Skip to main content
SpringerLink
Log in

Evolution of the effective moduli of an anisotropic, dense, granular material

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

Abstract

We analyze the behavior of a dense granular aggregate made by identical, elastic spheres, uni-axially compressed at constant pressure. Our goal is to predict the evolution of the effective moduli along the loading path when small perturbations are applied to stressed states. The analytical model is based upon the average strain theory. We show that the moduli in the anisotropic state normalized with the corresponding initial isotropic value, are captured by a so crude model. Numerical simulations support this result.

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

Access this article

Log in via an institution

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. Agarwal T.K., Ishibashi I.: Anisotropic elastic constants of granular assembly from wave velocity measurements. In: Shen, H.H. (eds) Advanced in Micromechanics of Granular Materials, pp. 51–60. Elsevier, Amsterdam (1992)

    Google Scholar 

  2. 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)

    Article  MathSciNet  ADS  Google Scholar 

  3. Chen Y.C., Ishibashi I., Jenkins J.T.: Dynamic shear modulus and fabric. Part I. Depositional and induced fabric. Géotechnique 38, 25–32 (1988)

    Article  Google Scholar 

  4. Chang C.S., Chao S.J., Chang Y.: Estimates of elastic moduli for granular material with anisotropic random packing structure. Int. J. Solids Struct. 32(14), 1989–2008 (1995)

    Article  MATH  Google Scholar 

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

    Article  Google Scholar 

  6. Elata D., Berryman J.G.: Contact force-displacement laws and the mechanical behavior of random packs of identical spheres. Mech. Mater. 24, 229–240 (1996)

    Article  Google Scholar 

  7. Emeriault F., Cambou B.: Micromechanical modelling of anisotropic non linear elasticity of granular medium. Int. J. Solids Struct. 33(18), 2591–2607 (1996)

    Article  MATH  Google Scholar 

  8. Gajo A., Muir Wood D., Bigoni D.: On certain critical material and testing characteristics affecting shear band development in sand. Géotechnique 57(5), 449–461 (2007)

    Article  Google Scholar 

  9. Ishibashi I., Jenkins J.T., Choi J.W., Parker IV C.L.: The influence of boundaries on the volumetric behavior of solid and hollow cylindrical specimens of glass beads. Soils Found. 36(2), 45–55 (1996)

    Article  Google Scholar 

  10. Jenkins J.T., Strack O.D.L.: Mean-field inelastic beavior of random arrays of identical spheres. Mech. Mater. 16, 25–33 (1993)

    Article  Google Scholar 

  11. Jenkins J.T., Johnson D.L., La Ragione L., Makse H.: Fluctuations and the effective moduli of an isotropic, random aggregate of identical, frictionless spheres. J. Mech. Phys. Solids 53, 197–225 (2005)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  12. Jiang G.-L., Tatsuoka F., Flora A., Koseki J.: Inherent and stress-induced anisotropy in very small strain stiffness of a sandy gravel. Géotechnique 47, 509–521 (1997)

    Article  Google Scholar 

  13. Johnson D.L., Norris A.N.: Rough elastic spheres in contact: memory effects and the transverse force. J. Mech. Phys. Solids 45, 1025–1036 (1996)

    Article  MathSciNet  ADS  Google Scholar 

  14. Khidas Y., Jia X.: Anisotropic nonlinear elasticity in a sphereical-bead pack: influence of the fabric anisotropy. Phys. Rev. E 81, 021303 (2010)

    Article  ADS  Google Scholar 

  15. Koenders M.A.: The incremental stiffness of an assembly of particles. Acta Mech. 70, 31–49 (1987)

    Article  MATH  Google Scholar 

  16. Koenders M.A.: Localised deformation using higher order deformation gradients. Trans. Am. Soc. Mech. Eng. (J. En. Rec. Tech.) 112(1), 51–53 (1990)

    Google Scholar 

  17. Kuhn M.: Micro-mechanics of fabric and failure in granular materials. Mech. Mater. 42, 827–840 (2010)

    Article  Google Scholar 

  18. Kuwano R., Jardine R.J.: On the applicability of cross- anisotropic elasticity to granular materials at very small strains. Géotechnique 52(10), 727–749 (2002)

    Article  Google Scholar 

  19. La Ragione L., Jenkins J.T.: The initial response of an idealized granular material. Proc. R. Soc. A. 463, 735–758 (2007)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  20. La Ragione L., Jenkins J.T.: The influence of particle fluctuations on the average rotation in an idealized granular material. J. Mech. Phys. Solids 57, 1449–1458 (2009)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  21. La Ragione L., Magnanimo V.: Contact anisotropy and coordination number for a granular assembly: a comparison of distinct element method simulations and theory. Phys. Rev. E 85(3), 031304 (2012)

