Discrete element methods: basics and applications in engineering. (English) Zbl 1481.74725
De Lorenzis, Laura (ed.) et al., Modeling in engineering using innovative numerical methods for solids and fluids. Papers based on the presentations at the CISM course, Udine, Italy, October 15–19, 2018. Cham: Springer. CISM Courses Lect. 599, 1-30 (2020).
Summary: A computational approach is presented in this contribution that allows a direct numerical simulation of 3D particulate movements. The given approach is based on the Discrete Element Method (DEM) The particle properties are constitutively described by specific models that act at contact points. The equations of motion will be solved by appropriate time marching algorithms. Additionally coupling schemes with the Finite Element Method (FEM) are discussed for the numerical treatment of particle-solid and particle-fluid interaction. The presented approach will be verified by computational results and compared with those of the literature. Finally, the method is applied for the simulation of different engineering applications using computers with parallel architecture.
For the entire collection see [Zbl 1470.76007].
For the entire collection see [Zbl 1470.76007].
MSC:
| 74S99 | Numerical and other methods in solid mechanics |
| 74S05 | Finite element methods applied to problems in solid mechanics |
| 74M15 | Contact in solid mechanics |
| 65Y05 | Parallel numerical computation |
Keywords:
particle-solid interaction; particle-fluid interaction; particle-contact model; discrete-finite element coupling; parallel computationReferences:
| [1] | Wriggers, P. (2006). Computational Contact Mechanics(2nd ed.). Berlin Heidelberg: Springer. · Zbl 1104.74002 · doi:10.1007/978-3-540-32609-0 |
| [2] | Wriggers, P. (1987). On consistent tangent matrices for frictional contact problems. In G. Pande & J. Middleton (Eds.), Proceedings of NUMETA ’87. M. Nijhoff Publishers, Dordrecht. |
| [3] | Wellmann, C., & Wriggers, P. (2012). A two-scale model of granular materials. Computer Methods in Applied Mechanics and Engineering, 205-208, 46-58. · Zbl 1239.74083 · doi:10.1016/j.cma.2010.12.023 |
| [4] | Wellmann, C., Lillie, C., & Wriggers, P. (2008). A contact detection algorithm for superellipsoids based on the common-normal concept. Engineering Computations, 25(5-6), 432-442. · Zbl 1257.70021 · doi:10.1108/02644400810881374 |
| [5] | Sbalzarini, I. F., Walther, J. H., Bergdorf, M., Hieber, S. E., Kotsalis, E. M., & Koumoutsakos, P. (2006). PPM—A highly efficient parallel particle-mesh library for the simulation of continuum systems. Journal of Computational Physics, 215, 566-588. · Zbl 1173.76398 |
| [6] | Luding, S. (2004). Micro-macro transition for anisotropic, frictional granular packings. International Journal of Solids and Structures, 41(21), 5821-5836. · Zbl 1112.74364 · doi:10.1016/j.ijsolstr.2004.05.048 |
| [7] | Ishibashi, I., Perry, C., & Agarwal, T. K. (1994). Experimental determinations of contact friction for spherical glass particles. Soils and Foundations, 34, 79-84. · doi:10.3208/sandf1972.34.4_79 |
| [8] | Hertz, H. (1882). Über die Berührung fester elastischer Körper. Journal für die reine und angewandte Mathematik, 92, 156-171. · JFM 14.0807.01 |
| [9] | Allen, M. P., & Tildesley, D. J. (1987). Computer simulation of liquids. New York: Oxford University Press. · Zbl 0703.68099 |
| [10] | Alder, B. J., & Wainwright, T. E. (1957). Phase transition for a hard sphere system. Journal of Chemical Physics, 27(5), 1208-1209. · doi:10.1063/1.1743957 |
| [11] | Brilliantov N. V., Albers N., Spahn F., & Pöschel T. (2007). Collision dynamics of granular particles with adhesion. Physical Review E, 76(5, Part 1). |
| [12] | Avci, B., & Wriggers, P. (2012). A dem-fem coupling approach for the direct numerical simulation of 3d particulate flows. Journal of Applied Mechanics, 79, 01901. · doi:10.1115/1.4005093 |
| [13] | Brilliantov N. V., Spahn F., Hertzsch J. M., & Pöschel T. (1996). Model for collisions in granular gases. Physical Review E, 53(5, Part B), 5382-5392. |
| [14] | Choi, J., Kudrolli, A., & Bazant, M. Z. (2005). Velocity profile of granular flows inside silos and hoppers. Journal of Physics: Condensed Matter, 17, 2533-2548. |
| [15] | Choi, J., Kudrolli, A., Rosales, R. R., & Bazant, M. Z. (2004). Diffusion and mixing in gravity-driven dense granular flows. Physical Review Letters, 92, 174301. · doi:10.1103/PhysRevLett.92.174301 |
| [16] | Cundall, P. A., & Strack, O. D. L. (1979). Discrete numerical model for granular assemblies. Geotechnique, 29(1), 47-65. · doi:10.1680/geot.1979.29.1.47 |
| [17] | Dhia, H. B., & Rateau, G. (2005). The arlequin method as a flexible engineering design tool. International Journal of Numerical Methods in Engineering, 62, 1442-1462. · Zbl 1084.74049 · doi:10.1002/nme.1229 |
