Advertisement

Granular Matter

, 18:20 | Cite as

DEM investigations of two-dimensional granular vortex- and anti-vortex-structures during plane strain compression

  • J. Kozicki
  • J. TejchmanEmail author
Original Paper

Abstract

The paper presents simulation results of a quasi-static plane strain compression test on cohesionless initially dense sand under constant lateral pressure using a three-dimensional discrete element method. Grains were modelled by means of spheres with contact moments imitating irregular particle shapes. The material behaviour was studied at both global and local levels. The stress–strain and volumetric-strain curves, distribution of void ratio, resultant grain rotation and contact forces were calculated. The main attention was paid to the appearance of plane strain granular micro-structures like vortex and anti-vortex structures in the granular specimen during deformation. In order to detect two-dimensional vortex and anti-vortex structures, a method based on orientation angles of displacement fluctuation vectors of neighbouring single spheres was used. The effect of the method parameters was also analyzed.

Keywords

Plane strain compression testa Granular material Discrete element method Vortex Anti-vortex 

Notes

Acknowledgments

The authors would like to acknowledge the support by the Grant 2011/03/B/ST8/05865 “Experimental and theoretical investigations of micro-structural phenomena inside of shear localization in granular materials” financed by the Polish National Science Centre.

References

  1. 1.
    Utter, B., Behringer, R.P.: Self-diffusion in dense granular shear flows. Phys. Rev. E 69(3), 031308-1–031308-12 (2004)ADSCrossRefGoogle Scholar
  2. 2.
    Abedi, S., Rechenmacher, A.L., Orlando, A.D.: Vortex formation and dissolution in sheared sands. Granul. Matter 14, 695–705 (2012)CrossRefGoogle Scholar
  3. 3.
    Richefeu, V., Combe, G., Viggiani, G.: An experimental assessment of displacement fluctuations in a 2D granular material subjected to shear. Geotechn. Lett. 2, 113–118 (2012)CrossRefGoogle Scholar
  4. 4.
    Miller, T., Rognon, P., Metzger, B., et al.: Eddy viscosity in dense granular flows. Phys. Rev. Lett. 111(5), 058002 (2013)ADSCrossRefGoogle Scholar
  5. 5.
    Radjai, F., Roux, S.: Turbulent-like fluctuation in quasi-static flow of granular media. Phys. Rev. Lett. 89, 064302 (2002)ADSCrossRefGoogle Scholar
  6. 6.
    Williams, J.R., Rege, N.: Coherent vortex structures in deforming granular materials. Mech. Cohes. Frict. Mater. 2, 223–236 (1997)CrossRefGoogle Scholar
  7. 7.
    Kuhn, M.R.: Structured deformation in granular materials. Mech. Mater. 31, 407–442 (1999)CrossRefGoogle Scholar
  8. 8.
    Alonso-Marroquin, F., Vardoulakis, I., Herrmann, H., Weatherley, D., Mora, P.: Effect of rolling on dissipation in fault gouges. Phys. Rev. E 74, 031306 (2006)ADSCrossRefGoogle Scholar
  9. 9.
    Tordesillas, A., Muthuswamy, M., Walsh, S.D.C.: Mesoscale measures of nonaffine deformation in dense granular assemblies. J. Eng. Mech. 134(12), 1095–1113 (2008)CrossRefGoogle Scholar
  10. 10.
    Tordesillas, A., Pucilowski, S., Walker, D.M., Peters, J.F., Walizer, L.E.: Micromechanics of vortices in granular media: connection to shear bands and implications for continuum modelling of failure in geomaterials. Int. J. Numer. Anal. Meth. Geomech. 38(12), 1247–1275 (2014)CrossRefGoogle Scholar
