479:
thermo-mechanical coupling is considered, whereby the thermal properties of an individual element are considered in order to model heat flow through a macroscopic granular or multi-element medium subject to a mechanical loading. Interparticle forces, computed as a part of classical DEM, are used to determined areas of true interparticle contact and thus model the conductive transfer of heat from one solid element to another. A further aspect that is considered in DEM is the gas phase conduction, radiation and convection of heat in the interparticle spaces. To facilitate this, properties of the inter-element gaseous phase need to be considered in terms of pressure, gas conductivity and the mean-free path of gas molecules.
350:. 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.
32:
273:
280:. 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.
580:
utilized to conduct DEM simulations, due to the large number of computing cores on typical GPUs. In addition GPUs tend to be significantly more energy efficient than conventional computing clusters when conducting DEM simulations i.e. a DEM simulation solved on GPUs requires less energy than when it is solved on a conventional computing cluster.
520:); the same goes for the forces. The force is no longer taken into account after the so-called cut-off distance (usually half the length of a cell), so that a particle is not influenced by the mirror image of the same particle in the other side of the cell. One can now increase the number of particles by simply copying the cells.
176:
Discrete element methods are relatively computationally intensive, which limits either the length of a simulation or the number of particles. Several DEM codes, as do molecular dynamics codes, take advantage of parallel processing capabilities (shared or distributed systems) to scale up the number of
559:
DEM can be used to simulate a wide variety of granular flow and rock mechanics situations. Several research groups have independently developed simulation software that agrees well with experimental findings in a wide range of engineering applications, including adhesive powders, granular flow, and
492:
with the number of particles. This is not acceptable for simulations with large number of particles. A possible way to avoid this problem is to combine some particles, which are far away from the particle under consideration, into one pseudoparticle. Consider as an example the interaction between a
575:
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 on large cluster computing resources have only recently been able to approach this scale for sufficiently long time
152:
as well as stateful contact, particle deformation and often complicated geometries (including polyhedra). With advances in computing power and numerical algorithms for nearest neighbor sorting, it has become possible to numerically simulate millions of particles on a single processor. Today DEM is
579:
DEM is computationally demanding, which is the reason why it has not been so readily and widely adopted as continuum approaches in computational engineering sciences and industry. However, the actual program execution times can be reduced significantly when graphical processing units (GPUs) are
253:). The general method was originally developed by Cundall in 1971 to problems in rock mechanics. Williams 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
478:
The discrete element method is widely applied for the consideration of mechanical interactions in many-body problems, particularly granular materials. Among the various extensions to DEM, the consideration of heat flow is particularly useful. Generally speaking in
Thermal DEM methods, the
563:
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
257:. 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,
546:
Following the work by
Munjiza and Owen, the combined finite-discrete element method has been further developed to various irregular and deformable particles in many applications including pharmaceutical tableting, packaging and flow simulations, and impact analysis.
1200:
S. J. Antony, D. Chapman, J. Sujatha and T. Barakat (2015). "Interplay between the inclusions of different sizes and their proximity to the wall boundaries on the nature of their stress distribution within the inclusions inside particulate packing".
391:. 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.
153:
becoming widely accepted as an effective method of addressing engineering problems in granular and discontinuous materials, especially in granular flows, powder mechanics, ice and rock mechanics. DEM has been extended into the
289:
The fundamental assumption of the method is that the material consists of separate, discrete particles. These particles may have different shapes and properties that influence inter-particle contact. Some examples are:
487:
When long-range forces (typically gravity or the
Coulomb force) are taken into account, then the interaction between each pair of particles needs to be computed. Both the number of interactions and cost of computation
981:
Gan, Yixiang; Hernandez, Francisco; Hanaor, Dorian; Annabattula, Ratna; Kamlah, Marc; Pereslavtsev, Pavel (2014). "Thermal
Discrete Element Analysis of EU Solid Breeder Blanket Subjected to Neutron Irradiation".
516:
However, simulations in molecular dynamics divide the space in which the simulation take place into cells. Particles leaving through one side of a cell are simply inserted at the other side (periodic
1119:
Gethin, D. T.; Yang, X. S.; Lewis, R. W. (2006). "A two dimensional combined discrete and finite element scheme for simulating the flow and compaction of systems comprising irregular particulates".
715:
Trivino, L.F.; Mohanty, B. (2015). "Assessment of crack initiation and propagation in rock from explosion-induced stress waves and gas expansion by cross-hole seismometry and FEMâDEM method".
497:: The error arising from combining all the stars in the distant galaxy into one point mass is negligible. So-called tree algorithms are used to decide which particles can be combined into one
1397:
Bobet, A.; Fakhimi, A.; Johnson, S.; Morris, J.; Tonon, F.; Yeung, M. Ronald (November 2009). "Numerical Models in
Discontinuous Media: Review of Advances for Rock Mechanics Applications".
