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Computational Mechanics

, Volume 60, Issue 6, pp 997–1010 | Cite as

Accurate modelling of the elastic behavior of a continuum with the Discrete Element Method

  • M. A. Celigueta
  • S. Latorre
  • F. Arrufat
  • E. Oñate
Original Paper
  • 405 Downloads

Abstract

The Discrete Element Method (DEM) has been used for modelling continua, like concrete or rocks. However, it requires a big calibration effort, even to capture just the linear elastic behavior of a continuum modelled via the classical force-displacement relationships at the contact interfaces between particles. In this work we propose a new way for computing the contact forces between discrete particles. The newly proposed forces take into account the surroundings of the contact, not just the contact itself. This brings in the missing terms that provide an accurate approximation to an elastic continuum, and avoids calibration of the DEM parameters for the purely linear elastic range.

Keywords

DEM Continuum Elasticity Young’s modulus Poisson’s ratio 

Notes

Acknowledgements

This project was partially funded by the Office for Naval Research of the US and the European Research Council through projects NICE-SHIP and ICEBREAKER, respectively. We also acknowledge the financial support of the CERCA programme of the Generalitat de Catalunya. We would like to thank the Kratos Team [20] at CIMNE for their support during the implementation of the DEMpack code [21] used for the DEM computations, and the GiD Team [22] at CIMNE for their support in pre and postprocessing the computed cases. Thanks also to Prof. Juan Miquel and Dr. Miquel Santasusana for the fruitful discussions that sparked the interest in this research.

References

  1. 1.
    Cundall PA, Strack OD (1979) A discrete numerical model for granular assemblies. Geotechnique 29(1):47–65CrossRefGoogle Scholar
  2. 2.
    Langston PA, Tüzün U, Heyes DM (1995) Discrete element simulation of granular flow in 2D and 3D hoppers: dependence of discharge rate and wall stress on particle interactions. Chem Eng Sci 50(6):967–987CrossRefGoogle Scholar
  3. 3.
    Cleary PW, Sawley ML (2002) DEM modelling of industrial granular flows: 3D case studies and the effect of particle shape on hopper discharge. Appl Math Modell 26(2):89–111CrossRefzbMATHGoogle Scholar
  4. 4.
    Xu BH, Yu AB (1997) Numerical simulation of the gas-solid flow in a fluidized bed by combining discrete particle method with computational fluid dynamics. Chem Eng Sci 52(16):2785–2809CrossRefGoogle Scholar
  5. 5.
    Tsuji Y, Kawaguchi T, Tanaka T (1993) Discrete particle simulation of two-dimensional fluidized bed. Powder Technol 77(1):79–87CrossRefGoogle Scholar
  6. 6.
    Oñate E, Labra C, Zárate F, Rojek J (2012) Modelling and simulation of the effect of blast loading on structures using an adaptive blending of discrete and finite element methods. Risk Anal Dam Saf Dam Secur Crit Infrastruct Manag 53:365–372Google Scholar
  7. 7.
    Moreno R, Ghadiri M, Antony SJ (2003) Effect of the impact angle on the breakage of agglomerates: a numerical study using DEM. Powder Technol 130(1):132–137CrossRefGoogle Scholar
  8. 8.
    Oñate E, Zárate F, Miquel J, Santasusana M, Celigueta MA, Arrufat F, Gandikota R, Valiullin KM, Ring L (2015) A local constitutive model for the discrete element method. Application to geomaterials and concrete. Comput Part Mech 2(2):139–160CrossRefGoogle Scholar
  9. 9.
    Brown NJ, Chen JF, Ooi JY (2014) A bond model for DEM simulation of cementitious materials and deformable structures. Granular Matter 16(3):299–311CrossRefGoogle Scholar
  10. 10.
    Rojek J, Oñate E, Labra C, Kargl H (2011) Discrete element simulation of rock cutting. Int J Rock Mech Min Sci 48(6):996–1010CrossRefGoogle Scholar
  11. 11.
    Potyondy DO, Cundall PA (2004) A bonded-particle model for rock. Int J Rock Mech Min Sci 41(8):1329–1364CrossRefGoogle Scholar
  12. 12.
    Donzé F, Magnier SA (1995) Formulation of a 3D numerical model of brittle behaviour. Geophys J Int 122(3):790–802CrossRefGoogle Scholar
  13. 13.
    Oñate E, Rojek J (2004) Combination of discrete element and finite element methods for dynamic analysis of geomechanics problems. Comput Methods Appl Mech Eng 193(27):3087–3128CrossRefzbMATHGoogle Scholar
  14. 14.
    Hentz S, Daudeville L, Donzé FV (2004) Identification and validation of a discrete element model for concrete. J Eng Mech 130(6):709–719CrossRefGoogle Scholar
  15. 15.
    Labra CA (2012) Advances in the development of the discrete element method for excavation processes. Ph.D. Thesis, Universitat Politècnica de Catalunya, BarcelonaGoogle Scholar
  16. 16.
    Luding S (2008) Introduction to discrete element methods: basic of contact force models and how to perform the micro-macro transition to continuum theory. Eur J Environ Civ Eng 12(7–8):785–826CrossRefGoogle Scholar
  17. 17.
    Rojek J, Karlis GF, Malinowski LJ, Beer G (2013) Setting up virgin stress conditions in discrete element models. Comput Geotech 48:228–248CrossRefGoogle Scholar
  18. 18.
    Okabe A, Boots B, Sugihara K, Chiu SN (2009) Spatial tessellations: concepts and applications of Voronoi diagrams, vol 501. Wiley, HobokenzbMATHGoogle Scholar
  19. 19.
    Thornton C, Cummins SJ, Cleary PW (2011) An investigation of the comparative behaviour of alternative contact force models during elastic collisions. Powder Technol 210(3):189–197 ISO 690CrossRefGoogle Scholar
  20. 20.
    Dadvand P, Rossi R, Oñate E (2010) An object-oriented environment for developing finite element codes for multi-disciplinary applications. Arch Comput Methods Eng 17(3):253–297CrossRefzbMATHGoogle Scholar
  21. 21.
  22. 22.
    Ribó R, Pasenau M, Escolano E, Ronda JS, González LF (1998) GiD reference manual. CIMNE, BarcelonaGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany 2017

Authors and Affiliations

  • M. A. Celigueta
    • 1
    • 2
  • S. Latorre
    • 1
  • F. Arrufat
    • 1
  • E. Oñate
    • 1
    • 2
  1. 1.Centre Internacional de Metodes Numerics a l’Enginyeria - CIMNEBarcelonaSpain
  2. 2.Universitat Politècnica de Catalunya (UPC)BarcelonaSpain

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