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Macro-Meso Analysis of Stress and Strain Fields of Granular Materials

  • Shunying JiEmail author
  • Lu Liu
Chapter
  • 35 Downloads
Part of the Springer Tracts in Mechanical Engineering book series (STME)

Abstract

Compared with typical continuous materials, granular materials have many unique discrete, nonlinear physical and mechanical properties. Originally, granular materials were generally treated as a continuum from a macroscopic perspective, and the mechanical behaviors were analyzed by the finite element method (FEM) or meshless method.

References

  1. Alonso-Marroquín F (2011) Static equations of the Cosserat continuum derived from intra-granular stresses. Granular Matter 13(3):189–196CrossRefGoogle Scholar
  2. Bagi K (1996) Stress and strain in granular assemblies. Mech Mater 22:165–177CrossRefGoogle Scholar
  3. Bagi K (2006) Analysis of microstructural strain tensors for granular assemblies. Int J Solids Struct 43(10):3166–3184CrossRefGoogle Scholar
  4. Bardet JP, Vardoulakis I (2001) The asymmetry of stress in granular media. Int J Solids Struct 38(2):353–367CrossRefGoogle Scholar
  5. Cambou B (1998) Behaviour of granular materials. International Centre for Mechanical Sciences, 385Google Scholar
  6. Cambou B, Chaze M, Dedecher F (2000) Chang of scale in granular materials. Eur J Mech A/Solids 19(6):999–1014CrossRefGoogle Scholar
  7. Chang CS, Kuhn MR (2005) On virtual work and stress in granular media. Int J Solids Struct 42(13):3773–3793CrossRefGoogle Scholar
  8. Christoffersen J, Mehrabadi MM, Nematnasser S (1981) A micromechanical description of granular material behavior. J Appl Mech 48(2):339CrossRefGoogle Scholar
  9. Cundall PA, Strack ODL (1979) A discrete numerical model for granular assemblies. Géotechnque 29(1):47–65CrossRefGoogle Scholar
  10. Dedecker F, Chaze M, Dubujet P et al (2015) Specific features of strain in granular materials. Int J Numer Anal Meth Geomech 5(3):173–193Google Scholar
  11. Desrues J, Argilaga A, Caillerie D et al (2019) From discrete to continuum modelling of boundary value problems in geomechanics: an integrated FEM-DEM approach. Int J Numer Anal Meth Geomech 43:919–955CrossRefGoogle Scholar
  12. Drescher A, De Josselin de Jong G (1972) Photoelastic verification of a mechanical model for the flow of a granular material. J Mech Phys Solids 20(5):337–340CrossRefGoogle Scholar
  13. Ehlers W, Ramm E, Diebels S et al (2003) From particle ensembles to Cosserat continua: homogenization of contact forces towards stresses and couple stresses. Int J Solids Struct 40(24):6681–6702MathSciNetCrossRefGoogle Scholar
  14. Fortin J, Millet O, Saxcé GD (2002) Mean stress in a granular medium in dynamics. Mech Res Commun 29(4):235–240CrossRefGoogle Scholar
  15. Fortin J, Millet O, Saxcé GD (2003) Construction of an averaged stress tensor for a granular medium. Eur J Mech 22(4):567–582MathSciNetCrossRefGoogle Scholar
  16. Garcia FE, Bray JD (2019) Modeling the shear response of granular materials with discrete element assemblages of sphere-clusters. Comput Geotech 106:99–107CrossRefGoogle Scholar
  17. Kaneko K, Terada K, Kyoya T (2003) Global-local analysis of granular media in quasi-static equilibrium. Int J Solids Struct 40(5):4043–4069CrossRefGoogle Scholar
  18. Kishino Y (1989) Computer analysis of dissipation mechanism in granular media. Powders and grains. Balkema, Rotterdam, pp 323–330Google Scholar
  19. Kruyt NP, Rothenburg L (1996) Micromechanical definition of the strain tensor for granular materials. J Appl Mech 63(3):706–711CrossRefGoogle Scholar
  20. Kruyt NP, Rothenburg L (2004) Kinematic and static assumptions for homogenization in micromechanics of granular materials. Mech Mater 36(12):1157–1173CrossRefGoogle Scholar
  21. Kruyt NP, Rothenburg L (2014) On micromechanical characteristics of the critical state of two-dimensional granular materials. Acta Mech 225(8):2301–2318MathSciNetCrossRefGoogle Scholar