567:
The general characteristics of force-transmitting contacts in granular assemblies under external loading environments agree with experimental studies using Photo-stress analysis (PSA).
615:
Peng, Z.; Doroodchi, E.; Moghtaderi, B. (2020). "Heat transfer modelling in
Discrete Element Method (DEM)-based simulations of thermal processes: Theory and model development".
177:
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
250:
1573:
363:
1181:
S.J. Antony (2007). "Link between single-particle properties and macroscopic properties in particulate assemblies: role of structures within structures".
1066:
Lewis, R. W.; Gethin, D. T.; Yang, X. S.; Rowe, R. C. (2005). "A combined finite-discrete element method for simulating pharmaceutical powder tableting".
1612:
Shi, GenâHua (February 1992). "Discontinuous
Deformation Analysis: A New Numerical Model For The Statics And Dynamics of Deformable Block Structures".
1470:"Numerical simulation of two-dimensional fluidized beds using the discrete element method (comparison between the two- and three-dimensional models)"
384:
1439:
Kafashan, J.; WiÄ
cek, J.; Abd Rahman, N.; Gan, J. (2019). "Two-dimensional particle shapes modelling for DEM simulations in engineering: a review".
1220:
262:
258:
246:
217:
of the granular scale physics, however, are well-documented and should be considered carefully before attempting to use a continuum approach.
1469:
1543:
Zhu, H.P.; Zhou, Z.Y.; Yang, R.Y.; Yu, A.B. (July 2007). "Discrete particle simulation of particulate systems: Theoretical developments".
1633:
Williams, John R.; Pentland, Alex P. (February 1992). "Superquadrics and Modal
Dynamics For Discrete Elements in Interactive Design".
96:
1682:
428:
346:
A DEM-simulation is started by first generating a model, which results in spatially orienting all particles and assigning an initial
68:
49:
932:"Assessment of blending performance of pharmaceutical powder mixtures in a continuous mixer using Discrete Element Method (DEM)"
265:
et al. (see below). A comprehensive treatment of the combined Finite
Element-Discrete Element Method is contained in the book
75:
1663:
1380:
1361:
1312:
1293:
872:
889:
680:
Kafui, K.D.; Thornton, C.; Adams, M.J. (2002). "Discrete particle-continuum fluid modelling of gasâsolid fuidised beds".
234:
82:
144:
methods for computing the motion and effect of a large number of small particles. Though DEM is very closely related to
1340:
1322:
Williams, J. R.; Hocking, G.; Mustoe, G. G. W. (January 1985). "The
Theoretical Basis of the Discrete Element Method".
238:
648:"CFD modelling of the fast pyrolysis of biomass in fluidised bed reactors: Modelling the impact of biomass shrinkage"
115:
431:
is employed to compute the change in the position and the velocity of each particle during a certain time step from
64:
154:
788:
372:, the force of attraction between particles due to their mass, which is only relevant in astronomical simulations.
149:
53:
205:. In the case of liquid-like or gas-like granular flow, the continuum approach may treat the material as a
210:
166:
1284:
Bicanic, Ninad (2004). "Discrete Element Methods". In Stein, Erwin; De Borst; Hughes, Thomas J.R. (eds.).
751:
930:
Behjani, Mohammadreza Alizadeh; Motlagh, Yousef Ghaffari; Bayly, Andrew; Hassanpour, Ali (2019-11-07).
888:
Alizadeh, Mohammadreza; Hassanpour, Ali; Pasha, Mehrdad; Ghadiri, Mojtaba; Bayly, Andrew (2017-09-01).
432:
214:
1504:
Williams, J. R.; O'Connor, R. (December 1999). "Discrete element simulation and the contact problem".
1036:
818:
Williams, J. R.; O'Connor, R. (December 1999). "Discrete element simulation and the contact problem".
1418:
Cundall, P. A.; Strack, O. D. L. (March 1979). "A discrete numerical model for granular assemblies".
967:
595:
527:
414:
89:
1518:
832:
388:
1574:"Discrete particle simulation of particulate systems: A review of major applications and findings"
1351:
510:
226:
42:
1489:
1513:
827:
1234:
He, Yi; Bayly, Andrew E.; Hassanpour, Ali; Muller, Frans; Wu, Ke; Yang, Dongmin (2018-10-01).
1214:
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534:
459:
198:
170:
20:
1585:
1552:
1410:
1128:
1085:
1001:
724:
689:
376:
194:
190:
16:
Numerical methods for computing the motion and effect of a large number of small particles
8:
420:
245:) and the finite-discrete element method concurrently developed by several groups (e.g.,
178:
1589:
1556:
1132:
1089:
1005:
728:
693:
435:. Then, the new positions are used to compute the forces during the next step, and this
1531:
1456:
1101:
1075:
1017:
991:
959:
845:
628:
517:
447:
145:
141:
1485:
1154:
Chen, Y.; May, I. M. (2009). "Reinforced concrete members under drop-weight impacts".
