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Discrete Element Methods: Basics and Applications in Engineering

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Modeling in Engineering Using Innovative Numerical Methods for Solids and Fluids

Part of the book series: CISM International Centre for Mechanical Sciences ((CISM,volume 599))

Abstract

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.

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Notes

  1. 1.

    This factor A can also be used as a fitting parameter within specific simulations—like quasistatic predictions of granular material behaviour—to damp oscillations.

  2. 2.

    Analytical solution for the trajectory:

    \(\tilde{x}_{3,\max }=\displaystyle \frac{(v_0\sin \alpha )^2}{2\,b}\,,\tilde{x}_{1,k}=\displaystyle \frac{v_0^2\sin (2\,\alpha )}{b}\,,\tilde{t}_k=\displaystyle \frac{2\,v_0\sin \alpha }{b}\) .

References

  • Alder, B. J., & Wainwright, T. E. (1957). Phase transition for a hard sphere system. Journal of Chemical Physics, 27(5), 1208–1209.

    Article  Google Scholar 

  • Allen, M. P., & Tildesley, D. J. (1987). Computer simulation of liquids. New York: Oxford University Press.

    MATH  Google Scholar 

  • 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.

    Article  Google Scholar 

  • Brilliantov N. V., Albers N., Spahn F., & Pöschel T. (2007). Collision dynamics of granular particles with adhesion. Physical Review E, 76(5, Part 1).

    Google Scholar 

  • 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.

    Google Scholar 

  • 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.

    Google Scholar 

  • 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.

    Article  Google Scholar 

  • Cundall, P. A., & Strack, O. D. L. (1979). Discrete numerical model for granular assemblies. Geotechnique, 29(1), 47–65.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Google Scholar 

  • 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.

    Google Scholar 

  • Hertz, H. (1882). Ãœber die Berührung fester elastischer Körper. Journal für die reine und angewandte Mathematik, 92, 156–171.

    MATH  Google Scholar 

  • Ishibashi, I., Perry, C., & Agarwal, T. K. (1994). Experimental determinations of contact friction for spherical glass particles. Soils and Foundations, 34, 79–84.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Google Scholar 

  • 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.

    Google Scholar 

  • Kuhn, M., & Bagi, K. (2004). Alternative definition of particle rolling in a granular assembly. Journal of Engineering Mechanics-ASCE, 130(7), 826–835.

    Article  Google Scholar 

  • Loskofsky, C., Song, F., & Newby, B. Z. (2006). Underwater adhesion measurements using the JKR technique. Journal of Adhesion, 82(7), 713–730.

    Article  Google Scholar 

  • Luding, S. (2004). Micro-macro transition for anisotropic, frictional granular packings. International Journal of Solids and Structures, 41(21), 5821–5836.

    Article  Google Scholar 

  • 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.

    Google Scholar 

  • Maugis, D. (1992). Adhesion of spheres—The jkr-dmt transition using a dugdale model. Journal of Colloid and Interface Science, 150(1), 243–269.

    Article  Google Scholar 

  • Pöschel, T., & Schwager, T. (2005). Computational Granular Dynamics. Springer.

    Google Scholar 

  • Quentrec, B., & Brot, C. (1973). New method for searching for neighbors in molecular dynamics computations. Journal of Computational Physics, 13(3), 430–432.

    Article  Google Scholar 

  • 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.

    Google Scholar 

  • Springel, V. (2005). The cosmological simulation code gadget-2. Monthly Notices of the Royal Astronomical Society, 364, 1105–1134.

    Article  Google Scholar 

  • Ulrich, C., & Rung, T. (2006). Validation and application of a massively-parallel hydrodynamic SPH simulation code. Proceedings of NuTTS ’09.

    Google Scholar 

  • Verlet, L. (1967). Computer experiments on classical fluids. i. Thermodynamical properties of Lennard-Jones molecules. Physical Review, 159(1), 98–103.

    Article  Google Scholar 

  • 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.

    Google Scholar 

  • 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.

    Google Scholar 

  • 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.

    Article  Google Scholar 

  • Wellmann, C., & Wriggers, P. (2012). A two-scale model of granular materials. Computer Methods in Applied Mechanics and Engineering, 205–208, 46–58.

    Article  MathSciNet  Google Scholar 

  • 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.

    Google Scholar 

  • Wriggers, P. (2006). Computational Contact Mechanics (2nd ed.). Berlin Heidelberg: Springer.

    Book  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • Zohdi, T. I. (2007). Introduction to the modeling and simulation of particulate flows. SIAM.

    Google Scholar 

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Author information

Authors and Affiliations

  1. Faculty of Mechanical Engineering, Institut for Continuum Mechanics, Leibniz University Hannover, Hannover, Germany

    Peter Wriggers

  2. CADFEM GmbH, Hannover, Germany

    B. Avci

Authors
  1. Peter Wriggers
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  2. B. Avci
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Correspondence to Peter Wriggers .

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Editors and Affiliations

  1. Institute of Applied Mechanics, Braunschweig University of Technology, Braunschweig, Germany

    Laura De Lorenzis

  2. Numerical Structural Analysis with Application in Ship Technology (M-10), Hamburg University of Technology, Hamburg, Germany

    Alexander Düster

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Wriggers, P., Avci, B. (2020). Discrete Element Methods: Basics and Applications in Engineering. In: De Lorenzis, L., Düster, A. (eds) Modeling in Engineering Using Innovative Numerical Methods for Solids and Fluids. CISM International Centre for Mechanical Sciences, vol 599. Springer, Cham. https://doi.org/10.1007/978-3-030-37518-8_1

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  • DOI: https://doi.org/10.1007/978-3-030-37518-8_1

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