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The term '''discrete element method''' (aka, distinct element method or DEM) is a family of [[numerical analysis|numerical]] methods for computing the motion of a large number of particles likeof moleculesmicron-scale orsize grains ofand sandabove. TheThough methodDEM wasis originallyvery appliedclosely byrelated to [[Petermolecular A. Cundall|Cundalldynamics]], inthe 1971method tois problemsgenerally indistinguished rockby mechanics.its Theinclusion theoreticalof basisrotational degrees-of-freedom theas methodwell wasas establishedstateful bycontact theand brilliantoften scientistcomplicated andgeometries Mathematician(including Isaacpolyhedra). NewtonWith advances in 1697<!--computing 1967power isand INCORRECT!numerical --~~~~Aclariontalgorithms Septfor nearest neighbor 25sorting, 2009it (assumedhas become possible to numerically simulate millions of particles on a typosingle forprocessor. now)-->Today DEM is becoming widely accepted as an effective method of addressing engineering problems in granular and discontinuous materials, especially in granular flows, powder mechanics, and rock mechanics.
The idea of solving complex problems by integrating the equation of motion was unthinkable at this time. However, with the unprecedented advances of computer power it is possible to numerically simulate up to
one million particles in a single processor (Today, 2009). Today DEM is becoming along with Finite Element Method an everyday tool to solve engineering problems.[[John R. Williams|Williams]], [[Grant Hocking|Hocking]], and [[Graham Mustoe|Mustoe]] in 1985 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 Conferences 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 discrete element method]] proposed by [[Grant Hocking|Hocking]], [[John R. Williams|Williams]] and [[Graham Mustoe|Mustoe]] in 1985, the [[Discontinuous Deformation Analysis|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.
The various branches of the DEM family are the [[distinct element method]] proposed by [[Peter A. Cundall|Cundall]] in 1971, the [[generalized discrete element method]] proposed by [[Grant Hocking|Hocking]], [[John R. Williams|Williams]] and [[Graham Mustoe|Mustoe]] in 1985, the [[Discontinuous Deformation Analysis|discontinuous deformation analysis]] (DDA) proposed by [[Gen-hua Shi|Shi]] in 1988 and the finite-discrete element method concurrently developed by several groups (e.g., [[Ante Munjiza|Munjiza]] and [[Roger Owen|Owen]]). The general method was originally developed by [[Peter A. Cundall|Cundall]] in 1971 to problems in rock mechanics. The theoretical basis of the method was established by Sir Isaac Newton in 1697<!-- 1967 is INCORRECT! --~~~~Aclariont Sept 25, 2009 (assumed a typo for now)-->. [[John R. Williams|Williams]], [[Grant Hocking|Hocking]], and [[Graham Mustoe|Mustoe]] in 1985 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.. 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 [[John R. Williams|Williams]], [[Nenad Bicanic|Bicanic]], and [[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'' by [[Ante Munjiza|Munjiza]].
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 average the physics across many particles and thereby treat the material as a [[Continuum mechanics|continuum]]. In the case of [[solid]]-like granular behavior as in [[soil mechanics]], the continuum approach usually treats the material as [[Elasticity (physics)|elastic]] or [[Plasticity (physics)|elasto-plastic]] and models it with the [[finite element method]] or a [[Meshfree methods|mesh free method]]. In the case of liquid-like or gas-like granular flow, the continuum approach may treat the material as a [[fluid]] and use [[computational fluid dynamics]]. ▼
▲Discrete element methods are processorrelatively computationally intensive , and thiswhich limits either the length of a simulation or the number of particles. AdvancesSeveral inDEM thecodes, softwareas aredo beginningmolecular todynamics codes, 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 average the physics across many particles and thereby treat the material as a [[Continuum mechanics|continuum]]. In the case of [[solid]]-like granular behavior as in [[soil mechanics]], the continuum approach usually treats the material as [[Elasticity (physics)|elastic]] or [[Plasticity (physics)|elasto-plastic]] and models it with the [[finite element method]] or a [[Meshfree methods|mesh free method]]. In the case of liquid-like or gas-like granular flow, the continuum approach may treat the material as a [[fluid]] and use [[computational fluid dynamics]] . Drawbacks to [[homogenization]] of the granular scale physics, however, are well-documented and should be considered carefully before attempting to use a continuum approach.
==Applications==
* [[granular matter]], like [[sand]];
* [[Powder (substance)|powders]], like [[toner]].
* Blocky or jointed rock masses
Typical industries using DEM are:
==Outline of the method==
A DEM-simulation is started by puttingfirst allgenerating particlesa model, which results in aspatially certainorienting positionall andparticles givingand themassigning an initial [[velocity]]. ThenThe the forces which act on each particle are computed from the initial data and the relevant physical laws and contact models. Generally, a simulation consists of three parts: the initialization, explicit time-stepping, and post-processing. The time-stepping usually requires a nearest neighbor sorting step to reduce the number of possible contact pairs and decrease the computational requirements; this is often only performed periodically.
The following forces may have to be considered in macroscopic simulations:
* [[friction]], when two particles touch each other;
* [[contact plasticity]], or recoil, when two particles collide;
* [[gravity]] , (the force of attraction between particles due to their mass), which is only relevant in astronomical simulations. ▼* [[damping]], when energy is lost during the compression and recoil of grains in a collision;
* attractive potentials, such as [[cohesion]], [[adhesion]], [[liquid bridging]], [[electrostatic attraction]]. Note that, because of the overhead from determining nearest neighbor pairs, exact resolution of long-range, compared with particle size, forces can increase computational cost or require specialized algorithms to resolve these interactions.
▲* [[gravity]] (the force of attraction between particles due to their mass), which is only relevant in astronomical simulations.
* cohesion and/or adhesion (when two particles collide and stick to each other)
* liquid bridging (wet particles in contact may have a thin liquid film exerting a force on both particles)
Any other type of inter-particular forces may be considered, example electrostatic attraction or repulsion, etc. However, the computational cost increases as the particle-particle force model is made more complex.
On a molecular level, we may consider
==Advantages and Limitations==
Advantages
* DEM can be used to simulate a wide variety of granular flow and rock mechanics situations. TheSeveral resultsresearch obtainedgroups byhave competentindependently researchersdeveloped agreesimulation software that agrees well with experimental findings in a wide range of engineering applications, including adhesive powders, granular flow, and jointed rock masses.
* DEM allows a more detailed study of the micro-dynamics of powder flows than is often possible using physical experiments. For example, the force networks formed in a granular media can be visualized using DEM. Such measurements are nearly impossible in experiments with small and many particles.
Disadvantages
* The maximum number of particles, and duration of a virtual simulation is limited by computational power. Typical flows contain billions of particles, but contemporary DEM simulations haveon beenlarge ablecluster tocomputing simulateresources ofhave theonly orderrecently ofbeen able to aapproach millionthis particlesscale for sufficiently long time (virtualsimulated time, not actual program execution time).
* Even though any random particle geometry can be simulated, simulations are generally limited to spherical particles due to the increase in cost of computation with increasing complexity of geometry.
==Bibliography==
* 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
* Ante Munjiza, ''The Combined Finite-Discrete Element Method'' Wiley, 2004, ISBN 0-470-84199-0
* A. Bobet, A. Fakhimi, S. Johnson, J. Morris, F. Tonon, and M. Ronald Yeung (2009) "Numerical Models in Discontinuous Media: Review of Advances for Rock Mechanics Applications", J. Geotech. and Geoenvir. Engrg., 135 (11) pp. 1547-1561
==Software==
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