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A thermomicromechanical approach to multiscale continuum modeling of dense granular materials

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Abstract

A new method is proposed for the development of a class of elastoplastic thermomicromechanical constitutive laws for granular materials. The method engenders physical transparency in the constitutive formulation of multiscale phenomena from the particle to bulk. We demonstrate this approach for dense, cohesionless granular media under quasi-static loading conditions. The resulting constitutive law—expressed solely in terms of particle scale properties—is the first of its kind. Micromechanical relations for the internal variables, tied to nonaffine deformation, and their evolution laws, are derived from a structural mechanical analysis of a particular mesoscopic event: confined, elastoplastic buckling of a force chain. It is shown that the constitutive law can reproduce the defining behavior of strain-softening under dilatation in both the mesoscopic and macroscopic scales, and reliably predict the formation and evolution of shear bands. The thickness and angle of the shear band, the distribution of particle rotation and the evolution of the normal contact force anisotropy inside the band, are consistent with those observed in discrete element simulations and physical experiments.

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References

  1. Aharonov E, Sparks D (2004) Stick-slip motion in simulated granular layers. J Geophys Res 109:B09306

    Article  Google Scholar 

  2. Albert I, Tegzes P, Albert R, A.-L. Barabasi, Vicsek T, Kahng B, Schiffer P (2001) Stick-slip fluctuations in granular drag. Phys Rev E 64(3):031307

    Article  Google Scholar 

  3. Bathurst RJ, Rothenburg L (1990) Observations on stress–force–fabric relationships in idealized granular materials. Mech Mater 9:65

    Article  Google Scholar 

  4. da Cruz F, Emam S, Prochnow M, Roux J-N, Chevoir F (2005) Rheophysics of dense granular materials: discrete simulation of plane shear flows. Phys Rev E 72(2):021309

    Article  Google Scholar 

  5. Dalton F, Corcoran D (2001) Self-organized criticality in a sheared granular stick-slip system. Phys Rev E 63(6):061312

    Article  Google Scholar 

  6. Dennin M (2004) Statistics of bubble rearrangements in a slowly sheared two-dimensional foam. Phys Rev E 70:041406

    Google Scholar 

  7. Falk ML, Langer JS (1998) Dynamics of viscoplastic deformation in amorphous solids. Phys Rev E 57(6):7192–7205

    Article  Google Scholar 

  8. Gardiner BS, Tordesillas A (2005) Micromechanical constitutive modelling of granular media: evolution and loss of contact in particle clusters. J Eng Math 52:93–106

    MATH  MathSciNet  Google Scholar 

  9. Iwashita K, Oda M (2000) Micro-deformation mechanism of shear banding process based on modified distinct element method. Powder Technol 109(1):192–205

    Google Scholar 

  10. Kabla A, Debregeas G (2003) Local stress relaxation and shear banding in a dry foam under shear. Phys Rev Lett 90(25):258303

    Google Scholar 

  11. Koenders MA (1997) Evolution of spatially structured elastic materials using a harmonic density function. Phys Rev E 56(5):5585–5593

    Google Scholar 

  12. Kruyt NP, Rothenburg L (2001) Statistics of the elastic behavior of granular materials. Int J Solids Struct 38(28–29):4879-4899

    Article  MATH  Google Scholar 

  13. Lemaitre A (2002) Origin of a repose angle: kinetics of rearrangement for granular materials. Phys Rev Lett 89:6

    Google Scholar 

  14. Lemaitre A (2002) Rearrangements and dilatancy for sheared dense materials. Phys Rev Lett 89:19

    Google Scholar 

  15. Muthuswamy M, Tordesillas A (2006) How do interparticle contact friction, packing density and degree of polydispersity affect force propagation in particulate assemblies? J Stat Mech Theory Exp:P09013

  16. Nasuno S, Kudrolli A, Bak A, Gollub JP (1998) Time-resolved studies of stick-slip friction in sheared granular layers. Phys Rev E 58(2):2161–2171

    Article  Google Scholar 

  17. Nemat-Nasser S, Hori M (eds) (1993) Micromechanics: overall properties of heterogeneous materials. Elsevier, Amsterdam

  18. Oda M, Iwashita K (2000) Study on couple stress and shear band development in granular media based on numerical simulation analyses. Int J Eng Sci 38(15):1713

