Advertisement

Granular Matter

, 21:91 | Cite as

Conceptual experiments and discrete element simulations with polygonal particles

  • Benjamin SchneiderEmail author
  • Ekkehard Ramm
Original Paper
  • 91 Downloads

Abstract

In the present work intentionally polygonal particles with a regular hexagonal geometry are investigated. This allows removing the complexity of randomly shaped particles thus concentrating on the interaction between adjacent particles. For this purpose, conceptual compression experiments on assemblies of hexagonal steel nuts are performed and subsequently simulated by a discrete element method. The interaction models for contact of two particles are as follows: in normal direction an elastic model augmented by a viscous supplement and in tangential direction an elasto-plastic model are applied; furthermore, an elasto-plastic model describes the contact of a particle with a plane underground. For an adhering bond between particles an elasto-damage beam including an axial force is introduced between the centers of adjacent particles. It allows modeling gradual failure of the bond. In order to test the capability of these models in a direct way, the conceptual experiments on simple regular particle arrangements are compared with their corresponding simulations. For samples of unglued particles relevant characteristics like shear bands are reproduced. For assemblies of particles glued together by an adhesive the study describes important failure properties like localization in cracks as well as ductile failure.

Keywords

Discrete element method Polygonal particles Contact model Adhering bond model Conceptual experiments 

Notes

Acknowledgements

Many thanks to the German Research Foundation (DFG) for funding the project “Fragmentierung kohäsiver Reibungsmaterialien mit diskretem Partikelmodell” (RA 218/22-1) and the project “Discrete element modeling of failure at mesoscopic scale” within the Cluster of Excellence Simulation Technology (EXC 310/1) at the University of Stuttgart. Thanks to W. Haase, J. Braig, and M. Berndt at the Institute of Lightweight Structures and Conceptual Design as well as to C. Gehlen and S. Mönnig at the Institute of Construction Materials at the University of Stuttgart for their support with the experiments.

Compliance with ethical standards

Conflict of interest

All the authors declare that they have no conflict of interest.

