Skip to main content
SpringerLink
Log in

From micro scale to boundary value problem: using a micromechanically based model

  • Research Paper
  • Published:
Acta Geotechnica Aims and scope Submit manuscript

Abstract

A 3D multi-scale approach is presented to investigate the mechanical behavior of a macroscopic specimen consisting of a granular assembly, as a boundary value problem. The core of this approach is a multi-scale coupling, wherein the finite element method is used to solve a boundary value problem and a micromechanically based model is employed as constitutive relationship used at a representative volume element scale. This approach provides a convenient way to link the macroscopic observations with intrinsic microscopic mechanisms. The plane strain triaxial loading condition is selected to simulate the occurrence of strain localization. A series of tests are performed, wherein distinct failure patterns are observed and analyzed. A system of shear band naturally appears in a homogeneous setting specimen. By defining the shear band area, microstructural mechanisms are separately investigated inside and outside the shear band. The normalized second-order work introduced as an indicator of instability occurrence is analyzed not only on the macroscale but also on the micro scale.

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.

Institutional subscriptions

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
Fig. 15
Fig. 16
Fig. 17
Fig. 18
Fig. 19
Fig. 20
Fig. 21
Fig. 22
Fig. 23
Fig. 24

Similar content being viewed by others

References

  1. Alshibli KA, Batiste SN, Sture S (2003) Strain localization in sand: plane strain versus triaxial compression. J Geotech Geoenviron Eng 129:483–494

    Article  Google Scholar 

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

    Article  Google Scholar 

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

    Article  Google Scholar 

  4. Cambou B, Dubujet P, Emeriault F, Sidoroff F (1995) Homogenization for granular materials. Eur J Mech A Solids 14:255–276

    MathSciNet  MATH  Google Scholar 

  5. Chang C, Yin ZY, Hicher PY (2010) Micromechanical analysis for interparticle and assembly instability of sand. J Eng Mech 137:155–168

    Article  Google Scholar 

  6. Chang CS, Yin ZY (2009) Micromechanical modeling for inherent anisotropy in granular materials. J Eng Mech 136:830–839

    Article  Google Scholar 

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

    Article  Google Scholar 

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

    Article  Google Scholar 

  9. Daouadji A, Darve F, Al Gali H, Hicher P, Laouafa F, Lignon S, Nicot F, Nova R, Pinheiro M, Prunier F (2011) Diffuse failure in geomaterials: experiments, theory and modelling. Int J Numer Anal Methods Geomech 35:1731–1773

    Article  Google Scholar 

  10. Darve F, Servant G, Laouafa F, Khoa H (2004) Failure in geomaterials: continuous and discrete analyses. Comput Methods Appl Mech Eng 193:3057–3085

    Article  Google Scholar 

  11. De Saxcé G, Fortin J, Millet O (2004) About the numerical simulation of the dynamics of granular media and the definition of the mean stress tensor. Mech Mater 36:1175–1184

    Article  Google Scholar 

  12. Desrues J, Chambon R, Mokni M, Mazerolle F (1996) Void ratio evolution inside shear bands in triaxial sand specimens studied by computed tomography. Géotechnique 46:529–546

    Article  Google Scholar 

  13. Desrues J, Viggiani G (2004) Strain localization in sand: an overview of the experimental results obtained in Grenoble using stereophotogrammetry. Int J Numer Anal Methods Geomech 28:279–321

    Article  Google Scholar 

  14. Guo N, Zhao JD (2013) A hierarchical model for cross-scale simulation of granular media. In: AIP conference proceedings, pp 1222–1225

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

    Article  MathSciNet  Google Scholar 

  16. Guo N, Zhao JD (2016a) 3D multiscale modeling of strain localization in granular media. Comput Geotech 80:360–372

    Article  Google Scholar 

  17. Guo N, Zhao JD (2016b) Parallel hierarchical multiscale modelling of hydro-mechanical problems for saturated granular soils. Comput Methods Appl Mech Eng 305:37–61