| [18] | Gingold, R. A., & Monaghan, J. J. (1977). Smoothed particle hydrodynamics: Theory and application to non-spherical stars. Monthly Notices of the Royal Astronomical Society, 181(3), 375-389. · Zbl 0421.76032 · doi:10.1093/mnras/181.3.375 |
| [19] | Dominik, C., & Tielens, A. G. G. M. (1995). Resistance to rolling in the adhesive contact of 2 elastic spheres. Philosophical Magazine A—Physics of Condensed Matter Structure Defects and Mechanical Properties, 72(3), 783-803. |
| [20] | Gómez-Gesteira, M., Crespo, A. J., Rogers, B. D., Dalrymple, R. A., Dominguez, J. M., & Barreiro, A. (2012a). Sphysics-development of a free-surface fluid solver-part 2: Efficiency and test cases. Computers & Geosciences, 48, 300-307. |
| [21] | Gomez-Gesteira, M., Rogers, B. D., Crespo, A. J., Dalrymple, R. A., Narayanaswamy, M., & Dominguez, J. M. (2012b). Sphysics-development of a free-surface fluid solver-part 1: Theory and formulations. Computers & Geosciences, 48, 289-299. |
| [22] | Johnson, A. A., & Tezduyar, T. E. (1997). 3d simulation of fluid-particle interactions with the number of particles reaching 100. Computer Methods in Applied Mechanics and Engineering, 145(3-4), 301-321. · Zbl 0893.76043 · doi:10.1016/S0045-7825(96)01223-6 |
| [23] | Iwashita, K., & Oda, M. (1998). Rolling resistance at contacts in simulation of shear band development by dem. Journal of Engineering Mechanics-ASCE, 124(3), 285-292. · doi:10.1061/(ASCE)0733-9399(1998)124:3(285) |
| [24] | Johnson, K. L., Kendall, K., & Roberts, A. D. (1971). Surface energy and contact of elastic solids. Proceedings of the Royal Society of London Series A-Mathematical and Physical Sciences, 324(1558), 301-313. |
| [25] | Kruggel-Emden, H., Sturm, M., Wirtz, S., & Scherer, V. (2008). Selection of an appropriate time integration scheme for the discrete element method (dem). Computers & Chemical Engineering, 32(10), 2263-2279. |
| [26] | Loskofsky, C., Song, F., & Newby, B. Z. (2006). Underwater adhesion measurements using the JKR technique. Journal of Adhesion, 82(7), 713-730. · doi:10.1080/00218460600775807 |
| [27] | Kuhn, M., & Bagi, K. (2004). Alternative definition of particle rolling in a granular assembly. Journal of Engineering Mechanics-ASCE, 130(7), 826-835. · Zbl 1111.74315 · doi:10.1061/(ASCE)0733-9399(2004)130:7(826) |
| [28] | Maruzewski, P., Le Touze, D., & Oger, G. (2009). Sph high-performance computing simulations of rigid solids impacting the free-surface of water. Journal of Hydraulic Research, 47, 126-134. |
| [29] | Maugis, D. (1992). Adhesion of spheres—The jkr-dmt transition using a dugdale model. Journal of Colloid and Interface Science, 150(1), 243-269. · doi:10.1016/0021-9797(92)90285-T |
| [30] | Pöschel, T., & Schwager, T. (2005). Computational Granular Dynamics. Springer. |
| [31] | Springel, V. (2005). The cosmological simulation code gadget-2. Monthly Notices of the Royal Astronomical Society, 364, 1105-1134. · doi:10.1111/j.1365-2966.2005.09655.x |
| [32] | Quentrec, B., & Brot, C. (1973). New method for searching for neighbors in molecular dynamics computations. Journal of Computational Physics, 13(3), 430-432. · doi:10.1016/0021-9991(73)90046-6 |
| [33] | Ulrich, C., & Rung, T. (2006). Validation and application of a massively-parallel hydrodynamic SPH simulation code. Proceedings of NuTTS ’09. |
| [34] | Walther, J. H., & Sbalzarini, I. F. (2009). Large-scale parallel discrete element simulations of granular flow. Engineering Computations, 26(6, Sp. Iss. SI), 688-697; 4th International Conference on Discrete Element Methods(2007). Australia, Brisbane. |
| [35] | Verlet, L. (1967). Computer experiments on classical fluids. i. Thermodynamical properties of Lennard-Jones molecules. Physical Review, 159(1), 98-103. · doi:10.1103/PhysRev.159.98 |
| [36] | Wellmann, C. (2011) A Two-Scale Model of Granular Materials Using a Coupled Discrete-Finite Element Approach. Dissertation, B11/1, Institute for Continuum Mechanics, Leibniz University Hannover. |
| [37] | Wriggers, P., Van, T. V., & Stein, E. (1990). Finite-element-formulation of large deformation impact- contact-problems with friction. Computers and Structures, 37, 319-333. · Zbl 0727.73080 · doi:10.1016/0045-7949(90)90324-U |
| [38] | Zohdi, T. I. (2007). Introduction to the modeling and simulation of particulate flows. SIAM · Zbl 1120.76001 |
| [39] | Zhu, H. P., Zhou, Z. Y., Yang, R. Y., & Yu, A. B. (2007). Discrete particle simulation of particulate systems: Theoretical developments. Chemical Engineering Science, 62(13), 3378-3396. · doi:10.1016/j.ces.2006.12.089 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
