Skip to main content
Log in

Granular contact dynamics with particle elasticity

  • Original Paper
  • Published:
Granular Matter Aims and scope Submit manuscript

Abstract

A granular contact dynamics formulation for elastically deformable particles is detailed. The resulting scheme bears some similarity to traditional molecular dynamics schemes in that the consideration of a finite elastic contact stiffness implies the possibility for inter-particle penetration. However, in contrast to traditional molecular dynamics schemes, there are no algorithmic repercussions from operating with a large or, in the extreme case infinite, contact stiffness. Indeed, the algorithm used—a standard second-order cone programming solver—is independent of the particle scale model and is applicable to rigid as well as elastically deformable particles.

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

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

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

    Article  Google Scholar 

  2. Cundall P.A., Hart D.H.: Numerical modelling of discontinua. Eng. Comput. 9, 101–113 (1992)

    Article  Google Scholar 

  3. Belheine N., Plassiard J.P., Donze F.V., Darve F., Seridi A.: Numerical simulation of drained triaxial test using 3d discrete element modeling. Comput. Geotech. 36, 320–331 (2009)

    Article  Google Scholar 

  4. Ng T.T.: Input parameters of discrete element methods. J. Eng. Mech. 132, 723–729 (2006)

    Article  Google Scholar 

  5. Antony S.J., Kruyt N.P.: Role of interparticle friction and particle-scale elasticity in the shear-strength mechanism of three-dimensional granular media. Phys. Rev. E 79, 031308 (2009)

    Article  ADS  Google Scholar 

  6. Ding Y., Gravish N., Goldman D.I.: Drag induced lift in granular media. Phys. Rev. Lett. 106, 028001 (2011)

    Article  ADS  Google Scholar 

  7. Moreau, J.J.: Bounded variation in time. In: Panagiotopoulos, P.D., Strang, G. (eds.) Topics in Nonsmooth Mechanics, vol. 1, pp. 1–74 (1987)

  8. Moreau, J.J.: Unilateral contact and dry friction in finite freedom dynamics. In: Moreau, J.J., Panagiotopoulos, P. (eds.) Non-Smooth Mechanics and Applications, CISM Courses and Lectures, vol. 302, pp. 1–82. Springer, Berlin (1988)

  9. Moreau J.J.: Some numerical methods in multibody dynamics: application to granular materials. Eur. J. Mech. A Solids 13, 93–114 (1994)

    MathSciNet  MATH  Google Scholar 

  10. Jean M.: The non-smooth contact dynamics method. Comput. Methods Appl. Mech. Eng. 177, 235–257 (1999)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  11. Radjai F., Michel J., Moreau J.J., Roux S.: Force distributions in dense two-dimensional granular systems. Phys. Rev. Lett. 77, 274–277 (1996)

    Article  ADS  Google Scholar 

  12. Nouguier-Lehon C., Cambou B., Vincens E.: Influence of particle shape and angularity on the behavior of granular materials: a numerical analysis. Int. J. Numer. Anal. Methods Geomech. 27, 1207–1226 (2003)

    Article  MATH  Google Scholar 

  13. McNamara S., Herrmann H.: Measurement of indeterminacy in packings of perfectly rigid disks. Phys. Rev. E 70, 061303 (2004)

    Article  MathSciNet  ADS  Google Scholar 

  14. Renouf M., Dubois F., Alart P.: A parallel version of the non smooth contact dynamics algorithm applied to the simulation of granular media. J. Comput. Appl. Math. 168, 375–382 (2004)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  15. Taboada A., Chang K.J., Radjai F., Bouchette F.: Rheology force transmission and shear instabilities in frictional granular media from biaxial numerical test using the contact dynamics method. J. Geophys. Res. 110, 1–24 (2005)

    Article  Google Scholar 

  16. Staron L., Hinch E.J.: Study of the collapse of granular columns using two-dimensional discrete-grain simulation. J. Fluid Mech. 545, 1–27 (2005)

    Article  ADS  MATH  Google Scholar 

  17. Bartels G., Unger T., Kadau D., Wolf D.E., Kertesz J.: The effect of contact torques on porosity of cohesive powders. Granul. Matter 7, 139–143 (2005)

