A unified numerical framework for rigid and compliant granular materials

Article

Abstract

A numerical framework for the simulation of granular materials composed of mixed rigid and compliant grains is presented in this paper. This approach is based on a multibody meshfree technique, coupled in a very natural way with classic concepts from the discrete element method. The equations of motion (for the rigid grains) and of continuum mechanics (for the compliant ones) are solved using an adaptive explicit scheme, in fully dynamic conditions. The parallelization strategy is described and tested on an illustrative simulation involving both kinds of grains.

Keywords

Granular materials Meshfree methods Discrete element modelling Multibody dynamics 

Notes

Compliance with ethical standards

Conflict of interest

The author acknowledges that this study contains original material, as a result of a purely academic study without any kind of private funding or conflict of interest. Its publication has been approved tacitly by the responsible authorities at the institute where the work has been carried out.

References

  1. 1.
    M Cundall PA, Strack ODL (1979) A discrete numerical model for granular assemblies. Géotechnique 29(1):47–65CrossRefGoogle Scholar
  2. 2.
    Azema E, Radjai F, Saussine G (2009) Quasistatic rheology, force transmission and fabric properties of a packing of irregular polyhedral particles. Mech Mater 41:729–741CrossRefGoogle Scholar
  3. 3.
    Mollon G, Richefeu V, Villard P, Daudon D (2015) Discrete modelling of rock avalanches: sensitivity to block and slope geometries. Granul Matter 17(5):645–666CrossRefGoogle Scholar
  4. 4.
    Stahl M, Konietzky H (2011) Discrete element simulation of ballast and gravel under special consideration of grain-shape, grain-size and relative density. Granul Matter 13:417–428CrossRefGoogle Scholar
  5. 5.
    Mollon G, Zhao J (2013) Characterization of fluctuations in granular hopper flow. Granul Matter 15(6):827–840CrossRefGoogle Scholar
  6. 6.
    Herbst JA, Potapov AV (2004) Making a discrete grain breakage model practical for comminution equipment performance simulation. Powder Technol 143:144–150CrossRefGoogle Scholar
  7. 7.
    Zhao J, Shan T (2013) Coupled CFD-DEM simulation of fluid–particle interaction in geomechanics. Powder Technol 239:248–258CrossRefGoogle Scholar
  8. 8.
    Richard D, Iordanof I, Renouf M, Berthier Y (2008) Thermal study of the dry sliding contact with third-body presence. ASME J Tribol 130(3):031404CrossRefGoogle Scholar
  9. 9.
    O’Sullivan C (2011) Particle-based discrete element modeling: geomechanics perspective. Int J Geomech 11(6):449–464CrossRefGoogle Scholar
  10. 10.
    Darve F, Duriez J, Wan R (2016) DEM modelling in geomechanics: some recent breakthroughs. In: Proceedings of the 7th international conference on discrete element method, pp 3–12Google Scholar
  11. 11.
    Cagnoli B, Piersanti A (2015) Grain size and flow volume effects on granular flow mobility in numerical simulations: 3-D discrete element modeling of flows of angular fragments. J Geophys Res Solid Earth 120(4):2350–2366CrossRefGoogle Scholar
  12. 12.
    Tijskens E, Ramon H, De Baerdemaeker J (2003) Discrete element modelling for process simulation in agriculture. J Sound Vib 66:493–514CrossRefGoogle Scholar
  13. 13.
    Ouhbi N, Voivret C, Perrin G, Roux JN (2016) Railway ballast: grain shape characterization to study its influence on the mechanical behaviour. Procedia Eng 143:1120–1127CrossRefGoogle Scholar
  14. 14.
    Fillot N, Iordanof I, Berthier Y (2004) A granular dynamic model for the degradation of material. ASME J Tribol 126(3):606–14CrossRefGoogle Scholar
  15. 15.
    Mollon G (2015) A numerical framework for discrete modelling of friction and wear using Voronoi polyhedrons. Tribol Int 90:343–355CrossRefGoogle Scholar