701:
1659:
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1376:
1357:
1336:
1308:
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1105:
963:
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1021:
849:
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620:
489:
277:
230:
202:
427:
All these forces are added up to find the total force acting on each particle. An
1656:
Proceedings of the 2nd International Conference on Discrete Element Methods (DEM)
1252:
1235:
1052:
947:
908:
890:"The effect of particle shape on predicted segregation in binary powder mixtures"
736:
647:
466:
453:
408:
1236:"A GPU-based coupled SPH-DEM method for particle-fluid flow with free surfaces"
1167:
624:
498:
186:
1597:
1564:
1452:
1431:
1140:
770:
666:
1676:
1261:
1037:"Thermal DEMâCFD modeling and simulation of heat transfer through packed bed"
955:
916:
404:
400:
158:
436:
353:
The following forces may have to be considered in macroscopic simulations:
931:
1527:
1013:
841:
148:, the method is generally distinguished by its inclusion of rotational
1324:
NUMETA 1985, Numerical Methods of Engineering, Theory and Applications
793:
NUMETA 1985, Numerical Methods of Engineering, Theory and Applications
1646:
1625:
1097:
276:
Discrete-element simulation with particles arranged after a photo of
1183:
Philosophical Transactions of the Royal Society of London, Series: A
31:
502:
442:
Typical integration methods used in a discrete element method are:
380:
357:
347:
1080:
996:
369:
787:
Williams, J. R.; Hocking, G.; Mustoe, G. G. W. (January 1985).
506:
494:
887:
272:
980:
929:
717:
International Journal of Rock Mechanics & Mining Sciences
206:
182:
1035:
Tsory, Tal; Ben-Jacob, Nir; Brosh, Tamir; Levy, Avi (2013).
799:
1438:
1068:
International Journal for Numerical Methods in Engineering
541:
1396:
294:
liquids and solutions, for instance of sugar or proteins;
1399:
Journal of Geotechnical and Geoenvironmental Engineering
189:, the continuum approach usually treats the material as
1233:
1034:
614:
1654:
Williams, John R.; Mustoe, Graham G. W., eds. (1993).
1373:
Computational Granular Dynamics: Models and Algorithms
789:"The Theoretical Basis of the Discrete Element Method"
501:. These algorithms arrange all particles in a tree, a
1321:
1121:
Computer Methods in Applied Mechanics and Engineering
786:
645:
1503:
1467:
817:
576:(simulated time, not actual program execution time).
1065:
56:. Unsourced material may be challenged and removed.
1658:(2nd ed.). Cambridge, MA: IESL Publications.
752:"Discrete numerical model for granular assemblies"
679:
523:Algorithms to deal with long-range force include:
1468:Kawaguchi, T.; Tanaka, T.; Tsuji, Y. (May 1998).
1330:
1156:Proceedings of the ICE - Structures and Buildings
805:
1674:
1632:
1506:Archives of Computational Methods in Engineering
820:Archives of Computational Methods in Engineering
646:Papadikis, K.; Gu, S.; Bridgwater, A.V. (2009).
1370:
1353:Discrete-element modeling of granular materials
1350:Radjai, Farang; Dubois, Frédéric, eds. (2011).
1331:Williams, J. R.; Pande, G.; Beer, J.R. (1990).
1118:
750:Cundall, Peter. A.; Strack, Otto D. L. (1979).
225:The various branches of the DEM family are the
1653:
714:
407:attraction or repulsion of particles carrying
1571:
1542:
1417:
749:
550:
417:, when two atoms approach each other closely;
297:bulk materials in storage silos, like cereal;
1572:Zhu, HP; Zhou, ZY; Yang, RY; Yu, AB (2008).
1349:
1219:: CS1 maint: multiple names: authors list (
1371:Pöschel, Thorsten; Schwager, Thoms (2005).
1305:Numerische Simulation in der MolekĂŒldynamik
1180:
865:The Combined Finite-Discrete Element Method
856:
267:The Combined Finite-Discrete Element Method
1517:
1251:
1079:
995:
831:
617:Progress in Energy and Combustion Science
116:Learn how and when to remove this message
639:
366:, or recoil, when two particles collide;
341:
271:
1302:
1286:Encyclopedia of Computational Mechanics
1283:
1153:
862:
782:
780:
542:Combined finite-discrete element method
439:is repeated until the simulation ends.
395:On a molecular level, we may consider:
1675:
1303:Griebel, Michael; et al. (2003).
