Skip to main content

Discrete and continuum modelling of granular materials

  • Chapter
  • First Online:
Continuous and Discontinuous Modelling of Cohesive-Frictional Materials

Part of the book series: Lecture Notes in Physics ((LNP,volume 568))

Abstract

We give an outline of discrete element and continuum models for granular flows involving large deformations, and arbitrary particle shapes. A symbolic solution in the form of a finite element based, particle in cell formulation is also presented. The theories and methods are illustrated by examples such as silo flow, simulated triaxial tests, and trapdoor problems.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 54.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. J. P. Bardet, J. Proubet: A numerical investigation into the structure of persistent shear bands in granular media. Géotechnique 41 (4)L 5(1991) pp. 99–613

    Article  Google Scholar 

  2. S. Chandrasekar: Liquid Crystals, 2nd Edition, (Cambridge University Press, 1992)

    Google Scholar 

  3. S. Chapman, T. G. Cowling: The mathematical theory of non-uniform gases, (Cambridge University Press, Cambridge, 1995)

    Google Scholar 

  4. P. A. Cundall, O. D. L. Strack: A discrete numerical model for granular assemblies. Géotechnique. 29 (1979) pp. 47–65.

    Article  Google Scholar 

  5. P. G. de Gennes, J. Prost: The physics of liquid crystals, 2nd Edition, (Clarendon Press, Oxford, 1995)

    Google Scholar 

  6. T. J. R. Hughes: The finite element method, (Prentice Hall, Englewood-Cliffs, New Jersey, 1987)

    MATH  Google Scholar 

  7. L. Moresi, H.-B. Mühlhaus, F. Dufour: Particle-in-cell solutions for creeping viscous flows with internal interfaces, Proc. 5th Int. Workshop on Bifurcation and Localisation in Geomechanics, Perth, Australia (Balkema, 2000) in press.

    Google Scholar 

  8. H.-B. Mühlhaus, F. Oka: Dispersion and wave propogation in discrete and continuous models for granular materials. Int. J. Solids Structures, 33 (1996) pp. 2841–2858

    Article  MATH  Google Scholar 

  9. H.-B. Mühlhaus, P. Hornby: On the reality of antisymmetric stresses in fast granular flows. Proc. IUTAM Conf. on Granular and Porous Media, eds. Fleck and Cocks, (Kluwer Academic Publishers, 1997) pp 299–311.

    Google Scholar 

  10. H.-B. Mühlhaus, P. Hornby: Polar continua and the micromechanics of granular materials. Chapter 2.2 Mechanics of granular materials, an introduction, eds. M. Oda and K. Iwashita, (A. A. Balkema: Rotterdam, 1999) pp. 86–106

    Google Scholar 

  11. H.-B. Mühlhaus, L. Moresi, R. Freij-Ayoub: Lagrangian particle modelling of granular flows, 2nd Australian Congress on Applied Mechanics, Canberra, 10–12, (February, 1999) pp. 482–487

    Google Scholar 

  12. H. Sakaguchi, H.-B. Mühlhaus: Mesh free modelling of failure and localization in brittle materials. In: Deformation and progressive failure in geomechanics, Proc. IS-Nagoya’ 97 eds. Asaoka, A., Adachi, T. and Oka, F. (Pergamon, 1997) pp.15–21

    Google Scholar 

  13. S. B. Savage: Analysis of slow, high concentration flows of granular materials. J. Fluid Mech. 377 (1998) pp. 1–26

    Article  MATH  ADS  MathSciNet  Google Scholar 

  14. D. Sulsky, Z. Chen, H. L. Schreyer: A particle method for history dependent materials, Comput. Methods Appl. Mech. Engrg., 118 (1994) pp. 179–196

    Article  MATH  MathSciNet  Google Scholar 

  15. C. Thornton: Microscopic approach contributions to constitutive modelling. In: Constitutive modelling of granular materials ed. D. Kolymbas (Springer-Verlag, 2000) pp. 193–208

    Google Scholar 

  16. J. G. M. van Mier, E. Schlangen, A. Vervuurt: Lattice type fracture models for concrete. In: Continuum Models for Materials with Microstructure ed. H.B. Mühlhaus (Wiley, 1995) pp.341–377

    Google Scholar 

  17. C. Zhao, B. E. Hobbs, H.-B. Mühlhaus, & A. Ord, A consistent point-searching algorithm for solution interpolation in unstructured meshes consisting of 4-node bilinear quadrilateral elements, Int J. Numer. Math. Engng, 45, 1509–1526. (1999)

    Article  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2001 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Mühlhaus, H.B., Sakaguchi, H., Moresi, L., Fahey, M. (2001). Discrete and continuum modelling of granular materials. In: Vermeer, P.A., Herrmann, H.J., Luding, S., Ehlers, W., Diebels, S., Ramm, E. (eds) Continuous and Discontinuous Modelling of Cohesive-Frictional Materials. Lecture Notes in Physics, vol 568. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44424-6_14

Download citation

  • DOI: https://doi.org/10.1007/3-540-44424-6_14

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-41525-1

  • Online ISBN: 978-3-540-44424-4

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics