Skip to main content

Multiscale characterization and modeling of granular materials through a computational mechanics avatar: a case study with experiment


Through a first-generation computational mechanics avatar that directly links advanced X-ray computed tomographic experimental techniques to a discrete computational model, we present a case study where we made the first attempt to characterize and model the grain-scale response inside the shear band of a real specimen of Caicos ooids subjected to triaxial compression. The avatar has enabled, for the first time, the transition from faithful representation of grain morphologies in X-ray tomograms of granular media to a morphologically accurate discrete computational model. Grain-scale information is extracted and upscaled into a continuum finite element model through a hierarchical multiscale scheme, and the onset and evolution of a persistent shear band is modeled, showing excellent quantitative agreement with experiment in terms of both grain-scale and continuum responses in the post-bifurcation regime. More importantly, consistency in results across characterization, discrete analysis and continuum response from multiscale calculations are found, achieving the first and long sought-after quantitative breakthrough in grain-scale analysis of real granular materials.

This is a preview of subscription content, access via your institution.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14


  1. 1.

    Alshibli KA, Hasan A (2008) Spatial variation of void ratio and shear band thickness in sand using X-ray computed tomography. Géotechnique 58(4):249–257

    Article  Google Scholar 

  2. 2.

    Andò E, Hall SA, Viggiani G, Desrues J, Besuelle P (2012) Grain-scale experimental investigation of localised deformation in sand: a discrete particle tracking approach. Acta Geotechn 7(1):1–13

    Article  Google Scholar 

  3. 3.

    Andrade JE, Avila CF (2012) Granular element method (GEM): linking inter-particle forces with macroscopic loading. Granul Matter 14:1–13

    Article  Google Scholar 

  4. 4.

    Andrade JE, Tu X (2009) Multiscale framework for behavior prediction in granular media. Mech Mater 41:652–669

    Article  Google Scholar 

  5. 5.

    Andrade JE, Avila CF, Lenoir N, Hall SA, Viggiani G (2011) Multiscale modeling and characterization of granular matter: from grain scale kinematics to continuum mechanics. J Mech Phys Solids 59:237–250

    Article  MATH  Google Scholar 

  6. 6.

    Andrade JE, Lim K-W, Avila CF, Vlahinić I (2012) Granular element method for computational particle mechanics. Comput Methods Appl Mech Eng 241–244:262–274

    Article  Google Scholar 

  7. 7.

    Andrade JE, Vlahinić I, Lim K-W, Jerves A (2012) Multiscale ‘tomography-to-simulation’ framework for granular matter: the road ahead. Géotechn Lett 2(3):135–139

    Article  Google Scholar 

  8. 8.

    Ashmawy AK, Sukumaran B, Hoang AV (2003) Evaluating the influence of particle shape on liquefaction behavior using discrete element method. In: Proceedings of the thirteenth international offshore and polar engineering conference (ISOPE 2003) Honolulu, Hawaii, May

  9. 9.

    Bowman ET, Soga K, Drummond W (2001) Particle shape characterisation using fourier descriptor analysis. Géotechnique 51(6):545–554

    Article  Google Scholar 

  10. 10.

    Cho GC, Dodds J, Santamarina JC (2006) Particle shape effects on packing density, stiffness, and strength: natural and crushed sands. J Geotechn Geoenviron Eng 132(5):591–602

    Article  Google Scholar 

  11. 11.

    Christoffersen J, Mehrabadi MM, Nemat-Nasser S (1981) A micromechanical description of granular material behavior. J Appl Mech 48:339–344

    Article  MATH  Google Scholar 

  12. 12.

    Cundall PA (1988) Formulation of a three-dimensional distinct element model—part I: a scheme to detect and represent contacts in a system composed of many polyhedral blocks. Int J Rock Mech Min Sci 25(3):107–116

    Article  Google Scholar 

  13. 13.

    Cundall PA, Strack ODL (1979) A discrete numerical model for granular assemblies. Géotechnique 29:47–65

    Article  Google Scholar 

  14. 14.

    Dascalu C, Cambou B (2008) Special issue on multiscale approaches to geomaterials. In: Dascalau C, Cambou B (eds) Acta Geotechn, vol 3. Springer, Berlin

    Google Scholar 

  15. 15.

    Dubois F, Jean M (2006) The non smooth contact dynamic method: recent LMGC90 software developments and application. In: Wriggers P, Nackenhorst U (eds) Analysis and simulation of contact problems, volume 27 of lecture notes in applied and computational mechanics. Springer, Berlin, Heidelberg, pp 375–378

  16. 16.

    Garboczi EJ (2002) Three-dimensional mathematical analysis of particle shape using X-ray tomography and spherical harmonics: application to aggregates used in concrete. Cem Concr Res 32(10):1621–1638

    Article  Google Scholar 

  17. 17.

    Garcia X, Latham J-P, Xiang J, Harrison JP (2009) A clustered overlapping sphere algorithm to represent real particles in discrete element modelling. Géotechnique 59:779–784

    Article  Google Scholar 

  18. 18.

    Guo N, Zhao J (2014) A coupled FEM/DEM approach for hierarchical multiscale modelling of granular media. Int J Numer Methods Eng 99(11):789–818

    MathSciNet  Article  Google Scholar 

  19. 19.

    Hall SA, Bornert M, Desrues J, Pannier Y, Lenoir N, Viggiani G, Bésuelle P (2010) Discrete and continuum analysis of localized deformation in sand using X-ray micro CT and volumetric digital image correlation. Géotechnique 60:315–322

    Article  Google Scholar 

  20. 20.