708:
360:, when two particles touch each other;
777:
673:
482:
54:adding citations to reliable sources
25:
1611:
1333:Numerical Methods in Rock Mechanics
608:
505:in the two-dimensional case and an
255:Numerical Methods in Rock Mechanics
242:
235:generalized discrete element method
233:and Otto D. L. Strack in 1979, the
13:
1411:10.1061/(ASCE)GT.1943-5606.0000133
310:Typical industries using DEM are:
239:discontinuous deformation analysis
14:
1694:
220:
1683:Numerical differential equations
155:Extended Discrete Element Method
30:
1272:
1227:
1193:
1174:
1147:
1112:
1059:
1028:
974:
923:
881:
806:Williams, Pande & Beer 1990
375:attractive potentials, such as
284:
41:needs additional citations for
811:
743:
473:
185:-like granular behavior as in
1:
1486:10.1016/S0032-5910(97)03366-4
984:Fusion Science and Technology
702:10.1016/S0009-2509(02)00140-9
601:
314:Agriculture and food handling
306:Blocky or jointed rock masses
1578:Chemical Engineering Science
1545:Chemical Engineering Science
1253:10.1016/j.powtec.2018.07.043
1053:10.1016/j.powtec.2013.04.013
948:10.1016/j.powtec.2019.10.102
909:10.1016/j.powtec.2017.06.059
737:10.1016/j.ijrmms.2015.03.036
682:Chemical Engineering Science
655:Chemical Engineering Journal
211:computational fluid dynamics
7:
584:
300:granular matter, like sand;
10:
1699:
1326:. Rotterdam: A.A. Balkema.
1168:10.1680/stbu.2009.162.1.45
795:. Rotterdam: A.A. Balkema.
625:10.1016/j.pecs.2020.100847
551:Advantages and limitations
18:
1598:10.1016/j.ces.2008.08.006
1565:10.1016/j.ces.2006.12.089
1453:10.1007/s10035-019-0935-1
1432:10.1680/geot.1979.29.1.47
1141:10.1016/j.cma.2005.10.025
771:10.1680/geot.1979.29.1.47
667:10.1016/j.cej.2009.01.036
596:Movable Cellular Automata
65:"Discrete element method"
1635:Engineering Computations
1614:Engineering Computations
389:electrostatic attraction
140:, is any of a family of
19:Not to be confused with
433:Newton's laws of motion
332:Pharmaceutical industry
227:distinct element method
197:and models it with the
138:distinct element method
130:discrete element method
1356:. London: Wiley-ISTE.
1288:. Vol. 1. Wiley.
863:Munjiza, Ante (2004).
619:. 79, 100847: 100847.
490:increase quadratically
460:symplectic integrators
281:
1335:. Chichester: Wiley.
867:. Chichester: Wiley.
591:Compaction simulation
535:fast multipole method
528:BarnesâHut simulation
342:Outline of the method
275:
199:finite element method
21:finite element method
1375:. Berlin: Springer.
1307:. Berlin: Springer.
560:jointed rock masses.
303:powders, like toner.
50:improve this article
1590:2008ChEnS..63.5728Z
1557:2007ChEnS..62.3378Z
1133:2006CMAME.195.5552G
1090:2005IJNME..62..853L
1006:2014FuST...66...83G
729:2015IJRMM..77..287T
694:2002ChEnS..57.2395K
518:boundary conditions
493:star and a distant
421:van der Waals force
1528:10.1007/BF02818917
1014:10.13182/FST13-727
842:10.1007/BF02818917
429:integration method
364:contact plasticity
329:Mineral processing
282:
181:. In the case of
150:degrees-of-freedom
146:molecular dynamics
1665:978-0-918062-88-8
1584:(23): 5728â5770.
1551:(13): 3378â3396.
1474:Powder Technology
1405:(11): 1547â1561.
1382:978-3-540-21485-4
1363:978-1-84821-260-2
1314:978-3-540-41856-6
1295:978-0-470-84699-5
1240:Powder Technology
1203:Powder Technology
1041:Powder Technology
936:Powder Technology
897:Powder Technology
874:978-0-470-84199-0
688:(13): 2395â2410.
511:three-dimensional
483:Long-range forces
336:Powder metallurgy
163:chemical reaction
136:), also called a
126:
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278:Peter A. Cundall
231:Peter A. Cundall
203:mesh free method
165:and coupling to
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970:on 21 Feb 2020.
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476:
467:leapfrog method
454:velocity Verlet
415:Pauli repulsion
409:electric charge
385:liquid bridging
344:
287:
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213:. Drawbacks to
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571:Disadvantages
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499:pseudoparticle
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286:
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221:The DEM family
219:
215:homogenization
195:elasto-plastic
187:soil mechanics
173:into account.
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320:Detergents
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