  11. 11.
    Tordesillas, A., Pucilowski, S., Lin, Q, Peters, J.F., Behringer, R.P.: Granular vortices: identification, characterization and conditions for the localization of deformation. J. Mech. Phys. Solids (2016). doi: 10.1016/j.jmps.2016.02.032
  12. 12.
    Liu, X., Papon, A., Mühlhaus, H.B.: Numerical study of structural evolution in shear band. Philos. Mag. 92(28–30), 3501–3519 (2012)ADSCrossRefGoogle Scholar
  13. 13.
    Peters, J.F., Walizer, L.E.: Patterned non-affine motion in granular media. J. Eng. Mech. 139(10), 1479–1490 (2013)CrossRefGoogle Scholar
  14. 14.
    Nitka, M., Tejchman, J.: Modelling of concrete behaviour in uniaxial compression and tension with DEM. Granul. Matter 17(1), 145–164 (2014)CrossRefGoogle Scholar
  15. 15.
    Kozicki, J., Niedostatkiewicz, M., Tejchman, J., Mühlhaus, H.-B.: Discrete modelling results of a direct shear test for granular materials versus FE results. Granul. Matter 15(5), 607–627 (2013)Google Scholar
  16. 16.
    Nitka, M., Tejchman, J., Kozicki, J., Leśniewska, D.: DEM analysis of micro-structural events within granular shear zones under passive earth pressure conditions. Granul. Matter 3, 325–343 (2015)CrossRefGoogle Scholar
  17. 17.
    Rognon, P., Einav, I.: Thermal transients and convective particle motion in dense granular materials. Phys. Rev. Lett. 105(21), 218301 (2010)ADSCrossRefGoogle Scholar
  18. 18.
    Desrues, J., Viggiani, C.: Strain localization in sand: over- view of the experiments in Grenoble using stereophotogrammetry. J. Numer. Anal. Methods Geomech. 28(4), 279–321 (2004)CrossRefGoogle Scholar
  19. 19.
    Gudehus, G., Nűbel, K.: Evolution of shear bands in sand. Geotechnique 54(3), 187–201 (2004)CrossRefGoogle Scholar
  20. 20.
    Tejchman, J.: FE modeling of shear localization in granular bodies with micro-polar hypoplasticity. In: Wu, Borja, (eds.) Springer Series in Geomechanics and Geoengineering. Springer, Berlin (2008)Google Scholar
  21. 21.
    Tejchman, J., Gorski, J.: Computations of size effects in granular bodies within micro-polar hypoplasticity during plane strain compression. Int. J. Solids Struct. 45(6), 1546–1569 (2008)CrossRefzbMATHGoogle Scholar
  22. 22.
    Gudehus, G.: Phys. Soil Mech. Springer, Berlin (2011)CrossRefGoogle Scholar
  23. 23.
    Vardoulakis, I.: Shear band inclination and shear modulus in biaxial tests. Int. J. Numer. Anal. Methods Geomech. 4, 103–119 (1980)CrossRefzbMATHGoogle Scholar
  24. 24.
    Tatsuoka, F., Nakamura, S., Huang, C.C., Tani, K.: Strength anisotropy and shear band direction in plane strain test of sand. Soils Found. 30(1), 35–54 (1990)CrossRefGoogle Scholar
  25. 25.
    Han, C., Vardoulakis, I.: Plane strain compression experiments on water saturated fine-grained sand. Geotechnique 41, 49–78 (1991)CrossRefGoogle Scholar
  26. 26.
    Yoshida, T., Tatsuoka, F., Siddiquee, M.S.A.: Shear banding in sands observed in plane strain compression. In: Chambon, R., Desrues, J., Vardoulakis, I. (eds.) Localisation and Bifurcation Theory for Soils and Rocks, pp. 165–181. Balkema, Rotterdam (1994)Google Scholar
  27. 27.
    Harris, W.W., Viggiani, G., Mooney, M.A., Finno, R.J.: Use of stereophotogrammetry to analyze the development of shear bands in sand. Geotech. Test J. 18(4), 405–420 (1995)CrossRefGoogle Scholar
  28. 28.
