williams |first1=J. R. |last2=Hocking |first2=G. |last3=Mustoe |first3=G. G. W. |title=The Theoretical Basis of the Discrete Element Method |journal=NUMETA 1985, Numerical Methods of Engineering, Theory and Applications |publisher=A.A. Balkema |___location=Rotterdam |date=January 1985 }}

* {{cite book |last1=Williams |first1=GJ.N R. |last2=Pande |first2=G. |last3=Beer |first3=J.R. |title=Numerical Methods in Rock Mechanics |date=1990 |publisher=Wiley |___location=Chichester |isbn=978-0471920212 }}

* {{cite book |editor1-last=Radjai |editor1-first=Farang |editor2-last=Dubois |editor2-first=Frédéric |title=Discrete-element modeling of granular materials |date=2011 |publisher=Wiley-ISTE |___location=London |isbn=978-1-84821-260-2 |url=http://www.iste.co.uk/index.php?f=x&ACTION=View&id=384,}}

* {{cite book |last1=Pöschel |first1=Thorsten |last2=Schwager |first2=Thoms |title=Computational Granular Dynamics: Models and Algorithms |date=2005 |publisher=Springer |___location=Berlin |isbn=978-3-540-21485-4}}