  22. Kruyt NP, Agnolin I, Luding S et al (2010) Micromechanical study of elastic moduli of loose granular materials. J Mech Phys Solids 58(9):1286–1301MathSciNetCrossRefGoogle Scholar
  23. Kruyt NP, Millet O, Nicot F (2014) Macroscopic strains in granular materials accounting for grain rotations. Granular Matter 16(6):933–944CrossRefGoogle Scholar
  24. Kuhn MR (1999) Structured deformation in granular materials. Mech Mater 31(6):407–429CrossRefGoogle Scholar
  25. Kuhn MR (2005) Are granular materials simple? An experimental study of strain gradient effects and localization. Mech Mater 37(5):607–627CrossRefGoogle Scholar
  26. Kuhn MR (2010) An experimental method for determining the effects of strain gradients in a granular material. Int J Numer Methods Biomed Eng 19(8):573–580zbMATHGoogle Scholar
  27. Kuhn MR, Chang CS (2006) Stability, bifurcation, and softening in discrete systems: a conceptual approach for granular materials. Int J Solids Struct 43(20):6026–6051CrossRefGoogle Scholar
  28. Li X, Tang H (2005) A consistent return mapping algorithm for pressure-dependent elastoplastic Cosserat continua and modelling of strain localisation. Comput Struct 83(1):1–10CrossRefGoogle Scholar
  29. Li XK, Liu QP, Zhang JB (2010) A micro-macro homogenization approach for discrete particle assembly Cosserat continuum modeling of granular materials. Int J Solids Struct 47(2):291–303CrossRefGoogle Scholar
  30. Li X, Wang Z, Zhang S et al (2018) Multiscale modeling and characterization of coupled damage-healing-plasticity for granular materials in concurrent computational homogenization approach. Comput Methods Appl Mech Eng 342:354–383MathSciNetCrossRefGoogle Scholar
  31. Liao CL, Chang TP, Young DH et al (1997) Stress-strain relationship for granular materials based on the hypothesis of best fit. Int J Solids Struct 34(31–32):4087–4100CrossRefGoogle Scholar
  32. Liu Q, Liu X, Li X et al (2014) Micro–macro homogenization of granular materials based on the average-field theory of Cosserat continuum. Adv Powder Technol 25(1):436–449CrossRefGoogle Scholar
  33. Liu J, Bosco E, Suiker ASJ (2019) Multi-scale modelling of granular materials: numerical framework and study on micro-structural features. Comput Mech 63:409–427MathSciNetCrossRefGoogle Scholar
  34. Nguyen NS, Magoariec H, Cambou B et al (2009) Analysis of structure and strain at the meso-scale in 2D granular materials. Int J Solids Struct 46(17):3257–3271CrossRefGoogle Scholar
  35. Nicot F, Hadda N, Guessasma M et al (2013) On the definition of the stress tensor in granular media. Int J Solids Struct 50(14–15):2508–2517CrossRefGoogle Scholar
  36. 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):1713–1740CrossRefGoogle Scholar
  37. Saxcé GD, 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(12):1175–1184CrossRefGoogle Scholar
  38. Tang H, Dong Y, Wang T et al (2019) Simulation of strain localization with discrete element-Cosserat continuum finite element two scale method for granular materials. J Mech Phys Solids 122:450–471MathSciNetCrossRefGoogle Scholar
  39. Terada K, Kikuchi N (2001) A class of general algorithms for multi-scale analysis of heterogeneous media. Comput Methods Appl Mech Eng 90(40–41):5427–5464CrossRefGoogle Scholar
  40. Terada K, Hori M, Kyoya T et al (2000) Simulation of the multi-scale convergence in computational homogenization approaches. Int J Solids Struct 37(16):2285–2311CrossRefGoogle Scholar
  41. Xiong H, Yin Z, Nicot F (2019) A multiscale work-analysis approach for geotechnical structures. Int J Numer Anal Methods Geomechan 43:1230–1250CrossRefGoogle Scholar

Copyright information

© Science Press and Springer Nature Singapore Pte Ltd. 2020

Authors and Affiliations

  1. 1.Department of Engineering MechanicsDalian University of TechnologyDalianChina
  2. 2.Department of Engineering MechanicsDalian University of TechnologyDalianChina

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