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Shearrate diffusion and constitutive relations during transients in simple shear

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Abstract

Granular matter, consisting of hard, frictional, cohesionless spheres, sheared in a simple shear geometry with smooth walls undergoes a velocity driven transition from a jammed or creeping state (low wall velocity) to a flow state with a finite shear rate in the bulk (high wall velocity). In the flow state, the state variables volume fraction \(\nu \), inertial number I and the macroscopic friction \(\mu \) of the bulk follow an exponential transient. The characteristic time of this progression grows with the wall velocity and the system size and is typically large compared to the inverse shear rate. It is shown that I, first being stationary in the shear zones, spreads diffusively into the bulk. The other state variables follow according to the constitutive laws, well known from the steady state.

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References

  1. Silbert LE, Ertas D, Grest GS, Halsey TC, Levine D, Plimpton SJ (2001) Granular flow down an inclined plane: bagnold scaling and rheology. Phys Rev E 64:051302

    Article  Google Scholar 

  2. Geng J, Longhi E, Behringer RP, Howell DW (2001) Memory in two-dimensional heap experiments. Phys Rev E 64:060301

    Article  Google Scholar 

  3. Zhu H, Yu A (2003) The effects of wall and rolling resistance on the couple stress of granular materials in vertical flow. Phys A 325:347

    Article  MathSciNet  MATH  Google Scholar 

  4. Zhu HP, Yu AB (2005) Steady-state granular flow in a 3D cylindrical hopper with flat bottom: macroscopic analysis. Granular Matter 7:97

    Article  MATH  Google Scholar 

  5. Roscoe KH, Schofield AN, Wroth CP (1958) On the yielding of soils. Géotechnique 8:22. doi:10.1680/geot.1958.8.1.22

    Article  Google Scholar 

  6. Schofield A, Wroth C (1968) Critical state soil mechanics. McGraw-Hill, New York

    Google Scholar 

  7. Luding S, Alonso-Marroquin F (2011) The critical-state yield stress (termination locus) of adhesive powders from a single numerical experiment. Granular Matter 13(2, SI):109. doi:10.1007/s10035-010-0241-4

    Article  Google Scholar 

  8. Shojaaee Z, Brendel L, Wolf DE (2007) Rheological transition in granular media. In: Traffic and granular flow ’07, pp 653–658

  9. Shojaaee Z, Ries A, Brendel L, Wolf DE (2009) Rheological transitions in two- and three-dimensional granular media. Powders and Grains 2009 1145:519

    Article  Google Scholar 

  10. Kumar N., Luding S (2014) Memory of jamming and shear-jamming (in soft and granular matter). preprint (2014). arXiv:1407.6167 [cond-mat.soft]

  11. Unger T. (2010) Collective rheology in quasi static shear flow of granular media. preprint. arXiv:1009.3878 [cond-mat.soft]

  12. Kamrin K, Koval G (2012) Nonlocal constitutive relation for steady granular flow. Phys Rev Lett 108(17):178301. doi:10.1103/PhysRevLett.108.178301

    Article  Google Scholar 

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

    Article  Google Scholar 

  14. Chevoir F, Roux JN, da Cruz F, Rognon PG, Koval G Jr (2009) Friction law in dense granular flows. Powder Technol 190(1–2):264

  15. Chialvo S, Sun J, Sundaresan S (2012) Bridging the rheology of granular flows in three regimes. Phys Rev E 85(2):021305. doi:10.1103/PhysRevE.85.021305

    Article  Google Scholar 

  16. Peyneau PE, Roux JN (2008) Frictionless bead packs have macroscopic friction, but no dilatancy. Phys Rev E 78:011307

    Article  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  18. Brendel L, Unger T, Wolf DE (2004) Contact dynamics for beginners. In: Hinrichsen H, Wolf DE (eds) The physics of granular media. Wiley, Berlin, pp 325–343

    Google Scholar 

  19. Shojaaee Z, Roux JN, Chevoir F, Wolf DE (2012) Shear flow of dense granular materials near smooth walls. I. Shear localization and constitutive laws in the boundary region. Phys. Rev. E 86:011301. doi:10.1103/PhysRevE.86.011301

    Article  Google Scholar 

  20. Varnik F, Bocquet L, Barrat JL, Berthier L (2003) Shear localization in a model glass. Phys Rev Lett 90:095702. doi:10.1103/PhysRevLett.90.095702

    Article  Google Scholar 

  21. Kamrin K, Koval G (2014) Effect of particle surface friction on nonlocal constitutive behavior of flowing granular media. Comput Part Mech 1(2):169. doi:10.1007/s40571-014-0018-3

    Article  Google Scholar 

  22. Lubarda V, Krajcinovic D (1993) Damage tensors and the crack density distribution. Int J Solids Struct 30:2859

    Article  MATH  Google Scholar 

  23. Henann DL, Kamrin K (2013) A predictive, size-dependent continuum model for dense granular flows. PNAS 110(17):6730–6735. doi:10.1073/pnas.1219153110

    Article  MathSciNet  MATH  Google Scholar 

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Acknowledgments

We like to thank Ken Kamrin for clarifying a question about his model to us. This research was supported by DFG by the grant WO 577 / 8 within the Priority Program SPP 1486 “Particles in Contact” (PiKo).

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  1. Department of Physics, University of Duisburg-Essen, Lotharstr.1, 47057, Duisburg, Germany

    Alexander Ries, Lothar Brendel & Dietrich E. Wolf

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  1. Alexander Ries
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  2. Lothar Brendel
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  3. Dietrich E. Wolf
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Correspondence to Alexander Ries.

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Ries, A., Brendel, L. & Wolf, D.E. Shearrate diffusion and constitutive relations during transients in simple shear. Comp. Part. Mech. 3, 303–310 (2016). https://doi.org/10.1007/s40571-015-0058-3

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  • DOI: https://doi.org/10.1007/s40571-015-0058-3

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