    Article  MATH  Google Scholar 

  18. Kadau D., Schwesig D., Theuerkauf J., Wolf D.E.: Influence of particle elasticity in shear testers. Granul. Matter 8, 35–40 (2006)

    Article  Google Scholar 

  19. Saussine G., Cholet C., Gautier P.E., Dubois F., Bohatier C., Moreau J.J.: Modelling ballast behaviour under dynamic loading part 1.: A 2D polygonal discrete element method approach. Comput. Methods Appl. Mech. Eng. 195, 2841–2859 (2006)

    Article  ADS  MATH  Google Scholar 

  20. Staron L., Hinch E.J.: The spreading of a granular mass: role of grain properties and initial conditions. Granul. Matter 9, 205–217 (2007)

    Article  MATH  Google Scholar 

  21. Ries A., Wolf D.E., Unger T.: Shear zones in granular media: three-dimensional contact dynamics simulation. Phys. Rev. E 76, 051301 (2007)

    Article  ADS  Google Scholar 

  22. Radjai F., Richefeu V.: Contact dynamics as a nonsmooth discrete element method. Mech. Mater. 41, 715–728 (2009)

    Article  Google Scholar 

  23. Stegmann T., Török J., Brendel L., Wolf D.E.: Minimal dissipation theory and shear bands in biaxial tests. Granul. Matter 13, 565–572 (2011)

    Article  Google Scholar 

  24. Estrada N., Azema E., Radjai F., Taboada A.: Identification of rolling resistance as a shape parameter in sheared granular media. Phys. Rev. E 84, 011306 (2011)

    Article  ADS  Google Scholar 

  25. Kadau D., Andrade J.S. Jr, Herrman H.J.: A micromechanical model of collapsing quicksand. Granul. Matter 13, 219–223 (2011)

    Article  Google Scholar 

  26. Lagree, P.Y., Staron, L., Popinet, S.: The granular column collapse as a continuum: validity of a two-dimensional Navier–Stokes model with a μ(i)-rheology. J. Fluid Mech. 686, 378–408 (2011)

    Google Scholar 

  27. Petraa C., Gavreab B., Anitescu M., Potraa F.: A computational study of the use of an optimization-based method for simulating large multibody systems. Optim. Methods Softw. 24, 871–894 (2009)

    Article  MathSciNet  Google Scholar 

  28. Tasora A., Anitescu M.: A convex complementarity approach for simulating large granular flows. J. Comput. Nonlinear Dyn. 5, 031004 (2010)

    Article  Google Scholar 

  29. Tasora A., Anitescu M.: A matrix-free cone complementarity approach for solving large-scale, nonsmooth, rigid body dynamics. Comput. Methods Appl. Mech. Eng. 200, 439–453 (2011)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  30. Acary V., Brogliato B.: Numerical Methods for Nonsmooth Dynamical Systems. Springer, Berlin (2008)

    MATH  Google Scholar 

  31. Cambou B., Jean M., Radjai F.: Micromechanics of Granular Materials. Wiley, London (2009)

    Book  MATH  Google Scholar 

  32. Krabbenhoft, K., Lyamin, A.V., Huang, J., Vicente da Silva M.: Granular contact dynamics using mathematical programming methods. Comput. Geotech. 43, 165–176 (2012, in press)

    Google Scholar 

  33. Wood W.L.: Practical Time-Stepping Schemes. Oxford University Press, Oxford (1990)

    MATH  Google Scholar 

  34. Washizu K.: Variational Methods of Elasticity and Plasticity. Pergamon Press, Oxford (1982)

    Google Scholar 

  35. Krabbenhoft K., Lyamin A.V., Sloan S.W., Wriggers P.: An interior-point method for elastoplasticity. Int. J. Numer. Methods Eng. 69, 592–626 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  36. Krabbenhoft K., Lyamin A.V., Sloan S.W.: Formulation and solution of some plasticity problems as conic programs. Int. J. Solids Struct. 44, 1533–1549 (2007)

    Article  Google Scholar 

  37. Krabbenhoft K., Lyamin A.V.: Computational Cam clay plasticity using second-order cone programming. Comput. Methods Appl. Mech. Eng. 209–212, 239–249 (2012)