    Hall SA, Wright J, Pirling T, Andò E, Hughes DJ, Viggiani G (2011) Can intergranular force transmission be identified in sand? Granul Matter. doi:10.1007/s10035-011-0251-x

  21. 21.

    Hurley R, Marteau E, Ravichandran G, Andrade JE (2014) Extracting inter-particle forces in opaque granular materials: beyond photoelasticity. J Mech Phys Solids 63:154–166

    Article  Google Scholar 

  22. 22.

    Jones DR, Perttunen CD, Stuckman BE (1993) Lipschitzian optimization without the Lipschitz constant. J Optim Theory Appl 79(1):157–181

    MathSciNet  Article  MATH  Google Scholar 

  23. 23.

    Koynov A, Akseli I, Cuitino AM (2011) Modeling and simulation of compact strength due to particle bonding using a hybrid discrete-continuum approach. Int J Pharm 418:273–285

    Article  Google Scholar 

  24. 24.

    Laursen TA (2002) Computational contact and impact mechanics: fundamentals of modeling interfacial phenomena in nonlinear finite element analysis. Springer, Berlin

    MATH  Google Scholar 

  25. 25.

    Lenoir N, Bornert M, Desrues J, Viggiani G (2007) 3D digital image correlation applied to X-ray microtomography images from triaxial compression tests on argillaceous rock. Strain 43:193–205

    Article  Google Scholar 

  26. 26.

    Lim K-W, Andrade JE (2014) Granular element method for three-dimensional discrete element calculations. Int J Numer Anal Methods Geomech 38(2):167–188

    Article  Google Scholar 

  27. 27.

    Lim K-W, Krabbenhoft K, Andrade JE (2014) A contact dynamics approach to the granular element method. Comput Methods Appl Mech Eng 268:557–573

    MathSciNet  Article  MATH  Google Scholar 

  28. 28.

    Lim K-W, Krabbenhoft K, Andrade JE (2014) On the contact treatment of non-convex particles in the granular element method. Comput Part Mech 1(3):257–275

    Article  Google Scholar 

  29. 29.

    Meier HA, Steinmann P, Kuhl E (2008) Towards multiscale computation of confined granular media—contact forces, stresses and tangent operators. Techn Mech 28:32–43

    Google Scholar 

  30. 30.

    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 279:46–65

    Article  Google Scholar 

  31. 31.

    Nguyen TK, Combe G, Caillerie D, Desrues J (2014) FEM \(\times \) DEM modelling of cohesive granular materials: numerical homogenisation and multi-scale simulations. Acta Geophys 62(5):1109–1126

    Article  Google Scholar 

  32. 32.

    Nocedal J, Wright SJ (2006) Numerical optimization, 2nd edn. Springer, New York

    MATH  Google Scholar 

  33. 33.

    Oda M (1972) Initial fabrics and their relations to mechanical properties of granular materials. Soils Found 12:17–36

    Article  Google Scholar 

  34. 34.

    Phillips R (2001) Crystals, defects and microstructures: modeling across scales. Cambridge University Press, Cambridge

    Book  Google Scholar 

  35. 35.

    Rechenmacher AL, Finno RJ (2004) Digital image correlation to evaluate shear banding in dilative sands. Geotechn Test J ASCE 27:1–10

    Article  Google Scholar 

  36. 36.

    Regueiro RA, Yan B (2011) Concurrent multiscale computational modeling for dense dry granular materials interfacing deformable solid bodies. Springer series in geomechanics and geoengineering, pp 251–273

  37. 37.

    Saadatfar M, Turner ML, Arns CH, Averdunk H, Senden TJ, Sheppard AP, Sok RM, Pinczewski WV, Kelly J, Knackstedt MA (2005) Rock fabric and texture from digital core analysis. In: SPWLA 46th annual logging symposium, New Orleans, Louisiana, June, pp 26–29

  38. 38.

    Soille P (2004) Morphological image analysis, principles and applications, 2nd edn. Springer, Berlin

    Book  MATH  Google Scholar 

  39. 39.

    Tu X, Andrade JE (2008) Criteria for static equilibrium in particulate mechanics computations. Int J Numer Methods Eng 75:1581–1606

    Article  MATH  Google Scholar 

  40. 40.

    Vlahinić I, Andò E, Viggiani G, Andrade JE (2013) Towards a more accurate characterization of granular media: extracting quantitative descriptors from tomographic images. Granul Matter. doi:10.1007/s10035-013-0460-6

  41. 41.

    Weinan E (2011) Principles of multiscale modeling. Cambridge University Press, Cambridge

    MATH  Google Scholar 

  42. 42.

    Wellmann C, Lillie C, Wriggers P (2007) Homogenization of granular material modeled by a three-dimensional discrete element method. Comput Geotechn 35:394–405

    Article  Google Scholar 

Download references


This work is partially supported by the NSF CAREER Grant No. 1060087 and the AFOSR YIP Grant No. FA9550-11-1-0052 of the California Institute of Technology. This support is gratefully acknowledged.

Author information



Corresponding author

Correspondence to José E. Andrade.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Lim, KW., Kawamoto, R., Andò, E. et al. Multiscale characterization and modeling of granular materials through a computational mechanics avatar: a case study with experiment. Acta Geotech. 11, 243–253 (2016).

Download citation


  • Constitutive behavior
  • Granular media
  • Microstructure
  • Multiscale
  • X-ray computed tomography