    Article  MathSciNet  Google Scholar 

  18. Han C, Drescher A (1993) Shear bands in biaxial tests on dry coarse sand. Soils Found 33:118–132

    Article  Google Scholar 

  19. Hibbitt Karlsson Sorensen K (2001) ABAQUS/explicit: user’s manual, vol 1. Hibbitt Karlsson and Sorenson Incorporated, Plymouth, MI

    Google Scholar 

  20. Huang W, Huang L, Sheng D, Sloan SW (2015) Dem modelling of shear localization in a plane Couette shear test of granular materials. Acta Geotech 10:389–397

    Article  Google Scholar 

  21. Liu Y, Sun W, Yuan Z, Fish J (2016) A nonlocal multiscale discrete-continuum model for predicting mechanical behavior of granular materials. Int J Numer Methods Eng 106:129–160

    Article  Google Scholar 

  22. Love AEH (2013) A treatise on the mathematical theory of elasticity, vol 1. Cambridge University Press, Cambridge

    MATH  Google Scholar 

  23. Ma G, Regueiro RA, Zhou W, Liu J (2018) Spatiotemporal analysis of strain localization in dense granular materials. Acta Geotech. https://doi.org/10.1007/s11440-018-0685-y

    Article  Google Scholar 

  24. Mehrabadi MM, Nemat-Nasser S, Oda M (1982) On statistical description of stress and fabric in granular materials. Int J Numer Anal Methods Geomech 6:95–108

    Article  MathSciNet  Google Scholar 

  25. Meier HA, Steinmann P, Kuhl E (2008) Towards multiscale computation of confined granular media-contact forces, stresses and tangent operators. Tech Mech 28:32–42

    Google Scholar 

  26. Meier HA, Steinmann P, Kuhl E (2009) On the multiscale computation of confined granular media. In: ECCOMAS multidisciplinary jubilee symposium. Springer. pp 121–133

  27. Nguyen HN, Prunier F, Djeran-Maigre I, Nicot F (2016) Kinetic energy and collapse of granular materials. Granul Matter 18:1–10

    Article  Google Scholar 

  28. Nicot F (2003) Constitutive modelling of a snow cover with a change in scale. Eur J Mech A Solids 22:325–340

    Article  Google Scholar 

  29. Nicot F, Darve F (2011) The H-microdirectional model: accounting for a mesoscopic scale. Mech Mater 43:918–929

    Article  Google Scholar 

  30. Nicot F, Darve F, Dat Vu Khoa H (2007) Bifurcation and second-order work in geomaterials. Int J Numer Anal Methods Geomech 31:1007–1032

    Article  Google Scholar 

  31. Nicot F, Darve F, Group R (2005) A multi-scale approach to granular materials. Mech Mater 37:980–1006

    Google Scholar 

  32. Nicot F, Xiong H, Wautier A, Lerbet J, Darve F (2017) Force chain collapse as grain column buckling in granular materials. Granul Matter 19:18

    Article  Google Scholar 

  33. Prunier F, Laouafa F, Lignon S, Darve F (2009) Bifurcation modeling in geomaterials: From the second-order work criterion to spectral analyses. Int J Numer Anal Methods Geomech 33:1169–1202

    Article  Google Scholar 

  34. Radjaï F, Dubois F (2011) Discrete-element modeling of granular materials. Wiley, Hoboken

    Google Scholar 

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

    Article  Google Scholar 

  36. Rudnicki JW, Rice J (1975) Conditions for the localization of deformation in pressure-sensitive dilatant materials. J Mech Phys Solids 23:371–394

    Article  Google Scholar 

  37. Shi J, Guo P (2018) Fabric evolution of granular materials along imposed stress paths. Acta Geotech. https://doi.org/10.1007/s11440-018-0665-2

    Article  Google Scholar 

  38. Vardoulakis I, Goldscheider M, Gudehus G (1978) Formation of shear bands in sand bodies as a bifurcation problem. Int J Numer Anal Methods Geomech 2:99–128

