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FEM x DEM modelling of cohesive granular materials: numerical homogenization and multi-scale simulations

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Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
The article presents a multi-scale modelling approach of cohesive granular materials, its numerical implementation and its results. At micro-scopic level, Discrete Element Method (DEM) is used to model dense grain spacking. At the macroscopic level, the numerical solution is obtained by a Finite Element Method (FEM). In order to bridge the micro- and macro-scales, the concept of Representative Elementary Volume (REV) is applied, in which the average REV stress and the consistent tangent operators are obtained in each macroscopic integration point as the results of DEM’s simulation. In this way, the numerical constitutive law is determined through the detailed modelling of the microstructure, taking into account the nature of granular materials. We first elaborate the principle of the computation homogenisation (FEMDEM), then demonstrate the features of our multi-scale computation in terms of a biaxial compression test. Macroscopic strain location is observed and discussed.
Czasopismo
Rocznik
Strony
1109--1126
Opis fizyczny
Bibliogr. 31 poz.
Twórcy
autor
  • Université Joseph Fourier, Institut Polytechnique de Grenoble, CNRS UMR5521, 3SR Lab., Grenoble, France
autor
  • Université Joseph Fourier, Institut Polytechnique de Grenoble, CNRS UMR5521, 3SR Lab., Grenoble, France
autor
  • Université Joseph Fourier, Institut Polytechnique de Grenoble, CNRS UMR5521, 3SR Lab., Grenoble, France
autor
  • Université Joseph Fourier, Institut Polytechnique de Grenoble, CNRS UMR5521, 3SR Lab., Grenoble, France
Bibliografia
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  • 3. Bésuelle, P., R. Chambon, and F. Collin (2006), Switching deformation modes in post-localization solutions with a quasibrittle material, J. Mech. Mat. Struct.1, 7,1115-1134, DOI: 10.2140/jomms.2006.1.1115.
  • 4. Calvetti, F., G. Combe, and J. Lanier (1997), Experimental micromechanical analysis of a 2D granular material: relation between structure evolution and loading path, Mech. Cohes.-Frict. Mat.2, 2, 121-163, DOI: 10.1002/(SICI)1099-1484(199704)2:2<121::AID-CFM27>3.0.CO;2-2.
  • 5. Chambon, R., D. Caillerie, and N. El Hassan (1998), One dimensional localization studied with a second grade model, Europ. J. Mech. A17, 4, 637-656, DOI:10.1016/S0997-7538(99)80026-6.
  • 6. Charlier, R. (1987), Approche unifiée de quelques problèmes non linéaires de mé-canique des milieux continus par la méthode des éléments finis, Ph.D. Thesis,University of Liège, France.
  • 7. Chevalier, B., P. Villard, and G. Combe (2011), Investigation of load-transfer mechanisms in geotechnical earth structures with thin fill platforms reinforced by rigid inclusions, Int. J. Geomech.11, 3, 239-250, DOI:10.1061/(ASCE)GM.1943-5622.0000083.
  • 8. Combe, G., and J.-N. Roux (2003), Discrete numerical simulation, a quasistatic deformation and the origin of strain in granular materials. In: Proc. 3rd Int. Symp. Deformation Characteristics of Geomaterials, Lyon, France, 1070-1078.
  • 9. Cundall, P.A., and O.D.L. Strack (1979), A discrete numerical model for granular as-semblies,Geotechnique29, 1, 47-65, DOI: 10.1680/geot.1979.29.1.47.de
  • 10. Borst, R., and O.M. Heeres (2002), A unified approach to the implicit integration of standard, non-standard and viscous plasticity models, Int. J. Numer. Anal. Meth. Geomech.26, 11, 1059-1070, DOI: 10.1002/nag.234.
  • 11. Desrues, J. (1984), Strain localization in granular materials, Ph.D. Thesis, USMG and INPG, Grenoble, France (in French).
  • 12. Desrues, J., and R. Chambon (2002), Shear band analysis and shear moduli calibration, Int. J. Solids Struct.39, 13-14, 3757-3776, DOI: 10.1016/S0020-7683(02)00177-4.
  • 13. Desrues, J., and G. Viggiani (2004), Strain localization in sand: an overview of the experimental results obtained in Grenoble using stereophotogrammetry, Int.J. Numer. Anal. Meth. Geomech.28, 4, 279-321, DOI: 10.1002/nag.338.
