# Basic Description of DEM

• Daniel Gelnar
• Jiri Zegzulka
Chapter

## Abstract

Discrete Element Method (DEM) is a numerical method that considers the mutual interactions of discrete particles in contact and enables evaluations of mutual force interactions. This method requires equations of translation movement and equations of rotation movement for each particle. The basic model is solved using the linear visco-elasticity (Fig. 2.1). This calculation uses the parallel connection of the damper with spring (Voight model) as a substitution scheme for each contact, which incorporates rolling and shear friction. More complex calculations also use other inputs, e.g., plastic deformation. In these models, the components of normal forces are calculated according to the theory of Herz’s contacts [1]. In the kinetic Eq. (2.1), there are also the tangential forces that were defined by Mindlin [2] and Mindlin - Deresiewicz [3]. The basis of these frictional tangential forces is the Coulomb law of the friction model, which is explained in Cundall and Strack [4]. The equations also include the damper components of normal and tangential force for which the coefficient of damping relates to the coefficient of restitution. These parameters were explained in Tsuji, Tanaka, and Ishida [5].

## References

1. 1.
Hertz, H.: On the contact of elastic solids. J. reine und angewandte Mathematik. 92, 156–171 (1882)
2. 2.
Mindlin, R.D.: Compliance of elastic bodies in contact. J. Appl. Mech. 16, 259–268 (1949)
3. 3.
Mindlin, R.D., Deresiewicz, H.: Elastic spheres in contact under varying oblique forces. Trans. ASME, J. Appl. Mech. 20, 327–344 (1953)Google Scholar
4. 4.
Cundall, P.A., Strack, O.D.: A discrete numberical model for granular assemblies. Geotechnique. 29, 47–65 (1979)
5. 5.
Tsuji, Y., Tanaka, T., Ishida, T.: Lagrangian numerical simulation of plug flow of cohesionless particles in a horizontal pipe. Powder Technol. 71, 239–250 (1992)
6. 6.
Zegzulka, J.: Mechanics of Bulk Materials, 1st edn, p. 186. VŠB - Technical University of Ostrava, Ostrava (2004). ISBN 80-248-0699-1Google Scholar
7. 7.
Gelnar, D., Zegzulka, J., Šooš, Ĺ., Nečas, J., Juchelková, D.: Validation device and method of measuring static and dynamic angle of discharge. VŠB - Technical University of Ostrava, patent number 306123 (2015)Google Scholar
8. 8.
Gelnar, D., Rozbroj, J., Zegzulka, J., Nečas, J.: Measuring equipment of angle repose. VŠB - Technical University of Ostrava, industrial design number 36213 (2013)Google Scholar
9. 9.
Gelnar, D., Zegzuka, J., Nečas, J., Juchelková, D.: Validation bucket elevator for modelling of mechanical processes and method of modelling of mechanical processes. VŠB - Technical University of Ostrava, patent number 304329 (2013)Google Scholar
10. 10.
Gelnar, D., Zegzulka, J., Nečas, J., Juchelková, D.: Validation bucket elevator for modelling of mechanical processes. VŠB - Technical University of Ostrava, utility model number 26154 (2013)Google Scholar
11. 11.
Gelnar, D., Zegzulka, J., Nečas, J., Juchelková, D.: Validation bucket elevator. VŠB - Technical University of Ostrava, industrial design number 35542 (2012)Google Scholar
12. 12.
Zegzulka, J., Bortlík, P., Dokoupil, O., Brázda, R., Nečas, J.: Method of simulating kinetics of movement of bulk material particles and device for making the same. VŠB - Technical University of Ostrava, patent number 303348 (2008)Google Scholar
13. 13.
Rozbroj, J., Zegzulka, J., Nečas, J., Gelnar, D.: Validation vertical screw conveyor and method of modeling mechanical processes by making use thereof. VŠB - Technical University of Ostrava, patent number 305150 (2013)Google Scholar
14. 14.
Gelnar, D., Zegzulka, J., Nečas, J., Juchelková, D.: Method of modeling mechanical processes of bulk materials and device for making the same. VŠB - Technical University of Ostrava, patent number 305194 (2013)Google Scholar
15. 15.
Gelnar, D., Zegzulka, J., Nečas, J., Juchelková, D.: Device for modeling mechanical processes of bulk materials VŠB - Technical University of Ostrava, utility model number 27421 (2014)Google Scholar
16. 16.
Gelnar, D., Zegzulka, J., Nečas, J., Juchelková, D.: Validation vibration conveyor. VŠB - Technical University of Ostrava, industrial design number 35809 (2012)Google Scholar
17. 17.
Žídek, M., Zegzulka, J., Nečas, J., Juchelková, D.: Validation chain conveyor with drivers and method of modeling mechanical processes by making use thereof. VŠB - Technical University of Ostrava, patent number 305136 (2013)Google Scholar
18. 18.
Žurovec, D., Gelnar, D., Zegzulka, J., Nečas, J.: Validation storage device for measuring flow processes of bulk material using electrical capacitance tomography method. VŠB - Technical University of Ostrava, patent number 306017 (2014)Google Scholar
19. 19.
Žurovec, D., Gelnar, D., Zegzulka, J., Nečas, J.: Validation storage device for measuring flow processes by tomographic method. VŠB - Technical University of Ostrava, utility model number 28424 (2015)Google Scholar
20. 20.
Žídek, M., Rozbroj, J., Zegzulka, J., Nečas, J., Marschalko, M.: A validation system of traction and pressing tools. VŠB - Technical University of Ostrava, patent number 306578 (2015)Google Scholar
21. 21.
Žídek, M., Rozbroj, J., Zegzulka, J., Nečas, J., Marschalko, M.: Validation bucket elevator for modelling of mechanical processes. VŠB - Technical University of Ostrava, utility model number 28181 (2015)Google Scholar
22. 22.
Rozbroj, J., Zegzulka, J., Nečas, J., Gelnar, D.: Validation vertical screw conveyor. VŠB - Technical University of Ostrava, utility model number 28349 (2015)Google Scholar
23. 23.
Hlosta, J., Žurovec, D., Zádrapa, F., Zegzulka, J.: Device for measuring the aeration properties of powders and loose materials with a cylindrical chamber. VŠB - Technical University of Ostrava, industrial design number 40388 (2015)Google Scholar
24. 24.
Forsström, D., Pär, J.: Calibration and validation of a large scale abrasive wear model by coupling DEM-FEM: local failure prediction from abrasive wear of tipper bodies during unloading of granular material. Eng. Fail. Anal. 66, 274–283 (2016)
25. 25.
Hendrik, O., Kerst, K., Roloff, C., Janiga, G., Katterfeld, A.: CFD-DEM simulation and experimental investigation of the flow behavior of lunar regolith JSC-1A. Particuology. (2018). in pressGoogle Scholar
26. 26.
Barrios, G.K., Tavares, L.M.: A preliminary model of high pressure roll grinding using the discrete element method and multi-body dynamics coupling. Int. J. Miner. Process. 156, 32–42 (2016)

© Springer Nature Switzerland AG 2019

## Authors and Affiliations

• Daniel Gelnar
• 1
• Jiri Zegzulka
• 1
1. 1.Technical University of OstravaOstravaCzech Republic