References

  1. 1.
    Ascher, U.M., Petzold, L.R.: Computer Methods for Ordinary Differential Equations and Differential-Algebraic Equations. Society for Industrial and Applied Mathematics, Philadelphia (1998)CrossRefGoogle Scholar
  2. 2.
    Bićanić, N.: Discrete element methods. In: Stein, E., de Borst, R., Hughes, T.J.R. (eds.) Encyclopedia of Computational Mechanics: Volume 1: Fundamentals, Chap. 11, pp. 311–337. Wiley, Chichester (2004)Google Scholar
  3. 3.
    Bićanić, N.: Discrete element methods. In: Zienkiewicz, O.C., Taylor, R.L. (eds.) The Finite Element Method for Solid and Structural Mechanics, Chap. 9, 6th edn, pp. 245–277. Elsevier, Oxford (2006)Google Scholar
  4. 4.
    Cundall, P.A.: A computer model for simulating progressive, large-scale movements in blocky rock systems. In: Proceedings Symp. Int. Soc. Rock Mech., Nancy (1971)Google Scholar
  5. 5.
    Cundall, P.A., Hart, R.D.: Numerical modelling of discontinua. Eng. Comput. 9, 101–113 (1992)CrossRefGoogle Scholar
  6. 6.
    Cundall, P.A., Strack, O.D.L.: A discrete numerical model for granular assemblies. Géotechnique 29, 47–65 (1979)CrossRefGoogle Scholar
  7. 7.
    D’Addetta, G.A.: Discrete Models for Cohesive Frictional Materials. Ph.D. thesis, Bericht Nr. 42, Institut für Baustatik, Universität Stuttgart (2004)Google Scholar
  8. 8.
    D’Addetta, G.A., Kun, F., Ramm, E.: On the application of a discrete model to the fracture process of cohesive granular materials. Granul. Matter 4, 77–90 (2002)CrossRefGoogle Scholar
  9. 9.
    D’Addetta, G.A., Ramm, E.: A microstructure-based simulation environment on the basis of an interface enhanced particle model. Granul. Matter 8, 159–174 (2006)CrossRefGoogle Scholar
  10. 10.
    D’Addetta, G.A., Ramm, E., Diebels, S., Ehlers, W.: A particle center based homogenization strategy for granular assemblies. Eng. Comput. 21, 360–383 (2004)CrossRefGoogle Scholar
  11. 11.
    Dettmar, J.P.: Static and Dynamic Homogenization Analyses of Discrete Granular and Atomistic Structures on Different Time and Length Scales. Ph.D. thesis, Bericht Nr.: I-17, Institut für Mechanik (Bauwesen), Lehrstuhl I, Universität Stuttgart (2006)Google Scholar
  12. 12.
    Donzé, F., Mora, P., Magnier, S.-A.: Numerical simulation of faults and shear zones. Geophys. J. Int. 116, 46–52 (1994)CrossRefADSGoogle Scholar
  13. 13.
    Feng, Y.T., Owen, D.R.J.: A 2D polygon/polygon contact model: algorithmic aspects. Eng. Comput. 21, 265–277 (2004)CrossRefGoogle Scholar
  14. 14.
    Gear, C.W.: Numerical Initial Value Problems in Ordinary Differential Equations. Prentice-Hall Series in Automatic Computation. Prentice-Hall, Englewood Cliffs (1971)Google Scholar
  15. 15.
    Herrmann, H.J., Hansen, A., Roux, S.: Fracture of disordered, elastic lattices in two dimensions. Phys. Rev. B 39, 637–648 (1989)CrossRefADSGoogle Scholar
  16. 16.
    Kruggel-Emden, H.: Analysis and Improvement of the Time-Driven Discrete Element Method. Ph.D. thesis, Fakultät für Maschinenbau, Ruhr-Universität Bochum (2008)Google Scholar
  17. 17.
    Kun, F., D’Addetta, G.A., Herrmann, H.J., Ramm, E.: Two-dimensional dynamic simulation of fracture and fragmentation of solids. Comput. Assist. Mech. Eng. Sci. 6, 385–402 (1999)zbMATHGoogle Scholar
  18. 18.
    Kun, F., Herrmann, H.J.: A study of fragmentation processes using a discrete element method. Comput. Methods Appl. Mech. Eng. 138, 3–18 (1996)CrossRefADSGoogle Scholar
  19. 19.
    Lätzel, M.: From Microscopic Simulations towards a Macroscopic Description of Granular Media. Ph.D. thesis, Institut für Computeranwendungen 1, Universität Stuttgart (2003)Google Scholar
  20. 20.
    Lemaitre, J.: A Course on Damage Mechanics, 2nd edn. Springer, Berlin (1996)CrossRefGoogle Scholar
  21. 21.
    Munjiza, A.: The Combined Finite-Discrete Element Method. Wiley, Chichester (2005)zbMATHGoogle Scholar
  22. 22.
    Pöschel, T., Schwager, T.: Computational Granular Dynamics: Models and Algorithms. Springer, Berlin (2005)Google Scholar
  23. 23.
    Potapov, A.V., Hopkins, M.A., Campbell, C.S.: A two-dimensional dynamic simulation of solid fracture: part I: description of the model. Int. J. Mod. Phys. C 6, 371–398 (1995)CrossRefADSGoogle Scholar
  24. 24.
    Ramm, E., Bischoff, M., Schneider, B.: On some features of a polygonal discrete element model. In: Mueller-Hoeppe, D., Loehnert, S., Reese, S. (eds.) Recent Developments and Innovative Applications in Computational Mechanics, pp. 265–273. Springer, Berlin (2011)CrossRefGoogle Scholar
  25. 25.
    Schäfer, J.: Rohrfluß granularer Materie: Theorie und Simulationen (Pipe Flow of Granular Matter: Theory and Simulations). Ph.D. thesis, Berichte des Forschungszentrums Jülich; 3214, Universität-GH-Duisburg (1996)Google Scholar
  26. 26.
    Schäfer, J., Dippel, S., Wolf, D.E.: Force schemes in simulations of granular materials. J. Phys. I 6, 5–20 (1996)Google Scholar
  27. 27.
    Schneider, B., Bischoff, M., Ramm, E.: Modeling of material failure by the discrete element method. PAMM: Proc. Appl. Math. Mech. 10, 685–688 (2010)CrossRefGoogle Scholar
  28. 28.
    Schneider, B., D’Addetta, G.A., Ramm, E.: Application of the discrete element method to quasibrittle materials. In: Oñate, E., Owen, D.R.J. (eds.) Proceedings of the International Conference on Particle-Based Methods: Fundamentals and Applications (Particles 2009), pp. 97–100, 25–27 Nov 2009, Barcelona, Spain (2009)Google Scholar
  29. 29.
    Schneider, B., D’Addetta, G.A., Ramm, E.: On material modeling by polygonal discrete elements. In: Oñate, E., Owen, R. (eds.) Particle-Based Methods: Fundamentals and Applications. Computational Methods in Applied Sciences, vol. 25, pp. 159–185. Springer, Dordrecht (2011)CrossRefGoogle Scholar
  30. 30.
    Schneider, B.J.: Polygonale diskrete Elemente zur Modellierung heterogener Materialien (Polygonal Discrete Elements for the Modeling of Heterogeneous Materials). Ph.D. thesis, Bericht Nr. 56, Institut für Baustatik und Baudynamik, Universität Stuttgart (2012)Google Scholar
  31. 31.
    Simo, J.C., Hughes, T.J.R.: Computational Inelasticity. Interdisciplinary Applied Mathematics: Mechanics and Materials, vol. 7. Springer, New York (1998)Google Scholar
  32. 32.
    Tillemans, H.-J., Herrmann, H.J.: Simulating deformations of granular solids under shear. Phys. A 217, 261–288 (1995)CrossRefGoogle Scholar
  33. 33.
    Walton, O.R.: Explicit particle dynamics model for granular materials. In: Eisenstein, Z. (ed.) Proceedings of the 4th International Conference on Numerical Methods in Geomechanics, pp. 1261–1268, 31 May–4 June 1982, Edmonton, Canada (1982)Google Scholar
  34. 34.
    Zienkiewicz, O.C., Taylor, R.L., Zhu, J.Z.: The Finite Element Method: Its Basis and Fundamentals, 6th edn. Elsevier, Oxford (2006)zbMATHGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Corporate Sector Research and Advance EngineeringRobert Bosch GmbHRenningenGermany
  2. 2.Institute for Structural MechanicsUniversity of StuttgartStuttgartGermany

Personalised recommendations