Geodesic
A discrete element method for dynamic simulation of arbitrary bodies
Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, Tome 25 (2015) no. 4, pp. 473-482 Cet article a éte moissonné depuis la source Math-Net.Ru

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The paper deals with the statement of a problem of dynamic interaction of arbitrary solid bodies and its test solutions in the context of discrete element modeling. For discretization we use description of bodies with arbitrary shapes, composed of rigidly bound spheres. The clumps were built with different characteristics, which allowed to estimate their influence on the process of clump construction and the smoothness of obtained surface. A system of equations of motion relative to global axes for a clump of spheres is presented. The forces of interaction between the spheres are determined based on the Hertz–Mindlin contact model with due account for viscous damping. A problem of interaction of two spheres was chosen as a test case. Spheres' trajectories composed of clumps of spheres were calculated. The results were compared with the results for the case of motion and interaction of spheres in one-particle approximation.
Keywords: mathematical modeling, rigid body dynamics, discrete element method, clumps. 
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A. S. Karavaev; S. P. Kopysov; A. S. Sarmakeeva. A discrete element method for dynamic simulation of arbitrary bodies. Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, Tome 25 (2015) no. 4, pp. 473-482. http://geodesic.mathdoc.fr/item/VUU_2015_25_4_a3/

[1] Luding S., “Introduction to discrete element methods: basic of contact force models and how to perform the micro-macro transition to continuum theory”, European Journal of Environmental and Civil Engineering, 12:7–8 (2008), 785–826 | DOI

[2] Gray J. P., Monaghan J. J., Swift R. P., “SPH elastic dynamics”, Computer Methods in Applied Mechanics and Engineering, 190:49–50 (2001), 6641–6662 | DOI | Zbl

[3] Potapov A. P., Royz S. I., Petrov I. B., “Modeling of wave processes with smoothed particle hydrodynamics method”, Mat. Model., 21:7 (2009), 20–28 (in Russian) | Zbl

[4] Jing L., “Formulation of discontinuous deformation analysis (DDA) – an implicit discrete element model for block systems”, Int. J. Eng. Geol., 49 (1998), 371–381 | DOI

[5] Cundall P., Starck O., “A discrete numerical-model for granular assemblies”, Geotechnique, 29:1 (1979), 47–65 | DOI

[6] Ferellec J.-F., McDowell G. R., “A method to model realistic particle shape and inertia in DEM”, Granular Matter., 12:5 (2010), 459–467 | DOI | Zbl

[7] Kopysov S. P., Karavaev A. S., “Construction of computational models from voxel data for finite and discrete element method”, Problemy mekhaniki i materialovedeniya, Tr. Inst. Mekh. Ural. Otd. Ross. Akad. Nauk, Izhevsk, 2015, 85–108 (in Russian)

[8] Hockney R. W., Eastwood J. W., Computer simulation using particles, McGraw-Hill, 1981

[9] Dorofeenko S. O., Simulation of granular materials by discrete element method, Dr. Sci. (Phys.-Math.) Dissertation, Chernogolovka, 2008, 115 pp. (in Russian)

[10] Amel'kin N. I., Kinematics and dynamics of a rigid body, Moscow Institute of Physics and Technology, Moscow, 2000, 62 pp.

[11] Mindlin R. D., “Compliance of elastic bodies in contact”, Journal of Applied Mechanics, 16 (1949), 259–344 | MR

[12] Kuwabara G., Kono K., “Restitution coefficient in collision between two spheres”, Japanese Journal of Applied Physics, 26 (1987), 1230–1233 | DOI

[13] Karavaev A. S., Kopysov S. P., “The method of unstructured hexahedral mesh generation from volumetric data”, Komp. Issled. Model., 5:1 (2013), 11–24 (in Russian)