    Alshibli, K.A., Sture, S.: Shear band formation in plane strain experiments of sand. J. Geotech. Geoenviron. Eng. ASCE 126(6), 495–503 (2000)CrossRefGoogle Scholar
  29. 29.
    Mokni, M., Desrues, J.: Strain localization measurements in undrained plane strain biaxial tests on Hostun RF sand. Mech. Cohes. Frict. Mater. 4, 419–441 (1998)CrossRefGoogle Scholar
  30. 30.
    de Borst, R., Műhlhaus, H.B.: Gradient dependent plasticity: formulation and algorithmic aspects. Int. J. Numer. Methods Eng. 35, 521–539 (1992)CrossRefzbMATHGoogle Scholar
  31. 31.
    Tejchman, J., Wu, W.: Numerical study on shear band patterning in a Cosserat continuum. Acta Mech. 99, 61–74 (1993)CrossRefzbMATHGoogle Scholar
  32. 32.
    Brinkgreve, R.: Geomaterial models and numerical analysis of softening. Dissertation, Delft University, pp. 1–153 (1994)Google Scholar
  33. 33.
    Tejchman, J.: Influence of a characteristic length on shear zone formation in hypoplasticity with different enhancements. Comput. Geotech. 31(8), 595–611 (2004)CrossRefGoogle Scholar
  34. 34.
    Tejchman, J., Wu, W.: Modeling of textural anisotropy in granular materials with micro-polar hypoplasticity. Int. J. Non-Linear Mech. 42, 882–894 (2007)ADSCrossRefGoogle Scholar
  35. 35.
    Tejchman, J., Wu, W.: Non-coaxiality and stress-dilatancy rule in granular materials: FE investigation within micro-polar hypoplasticity. Int. J. Numer. Anal. Methods Geomech. 33(1), 117–142 (2009)CrossRefzbMATHGoogle Scholar
  36. 36.
    Tejchman, J., Górski, J.: FE study of patterns of shear zones in granular bodies during plane strain compression. Acta Geotech. 5(2), 95–112 (2010)CrossRefGoogle Scholar
  37. 37.
    Regueiro, R.A., Borja, R.I.: Plane strain finite element analysis of pressure sensitive plasticity with strong discontinuity. Int. J. Solids Struct. 38(21), 3647–3672 (2001)CrossRefzbMATHGoogle Scholar
  38. 38.
    Bobinski, J., Tejchman, J.: Simulations of shear zones and cracks in engineering materials using eXtended Finite Element Method. I. J. Numer. Anal. Meth. Geom. 40, 406–435 (2016)CrossRefGoogle Scholar
  39. 39.
    Oda, M., Kazama, H.: Microstructure of shear bands and its relation to the mechanisms of dilatancy and failure of dense granular soils. Geotechnique 48, 465–481 (1998)CrossRefGoogle Scholar
  40. 40.
    Ord, A., Hobbs, B., Regenauer-Lieb, K.: Shear band emergence in granular materials—a numerical study. Int. J. Numer. Anal. Methods Geomech. 31, 373–393 (2007)CrossRefzbMATHGoogle Scholar
  41. 41.
    Pena, A.A., Garcia-Rojo, R., Herrmann, H.J.: Influence of particle shape on sheared dense granular media. Granul. Matter 3–4, 279–292 (2007)CrossRefzbMATHGoogle Scholar
  42. 42.
    Bi, Z., Sun, Q., Jin, F., Zhang, M.: Numerical study on energy transformation in granular matter under biaxial compression. Granul. Matter 13, 503–510 (2011)CrossRefGoogle Scholar
  43. 43.
    Lätzel, M., Luding, S., Herrmann, H.J., Howell, D.W., Behringer, R.P.: Comparing simulation and experiment of a 2D granular couette shear device. Eur. Phys. J. E11, 325–333 (2003)Google Scholar
  44. 44.
    Rojek, J.: Discrete element modelling of rock cutting. Comput. Methods Mater. Sci. 7(2), 224–230 (2007)Google Scholar
  45. 45.
    Nitka, M., Combe, G., Dascalu, C., Desrues, J.: Two-scale modeling of granular materials: a DEM-FEM approach. Granul. Matter 13, 277–281 (2011)CrossRefGoogle Scholar