    Article  Google Scholar 

  19. Oda M, Kazama H (1998) Microstructure of shear bands and its relation to the mechanisms of dilatancy and failure of dense granular soils. Geotechnique 48(4):465

    Google Scholar 

  20. Oda M, Takemura T, Takahashi M (2004) Microstructure in shear band observed by microfocus x-ray computed tomography. Geotechnique 54(8):539

    Article  Google Scholar 

  21. Peters JF, Muthuswamy M, Wibowo J, Tordesillas A (2005) Characterization of force chains in granular material. Phys Rev E 72(4):041307

    Article  Google Scholar 

  22. Radjai F, Wolf DE, Jean M, Moreau JJ (1998) Bimodal character of stress transmission in granular packings. Phys Rev Lett 80(1):61

    Article  Google Scholar 

  23. Rechenmacher AL (2006) Grain-scale processes governing shear band initiation and evolution in sands. J Mech Phys Solids 54(1):22–45

    Article  MATH  Google Scholar 

  24. Sakaguchi H, Ozaki E, Igarashi T (1993) Plugging of the flow of granular materials during discharge from a silo. Int J Mod Phys B 7(9–10):1949–1963

    Article  Google Scholar 

  25. Suiker ASJ, Chang CS (2004) Modeling failure and deformation of an assembly of spheres with frictional contacts. J Eng Mech ASCE 130(3):283–293

    Article  Google Scholar 

  26. Thornton C (2000) Numerical simulations of deviatoric shear deformation of granular media. Geotechnique 50(1):43–53

    Article  Google Scholar 

  27. Tordesillas A (2007) Force chain buckling, unjamming transitions and shear banding in dense granular assemblies. Philos Mag 87(32):4987–5016

    Article  Google Scholar 

  28. Tordesillas A, Muthuswamy M (2008) On the modeling of the confined buckling of force chains. J Mech Phys Solids (submitted)

  29. Tordesillas A, Muthuswamy M, Walsh SDC (2008) Mesoscale measures of nonaffine deformation in dense granular assemblies. J Eng Mech. ASCE (in press)

  30. Tordesillas A, Peters JF, Gardiner B (2004) Shear band evolution and accumulated microstructural development in cosserat media. Int J Numer Anal Meth Geomech 28:981–1010

    Article  MATH  Google Scholar 

  31. Tordesillas A, Walsh SDC, Muthuswamy M (2008) The effect of local kinematics on the local and global deformations of granular systems. Math Mech Solids (in press)

  32. Tordesillas A, Zhang J, Behringer R (2008) Buckling force chains in dense granular assemblies: physical and numerical experiments. Geom GeoEng (in press)

  33. Torok J, Krishnamurthy S, Kertsz J, Roux S (2000) Self-organization, localization of shear bands, and aging in loose granular materials. Phys Rev Lett 84(17):3851–3854

    Article  Google Scholar 

  34. Volfson D, Tsimring LS, Aranson IS (2004) Stick-slip dynamics of a granular layer under shear. Phys Rev E 69(3):031302

    Article  Google Scholar 

  35. Walsh SDC, Tordesillas A, Peters JF (2007) Development of micromechanical models for granular media: the projection problem. Granul Matter 9(5):337–352

    Article  Google Scholar 

  36. Walsh SDC, Tordesillas A (2004) A thermomechanical approach to the development of micropolar constitutive models of granular media. Acta Mech 167(3–4):145–169

    Article  MATH  Google Scholar 

  37. Walsh SDC, Tordesillas A (2006) Finite element methods for micropolar models of granular materials. App Math Mod 30:1043–1055

    Article  MATH  Google Scholar 

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Acknowledgments

We acknowledge the support of the Australian Research Council (Discovery Grant DP0558808) and the US Army Research Office (Grant DAAD19-02-1-0216). We sincerely thank Dr Jingyu Shi for assistance in the preparation of this manuscript.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, University of Melbourne,  Parkville, VIC, Australia

    A. Tordesillas & M. Muthuswamy

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  1. A. Tordesillas
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  2. M. Muthuswamy
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Correspondence to A. Tordesillas.

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Tordesillas, A., Muthuswamy, M. A thermomicromechanical approach to multiscale continuum modeling of dense granular materials. Acta Geotech. 3, 225–240 (2008). https://doi.org/10.1007/s11440-008-0080-1

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