    Article  MathSciNet  Google Scholar 

  38. Anitescu M., Hart G.D.: A constraint-stabilized time-stepping approach for rigid multibody dynamics with joints, contact and friction. Int. J. Numer. Methods Eng. 60, 2335–2371 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  39. Anitescu M.: Optimization-based simulation of nonsmooth rigid multibody dynamics. Math. Program. A 105, 113–143 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  40. Tasora A., Anitescu M.: An iterative approach for cone complementarity problems for nonsmooth dynamics. Comput. Optim. Appl. 47, 207–235 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  41. Andersen E.D., Roos C., Terlaky T.: On implementing a primal-dual interior-point method for conic quadratic optimization. Math. Program. 95, 249–277 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  42. Sturm, J.F.: SeDuMi 1.02, a MATLAB toolbox for optimizing over symmetric cones. Optim. Methods Softw. 11–12, 625–653 (1999) http://sedumi.mcmaster.ca/

  43. Krabbenhoft K., Lyamin A.V., Hjiaj M., Sloan S.W.: A new discontinuous upper bound limit analysis formulation. Int. J. Numer. Methods Eng. 63, 1069–1088 (2005)

    Article  MATH  Google Scholar 

  44. Souloumiac P., Leroy Y.M., Maillot B., Krabbenhoft K.: Predicting stress distributions in fold-and-thrust belts and accretionary wedges by optimization. J. Geophys. Res. 114, B09404 (2009)

    Article  ADS  Google Scholar 

  45. Souloumiac P., Krabbenhoft K., Leroy Y.M., Maillot B.: Failure in accretionary wedges with the maximum strength theorem: numerical algorithm and 2d validation. Comput. Geosci. 14, 793–811 (2010)

    Article  MATH  Google Scholar 

  46. Radjai F., Brendel L., Roux S.: Nonsmoothness, indeterminacy, and friction in two-dimensional arrays of rigid particles. Phys. Rev. E 861, 54 (1996)

    Google Scholar 

  47. Snoeijer J.H., Vlugt T.J.H., Hecke M., Saarloos W.: Force network ensemble: a new approach to static granular matter. Phys. Rev. Lett. 054302, 92 (2004)

    Google Scholar 

  48. McNamara S., Garcia-Rojo R., Herrmann H.: Indeterminacy and the onset of motion in a simple granular packing. Phys. Rev. E 021304, 72 (2005)

    Google Scholar 

  49. Unger T., Kertesz J., Wolf D.E.: Force indeterminacy in the jammed state of hard disks. Phys. Rev. Lett. 178001, 94 (2005)

    Google Scholar 

  50. Chen W.F., Han D.J.: Plasticity for Structural Engineers. Springer, New York (1988)

    Book  MATH  Google Scholar 

  51. Mohamed A., Gutierrez M.: Comprehensive study of the effects of rolling resistance on the stressstrain and strain localization behavior of granular materials. Granul. Matter 12, 527–541 (2010)

    Article  Google Scholar 

  52. Lade P.V., Wang Q.: Analysis of shear banding in true triaxial tests on sand. J. Eng. Mech. 127, 762–768 (2001)

    Article  Google Scholar 

  53. Rechenmacher A.L.: Grain-scale processes governing shear band initiation and evolution in sands. J. Mech. Phys. Solids 54, 22–45 (2006)

    Article  ADS  MATH  Google Scholar 

  54. Nash S.G., Sofer A.: Linear and Nonlinear Programming. McGraw-Hill, New York (1996)

    Google Scholar 

  55. Vanderbei R.J.: Linear Programming: Foundations and Extensions. Springer, Berlin (2001)

    MATH  Google Scholar 

  56. Boyd S., Vandenberghe L.: Convex Optimization. Cambridge University Press, Cambridge (2006)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to K. Krabbenhoft.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Krabbenhoft, K., Huang, J., da Silva, M.V. et al. Granular contact dynamics with particle elasticity. Granular Matter 14, 607–619 (2012). https://doi.org/10.1007/s10035-012-0360-1

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10035-012-0360-1

Keywords

Navigation