    Article  Google Scholar 

  39. Voigt W (1889) Ueber die beziehung zwischen den beiden elasticitätsconstanten isotroper körper. Ann Phys 274:573–587

    Article  Google Scholar 

  40. Wan R, Nicot F, Darve F (2017) Failure in geomaterials: a contemporary treatise. Elsevier, New York

    Google Scholar 

  41. Wan R, Pinheiro M, Daouadji A, Jrad M, Darve F (2013) Diffuse instabilities with transition to localization in loose granular materials. Int J Numer Anal Methods Geomech 37:1292–1311

    Article  Google Scholar 

  42. Wang K, Sun W (2016) A semi-implicit discrete-continuum coupling method for porous media based on the effective stress principle at finite strain. Comput Methods Appl Mech Eng 304:546–583

    Article  MathSciNet  Google Scholar 

  43. Wang K, Sun W, Salager S, Na S, Khaddour G (2016) Identifying material parameters for a micro-polar plasticity model via X-ray micro-Ct images: lessons learned from the curve-fitting exercises. Int J Multiscale Comput Eng 14:389–413

    Article  Google Scholar 

  44. Wang P, Arson C (2018) Energy distribution during the quasi-static confined comminution of granular materials. Acta Geotech 13(5):1075–1083

    Article  Google Scholar 

  45. Xiong H, Nicot F, Yin Z (2017) A three-dimensional micromechanically based model. Int J Numer Anal Methods Geomech 41:1669–1686

    Article  Google Scholar 

  46. Yin ZY, Chang CS, Hicher PY (2010) Micromechanical modelling for effect of inherent anisotropy on cyclic behaviour of sand. Int J Solids Struct 47:1933–1951

    Article  Google Scholar 

  47. Yin ZY, Chang CS, Hicher PY, Karstunen M (2009) Micromechanical analysis of kinematic hardening in natural clay. Int J Plast 25:1413–1435

    Article  Google Scholar 

  48. Yin ZY, Hattab M, Hicher PY (2011) Multiscale modeling of a sensitive marine clay. Int J Numer Anal Methods Geomech 35:1682–1702

    Article  Google Scholar 

  49. Yin ZY, Zhao J, Hicher PY (2014) A micromechanics-based model for sand-silt mixtures. Int J Solids Struct 51:1350–1363

    Article  Google Scholar 

  50. Zhang Y, Shao J, Liu Z, Shi C, De Saxcé G (2018) Effects of confining pressure and loading path on deformation and strength of cohesive granular materials: a three-dimensional dem analysis. Acta Geotech. https://doi.org/10.1007/s11440-018-0671-4

    Article  Google Scholar 

  51. Zhou W, Liu J, Ma G, Chang X (2017) Three-dimensional dem investigation of critical state and dilatancy behaviors of granular materials. Acta Geotech 12:527–540

    Article  Google Scholar 

  52. Zhu H, Nguyen HN, Nicot F, Darve F (2016) On a common critical state in localized and diffuse failure modes. J Mech Phys Solids 95:112–131

    Article  Google Scholar 

Download references

Acknowledgements

The authors would like to express their sincere thanks to the scholarship from China Scholarship Council (CSC) under the Grant CSC Number 201406250016, the National Natural Science Foundation of China (Grant No. 51579179), the Region Pays de la Loire of France (Project RI-ADAPTCLIM) and the French Research Network GeoMech (Multi-physics and Multi-scale Couplings in Geo-environmental Mechanics, GDRI CNRS, 2016–2019).

Author information

Authors and Affiliations

  1. Department of Civil and Environmental Engineering, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong, China

    Hao Xiong & Zhenyu Yin

  2. Université Grenoble Alpes, IRSTEA, Geomechanics Group, ETNA, Grenoble, France

    François Nicot

Authors
  1. Hao Xiong
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. François Nicot
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Zhenyu Yin
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Zhenyu Yin.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Xiong, H., Nicot, F. & Yin, Z. From micro scale to boundary value problem: using a micromechanically based model. Acta Geotech. 14, 1307–1323 (2019). https://doi.org/10.1007/s11440-018-0717-7

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11440-018-0717-7

Keywords

Search

Navigation