  • 14. Feyel, F. (2003), A multilevel finite element method(FE2)to describe the response of highly non-linear structures using generalized continua, Comput. Method. Appl. Mech. Eng.192, 28-30, 3233-3244, DOI: 10.1016/S0045-7825(03)00348-7.
  • 15. Feyel, F., and J.-L. Chaboche (2000), FE2multiscale approach for modelling the elastoviscoplastic behaviour of long fibre SiC/Ti composite materials, Com-put. Meth. Appl. Mech. Eng.183, 3-4, 309-330, DOI: 10.1016/S0045-7825(99)00224-8.
  • 16. Gilabert, F.A., J.-N. Roux, and A. Castellanos (2007), Computer simulation of model cohesive powders: Influence of assembling procedure and contact laws on low consolidation states, Phys. Rev. E75, 1, 011303, 1-26, DOI: 10.1103/Phys-RevE.75.011303.
  • 17. Kouznetsova, V., W.A.M. Brekelmans, and F.P.T. Baaijens (2001), An approach to micro-macro modelling of heterogeneous materials, Comput. Mech.27, 1,37-48, DOI: 10.1007/s004660000212.
  • 18. Kouznetsova, V., M.D.G. Geers, and W.A.M. Brekelmans (2002), Multi-scale constitutive modelling of heterogeneous materials with a gradient-enhanced computational homogenization scheme, Int. J. Numer. Method. Eng.54, 8, 1235-1260, DOI: 10.1002/nme.541.
  • 19. Lanier, J. (2001),Mécanique des Milieux Granulaires, Hermes Sci. Publs., 366 pp.
  • 20. Matsushima, T., R. Chambon, and D. Caillerie (2002), Large strain finite element analysis of a local second gradient model: application to localization, Int. J. Numer. Method. Eng.54, 4, 499-521, DOI: 10.1002/nme.433.
  • 21. Meier, H.A., P. Steinmann, and E. Kuhl (2008), Towards multiscale computation of confined granular media, Tech. Mech.28, 1, 32-42.
  • 22. Miehe, C., and J. Dettmar (2004), A framework for micro-macro transitions in periodic particle aggregates of granular materials - contact forces, stresses and tan-gent operators, Comput. Method. Appl. Mech. Eng.193, 3-5, 225-256, DOI:10.1016/j.cma.2003.10.004.
  • 23. Miehe, C., J. Dettmar, and D. Zäh (2010), Homogenization and two-scale simulations of granular materials for different microstructural constraints, Int. J. Numer.Method. Eng.83, 8-9, 1206-1236, DOI: 10.1002/nme.2875.
  • 24. Nguyen, T.K., G. Combe, D. Caillerie, and J. Desrues (2013), Modeling of a cohesive granular materials by a multi-scale approach, AIP Conf. Proc.1542, 1194-1198, DOI: 10.1063/1.4812151.
  • 25. Pérez-Foguet, A., A. Rodríguez-Ferran, and A. Huerta (2000), Numerical differentiation for non-trivial consistent tangent matrices: an application to the MRS-Lade model, Int. J. Numer. Method. Eng.48, 2, 159-184, DOI: 10.1002/(SICI)1097-0207(20000520)48:2<159::AID-NME871>3.0.CO;2-Y.
  • 26. Radjai, F., and F. Dubois (eds.) (2011),Discrete Numerical Modeling of Granular Materials, John Wiley & Sons, 496 pp.
  • 27. Richefeu, V., G. Combe, and G. Viggiani (2012), An experimental assessment of dis-placement fluctuations in a 2D granular material subjected to shear,Geotech.Lett.2, 113-118, DOI: 10.1680/geolett.12.00029.
  • 28. Szarf, K., G. Combe, and P. Villard (2011), Polygons vs. clumps of discs: A numerical study of the influence of grain shape on the mechanical behaviour of granular materials, Powder Technol.208, 2, 279-288, DOI:10.1016/j.powtec.2010.08.017.
  • 29. Weber, J. (1966), Recherches concernant les contraintes intergranulaires dans les mi-lieux pulvérulents, Bull. Liaison des Ponts et Chaussées20, 1-20.
  • 30. Ypma, T.J. (1995), Historical development of the Newton–Raphson method,SIAMRev.37, 4, 531-551, DOI: 10.1137/1037125.
  • 31. Zienkiewicz, O.C. (1979),La Methode des Elements Finis: Traduit de “the Finite Element Method”, 3rd ed., McGraw
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-8111a3a7-f73a-401f-a55f-eefb94c7bd9e
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