    Article  ADS  Google Scholar 

  22. Luding S.: Molecular dynamics simulations of granular materials. In: Hinrichsen, H., Wolf, D.E (eds) The Physics of Granular Media, pp. 299–324. Wiley VCH, Weinheim/Germany (2004)

    Google Scholar 

  23. Luding S., Perdahcioglu S.: A local constitutive model with anisotropy for various homoge,neous 2D biaxial deformation modes. CIT (Chemie Ingenieur Technik) 38(5), 672–688 (2011)

    Article  Google Scholar 

  24. Magnanimo V., Luding S.: A local constitutive model with anisotropy for ratcheting under 2D biaxial isobaric deformation. Granul. Matter 13(3), 225–232 (2011)

    Article  Google Scholar 

  25. Magnanimo V., La Ragione L., Jenkins J.T., Wang P., Makse H.A.: Characterizing the shear and bulk moduli of an idealized granular material. Europhys. Lett. 81, 34006 (2008)

    Article  ADS  Google Scholar 

  26. Mindlin R.D., Deresiewicz H.: Elastic spheres in contact under varying oblique forces. J. Appl. Mech. 20, 327–344 (1953)

    MathSciNet  MATH  Google Scholar 

  27. Makse H.A., Gland N., Johnson D.L., Schwartz L.: Why effective medium theory fails in granular materials. Phys. Rev. Lett. 83, 5070–5073 (1999)

    Article  ADS  Google Scholar 

  28. Misra A., Chang C.S.: Effective elastic moduli of heterogeneous granular solids. Int. J. Solids Struct. 30, 2547–2566 (1993)

    Article  MATH  Google Scholar 

  29. Nicot F., Darve F.: Micro-mechanical bases of some salient constitutive features of granular materials. Int. J. Solids Struct. 44, 7420–7443 (2007)

    Article  MATH  Google Scholar 

  30. Nowak E.R., Knight J.B., Ben-Naim E., Jaeger H.M., Nagel S.R.: Density fluctuations in vibrated granular materials. Phys. Rev. E 2(57), 1971–1982 (1998)

    Article  ADS  Google Scholar 

  31. Oda M., Nemat-Nasser S., Konishi J.: Stress-induced anisotropy in granular masses. Soils Found. 25(3), 85–97 (1985)

    Article  Google Scholar 

  32. Oda M., Kazama H., Konishi J.: Effects of induced anisotropy on the development of shear bands in granular materials. Mech. Mater. 28(1–4), 103–111 (1998)

    Article  Google Scholar 

  33. Suiker A., Fleck N.F.: Frictional collapse of granular assemblies. J. Appl. Mech. 71, 350–358 (2004)

    Article  ADS  MATH  Google Scholar 

  34. Thornton C., Anthony S.J.: Quasi-static deformation of particulate media. Philos. Trans. R. Soc. Lond. Ser. A 356(1747), 2763–2782 (1998)

    Article  ADS  MATH  Google Scholar 

  35. Thornton C., Zhang L.: A numerical examination of shear banding and simple shear non-coaxial flow rules. Philos. Mag. 86(21–22), 3425–3452 (2006)

    Article  ADS  Google Scholar 

  36. Torquato S.: Random Heterogeneous Materials, 1st edn. Springer, NewYork (2001)

    Google Scholar 

  37. Yang J., Yang Z.X., Li X.S.: Quantifying and modelling fabric anisotropy of granular soils. Géotechnique 4(58), 237–248 (1998)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Dipartimento di Scienze dell’Ingegneria Civile e dell’Architettura, Politecnico di Bari, 70125, Bari, Italy

    Luigi La Ragione

  2. Multi Scale Mechanics (MSM), CTW, UTwente, P.O.Box 217, 7500 AE, Enschede, The Netherlands

    Vanessa Magnanimo

Authors
  1. Luigi La Ragione
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Vanessa Magnanimo
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Vanessa Magnanimo.

Rights and permissions

Reprints and permissions

About this article

Cite this article

La Ragione, L., Magnanimo, V. Evolution of the effective moduli of an anisotropic, dense, granular material. Granular Matter 14, 749–757 (2012). https://doi.org/10.1007/s10035-012-0368-6

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10035-012-0368-6

Keywords

Search

Navigation