Skip to main content
Top

2020 | OriginalPaper | Chapter

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

Authors : Shunying Ji, Lu Liu

Published in: Computational Granular Mechanics and Its Engineering Applications

Publisher: Springer Singapore

Activate our intelligent search to find suitable subject content or patents.

search-config
loading …

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.

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

Literature
go back to reference Alonso-Marroquín F (2011) Static equations of the Cosserat continuum derived from intra-granular stresses. Granular Matter 13(3):189–196CrossRef Alonso-Marroquín F (2011) Static equations of the Cosserat continuum derived from intra-granular stresses. Granular Matter 13(3):189–196CrossRef
go back to reference Bagi K (1996) Stress and strain in granular assemblies. Mech Mater 22:165–177CrossRef Bagi K (1996) Stress and strain in granular assemblies. Mech Mater 22:165–177CrossRef
go back to reference Bagi K (2006) Analysis of microstructural strain tensors for granular assemblies. Int J Solids Struct 43(10):3166–3184CrossRef Bagi K (2006) Analysis of microstructural strain tensors for granular assemblies. Int J Solids Struct 43(10):3166–3184CrossRef
go back to reference Bardet JP, Vardoulakis I (2001) The asymmetry of stress in granular media. Int J Solids Struct 38(2):353–367CrossRef Bardet JP, Vardoulakis I (2001) The asymmetry of stress in granular media. Int J Solids Struct 38(2):353–367CrossRef
go back to reference Cambou B (1998) Behaviour of granular materials. International Centre for Mechanical Sciences, 385 Cambou B (1998) Behaviour of granular materials. International Centre for Mechanical Sciences, 385
go back to reference Cambou B, Chaze M, Dedecher F (2000) Chang of scale in granular materials. Eur J Mech A/Solids 19(6):999–1014CrossRef Cambou B, Chaze M, Dedecher F (2000) Chang of scale in granular materials. Eur J Mech A/Solids 19(6):999–1014CrossRef
go back to reference Chang CS, Kuhn MR (2005) On virtual work and stress in granular media. Int J Solids Struct 42(13):3773–3793CrossRef Chang CS, Kuhn MR (2005) On virtual work and stress in granular media. Int J Solids Struct 42(13):3773–3793CrossRef
go back to reference Christoffersen J, Mehrabadi MM, Nematnasser S (1981) A micromechanical description of granular material behavior. J Appl Mech 48(2):339CrossRef Christoffersen J, Mehrabadi MM, Nematnasser S (1981) A micromechanical description of granular material behavior. J Appl Mech 48(2):339CrossRef
go back to reference Cundall PA, Strack ODL (1979) A discrete numerical model for granular assemblies. Géotechnque 29(1):47–65CrossRef Cundall PA, Strack ODL (1979) A discrete numerical model for granular assemblies. Géotechnque 29(1):47–65CrossRef
go back to reference Dedecker F, Chaze M, Dubujet P et al (2015) Specific features of strain in granular materials. Int J Numer Anal Meth Geomech 5(3):173–193 Dedecker F, Chaze M, Dubujet P et al (2015) Specific features of strain in granular materials. Int J Numer Anal Meth Geomech 5(3):173–193
go back to reference 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 43:919–955CrossRef 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 43:919–955CrossRef
go back to reference 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):337–340CrossRef 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):337–340CrossRef
go back to reference 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):6681–6702MathSciNetCrossRef 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):6681–6702MathSciNetCrossRef
go back to reference Fortin J, Millet O, Saxcé GD (2002) Mean stress in a granular medium in dynamics. Mech Res Commun 29(4):235–240CrossRef Fortin J, Millet O, Saxcé GD (2002) Mean stress in a granular medium in dynamics. Mech Res Commun 29(4):235–240CrossRef
go back to reference Fortin J, Millet O, Saxcé GD (2003) Construction of an averaged stress tensor for a granular medium. Eur J Mech 22(4):567–582MathSciNetCrossRef Fortin J, Millet O, Saxcé GD (2003) Construction of an averaged stress tensor for a granular medium. Eur J Mech 22(4):567–582MathSciNetCrossRef
go back to reference Garcia FE, Bray JD (2019) Modeling the shear response of granular materials with discrete element assemblages of sphere-clusters. Comput Geotech 106:99–107CrossRef Garcia FE, Bray JD (2019) Modeling the shear response of granular materials with discrete element assemblages of sphere-clusters. Comput Geotech 106:99–107CrossRef
go back to reference Kaneko K, Terada K, Kyoya T (2003) Global-local analysis of granular media in quasi-static equilibrium. Int J Solids Struct 40(5):4043–4069CrossRef Kaneko K, Terada K, Kyoya T (2003) Global-local analysis of granular media in quasi-static equilibrium. Int J Solids Struct 40(5):4043–4069CrossRef
go back to reference Kishino Y (1989) Computer analysis of dissipation mechanism in granular media. Powders and grains. Balkema, Rotterdam, pp 323–330 Kishino Y (1989) Computer analysis of dissipation mechanism in granular media. Powders and grains. Balkema, Rotterdam, pp 323–330
go back to reference Kruyt NP, Rothenburg L (1996) Micromechanical definition of the strain tensor for granular materials. J Appl Mech 63(3):706–711CrossRef Kruyt NP, Rothenburg L (1996) Micromechanical definition of the strain tensor for granular materials. J Appl Mech 63(3):706–711CrossRef