  16. 16.
    Richards K, Bithell M, Dove MT, Hodge RA (2004) Discrete-element modelling: methods and applications in the environmental sciences. Philos Trans R Soc A Math Phys Eng Sci 362(1822):1797–1816MathSciNetCrossRefMATHGoogle Scholar
  17. 17.
    Da Cruz F, Emam S, Prochnow M, Roux JN, Chevoir F (2005) Rheophysics of dense granular materials: discrete simulation of plans shear flows. Phys Rev E 72:021309CrossRefGoogle Scholar
  18. 18.
    Jean M (1999) The non-smooth contact dynamics method. Comput Methods Appl Mech Eng 177(3–4):235–257MathSciNetCrossRefMATHGoogle Scholar
  19. 19.
    Gethin DT, Lewis RW, Ransing RS (2003) A discrete deformable element approach for the compaction of powder systems. Model Simul Mater Sci Eng 11:101–114CrossRefGoogle Scholar
  20. 20.
    Mirea DA, Trunfio-Sfarghiu A-M, Matei CI, Munteanu B, Piednoir A, Rieu JP, Blanchin MG, Berthier Y (2013) Role of the biomolecular interactions in the structure and tribological properties of synovial fluid. Tribol Int 59:302–311CrossRefGoogle Scholar
  21. 21.
    Duvernois V, Marsden AL, Shadden SC (2013) Lagrangian analysis of hemodynamics data from FSI simulation. Int J Numer Methods Biomed Eng 29:445–461MathSciNetCrossRefGoogle Scholar
  22. 22.
    Descartes S, Saulot A, Godeaux C, Bondeux S, Dayot C, Berthier Y (2011) Wheel flange/rail gauge corner contact lubrication: tribological investigations. Wear 271:54–61CrossRefGoogle Scholar
  23. 23.
    Zhang J (2009) A study of composite particles by multi-particle finite element method. Compos Sci Technol 69:2048–2053CrossRefGoogle Scholar
  24. 24.
    Harthong B, Jerier J-F, Richefeu V, Chareyre B, Doremus P, Imbault D, Donzé F-V (2012) Contact impingement in packings of elastic–plastic spheres, application to powder compaction. Int J Mech Sci 61:32–43CrossRefGoogle Scholar
  25. 25.
    Gustafsson G, Haggblad H-A, Jonsen P (2013) Multi-particle finite element modelling of the compression of iron pellets with statistically distributed geometric and material data. Powder Technol 239:231–238CrossRefGoogle Scholar
  26. 26.
    Mollon G (2016) A multibody meshfree strategy for the simulation of highly deformable granular materials. Int J Numer Methods Eng 108(12):1477–1497MathSciNetCrossRefGoogle Scholar
  27. 27.
    Liu GR, Zhang GY, Gu YT, Wang YY (2005) A meshfree radial point interpolation method (RPIM) for three-dimensional solids. Comput Mech 36:421–430MathSciNetCrossRefMATHGoogle Scholar
  28. 28.
    Nayroles B, Touzot G, Villon P (1992) Generalizing the finite element method: diffuse approximation and diffuse elements. Comput Mech 10:307–318CrossRefMATHGoogle Scholar
  29. 29.
    Belytschko T, Lu YY, Gu L (1994) Element-free Galerkin methods. Int J Numer Methods Eng 37:229–256MathSciNetCrossRefMATHGoogle Scholar
  30. 30.
    Ferellec J-F, McDowell G (2010) A method to model realistic particle shape and inertia in DEM. Granul Matter 12:459–467CrossRefMATHGoogle Scholar
  31. 31.
    Cohen J, Lin MC, Manocha D, Ponamgi MK (1995) I-COLLIDE: an interactive and exact collision detection system for large scale environments. In: ACM interactive 3D graphics symposium, Monterey, USAGoogle Scholar
  32. 32.
    Mollon G, Zhao J (2012) Fourier–Voronoi-based generation of realistic samples for discrete modelling of granular materials. Granul Matter 14:621–638CrossRefGoogle Scholar
  33. 33.
    Mollon G, Zhao J (2014) 3D generation of realistic granular samples based on random fields theory and Fourier shape descriptors. Comput Methods Appl Mech Eng 279:46–65CrossRefGoogle Scholar

Copyright information

© OWZ 2018

Authors and Affiliations

  1. 1.Université de Lyon, LaMCoS, INSA-Lyon, CNRS UMR5259LyonFrance

Personalised recommendations