  46. 46.
    Kozicki, J., Donze, F.V.: A new open-source software developed for numerical simulations using discrete modelling methods. Comput. Methods Appl. Mech. Eng. 197, 4429–4443 (2008)ADSCrossRefzbMATHGoogle Scholar
  47. 47.
    Šmilauer, V., Chareyre, B.: Yade DEM Formulation. Manual, (2011)Google Scholar
  48. 48.
    Vardoulakis, I., Goldschneider, M., Gudehus, G.: Formation of shear bands in sand bodies as a bifurcation problem I. J. Numer. Anal. Methods Geomech. 2, 99–128 (1978)CrossRefGoogle Scholar
  49. 49.
    Gould, H., Tobochnik, J., Christian, W.: Introduction to computer simulation methods: application to physical systems (3rd edn), chapter 15, pp. 655. http://www.amazon.com/Introduction-Computer-Simulation-Methods-Addison-Wesley/dp/B00LZMC2N0 (2011)
  50. 50.
    Kozicki, J., Tejchman, J., Mróz, Z.: Effect of grain roughness on strength, volume changes, elastic and dissipated energies during quasi-static homogeneous triaxial compression using DEM. Granul. Matter 14(4), 457–468 (2012)CrossRefGoogle Scholar
  51. 51.
    Kozicki, J., Tejchman, J., Műhlhaus, H.B.: Discrete simulations of a triaxial compression test for sand by DEM. Int. J. Num. Anal. Methods Geomech. 38, 1923–1952 (2014)CrossRefGoogle Scholar
  52. 52.
    Iwashita, K., Oda, M.: Rolling resistance at contacts in simulation of shear band development by DEM. ASCE J. Eng. Mech. 124(3), 285–292 (1998)CrossRefGoogle Scholar
  53. 53.
    Cundall, P.A., Hart, R.: Numerical modeling of discontinua. J. Eng. Comput. 9, 101–113 (1992)CrossRefGoogle Scholar
  54. 54.
    Kolymbas, D., Wu, W.: Recent results of triaxial tests with granular materials. Powder Technol. 60(2), 99–119 (1990)CrossRefGoogle Scholar
  55. 55.
    Wu, W.: Hypoplastizität als mathematisches Modell zum mechanischen Verhalten granularer Stoffe. Heft 129, Institute for Soil- and Rock-Mechanics, University of Karlsruhe (1992)Google Scholar
  56. 56.
    Agnolin, I., Roux, J.N.: Internal states of model isotropic granular packings. I. Assembling process, geometry, and contact networks. Phys. Rev. E 76, 061302 (2007)ADSMathSciNetCrossRefGoogle Scholar
  57. 57.
    Ballhause, D., König, M., Kröplin, B.: Modelling fabric-reinforced membranes with the discrete element method. Comput. Methods Appl. Sci. 8, 51–67 (2008)CrossRefzbMATHGoogle Scholar
  58. 58.
    Cheung, G., O’Sullivan, C.: Effective simulation of flexible lateral boundaries in two- and three-dimensional DEM simulations. Particuology 6, 483–500 (2008)CrossRefGoogle Scholar
  59. 59.
    Wang, Y., Tonon, F.: Modelling triaxial test on intact rock using discrete element method with membrane boundary. J. Eng. Mech. 135(9), 1029–1037Google Scholar
  60. 60.
    Press, W.H.: Flicker noises in astronomy and elsewhere. Comments Astrophys. 7, 103. http://www.lanl.gov/dldstp/Flicker_Noise_1978.pdf (1978)
  61. 61.
    Uesugi, M., Kishida, H., Tsubakihara, Y.: Behaviour of sand particles in sand-steel friction. Soils Found. 28(1), 107–118 (1988)CrossRefGoogle Scholar
  62. 62.
    Skarżyński, L., Tejchman, J.: Experimental investigations of fracture process in concrete by means of X-ray micro-computed tomography. Strain 52, 26–45 (2016)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  1. 1.Faculty of Civil and Environmental EngineeringGdańsk University of TechnologyGdańskPoland

Personalised recommendations