go back to reference Kruyt NP, Rothenburg L (2004) Kinematic and static assumptions for homogenization in micromechanics of granular materials. Mech Mater 36(12):1157–1173CrossRef Kruyt NP, Rothenburg L (2004) Kinematic and static assumptions for homogenization in micromechanics of granular materials. Mech Mater 36(12):1157–1173CrossRef
go back to reference Kruyt NP, Rothenburg L (2014) On micromechanical characteristics of the critical state of two-dimensional granular materials. Acta Mech 225(8):2301–2318MathSciNetCrossRef Kruyt NP, Rothenburg L (2014) On micromechanical characteristics of the critical state of two-dimensional granular materials. Acta Mech 225(8):2301–2318MathSciNetCrossRef
go back to reference Kruyt NP, Agnolin I, Luding S et al (2010) Micromechanical study of elastic moduli of loose granular materials. J Mech Phys Solids 58(9):1286–1301MathSciNetCrossRef Kruyt NP, Agnolin I, Luding S et al (2010) Micromechanical study of elastic moduli of loose granular materials. J Mech Phys Solids 58(9):1286–1301MathSciNetCrossRef
go back to reference Kruyt NP, Millet O, Nicot F (2014) Macroscopic strains in granular materials accounting for grain rotations. Granular Matter 16(6):933–944CrossRef Kruyt NP, Millet O, Nicot F (2014) Macroscopic strains in granular materials accounting for grain rotations. Granular Matter 16(6):933–944CrossRef
go back to reference Kuhn MR (1999) Structured deformation in granular materials. Mech Mater 31(6):407–429CrossRef Kuhn MR (1999) Structured deformation in granular materials. Mech Mater 31(6):407–429CrossRef
go back to reference Kuhn MR (2005) Are granular materials simple? An experimental study of strain gradient effects and localization. Mech Mater 37(5):607–627CrossRef Kuhn MR (2005) Are granular materials simple? An experimental study of strain gradient effects and localization. Mech Mater 37(5):607–627CrossRef
go back to reference 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):573–580MATH 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):573–580MATH
go back to reference Kuhn MR, Chang CS (2006) Stability, bifurcation, and softening in discrete systems: a conceptual approach for granular materials. Int J Solids Struct 43(20):6026–6051CrossRef Kuhn MR, Chang CS (2006) Stability, bifurcation, and softening in discrete systems: a conceptual approach for granular materials. Int J Solids Struct 43(20):6026–6051CrossRef
go back to reference 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):1–10CrossRef 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):1–10CrossRef
go back to reference 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):291–303CrossRef 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):291–303CrossRef
go back to reference 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 342:354–383MathSciNetCrossRef 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 342:354–383MathSciNetCrossRef
go back to reference 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):4087–4100CrossRef 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):4087–4100CrossRef
go back to reference 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):436–449CrossRef 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):436–449CrossRef
go back to reference Liu J, Bosco E, Suiker ASJ (2019) Multi-scale modelling of granular materials: numerical framework and study on micro-structural features. Comput Mech 63:409–427MathSciNetCrossRef Liu J, Bosco E, Suiker ASJ (2019) Multi-scale modelling of granular materials: numerical framework and study on micro-structural features. Comput Mech 63:409–427MathSciNetCrossRef
go back to reference 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):3257–3271CrossRef 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):3257–3271CrossRef
go back to reference 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):2508–2517CrossRef 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):2508–2517CrossRef
go back to reference 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):1713–1740CrossRef 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):1713–1740CrossRef
go back to reference 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):1175–1184CrossRef 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):1175–1184CrossRef
go back to reference 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 122:450–471MathSciNetCrossRef 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 122:450–471MathSciNetCrossRef
go back to reference 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):5427–5464CrossRef 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):5427–5464CrossRef
go back to reference 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):2285–2311CrossRef 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):2285–2311CrossRef
go back to reference Xiong H, Yin Z, Nicot F (2019) A multiscale work-analysis approach for geotechnical structures. Int J Numer Anal Methods Geomechan 43:1230–1250CrossRef Xiong H, Yin Z, Nicot F (2019) A multiscale work-analysis approach for geotechnical structures. Int J Numer Anal Methods Geomechan 43:1230–1250CrossRef
Metadata
Title
Macro-Meso Analysis of Stress and Strain Fields of Granular Materials
Authors
Shunying Ji
Lu Liu
Copyright Year
2020
Publisher
Springer Singapore
DOI
https://doi.org/10.1007/978-981-15-3304-4_4

Premium Partners