Jump to ContentJump to Main Navigation
Show Summary Details

Acta Geophysica

6 Issues per year


IMPACT FACTOR 2015: 0.945
5-year IMPACT FACTOR: 1.061

SCImago Journal Rank (SJR) 2015: 0.581
Source Normalized Impact per Paper (SNIP) 2015: 0.779
Impact per Publication (IPP) 2015: 0.937

Open Access
Online
ISSN
1895-7455
See all formats and pricing
Volume 62, Issue 5 (Oct 2014)

Issues

FEM × DEM modelling of cohesive granular materials: Numerical homogenisation and multi-scale simulations

Trung Nguyen
  • Institut Polytechnique de Grenoble, CNRS UMR5521, 3SR Lab., Université Joseph Fourier, Grenoble, France
  • Email:
/ Gaël Combe
  • Institut Polytechnique de Grenoble, CNRS UMR5521, 3SR Lab., Université Joseph Fourier, Grenoble, France
  • Email:
/ Denis Caillerie
  • Institut Polytechnique de Grenoble, CNRS UMR5521, 3SR Lab., Université Joseph Fourier, Grenoble, France
  • Email:
/ Jacques Desrues
  • Institut Polytechnique de Grenoble, CNRS UMR5521, 3SR Lab., Université Joseph Fourier, Grenoble, France
  • Email:
Published Online: 2014-08-17 | DOI: https://doi.org/10.2478/s11600-014-0228-3

Abstract

The article presents a multi-scale modelling approach of cohesive granular materials, its numerical implementation and its results. At microscopic level, Discrete Element Method (DEM) is used to model dense grains packing. 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 (FEM × DEM), then demonstrate the features of our multiscale computation in terms of a biaxial compression test. Macroscopic strain location is observed and discussed.

Keywords: multi-scale; FEM; DEM; homogenisation; cohesive granular materials

  • [1] Atman, A.P.F., P. Claudin, and G. Combe (2009), Departure from elasticity in granular layers: Investigation of a crossover overload force, Comput. Phys. Commun. 180,4, 612–615, DOI: 10.1016/j.cpc.2008.12.017. http://dx.doi.org/10.1016/j.cpc.2008.12.017 [Crossref] [Web of Science]

  • [2] Bésuelle, P., J. Desrues, and S. Raynaud (2000), Experimental characterization of the localisation phenomenon inside a Vosges sandstone in a triaxial cell, Int. J. Rock Mech. Min. Sci. 37,8, 1223–1237, DOI: 10.1016/S1365-1609(00)00057-5. http://dx.doi.org/10.1016/S1365-1609(00)00057-5 [Crossref]

  • [3] Bésuelle, P., R. Chambon, and F. Collin (2006), Switching deformation modes in postlocalization solutions with a quasibrittle material, J. Mech. Mat. Struct. 1,7, 1115–1134, DOI: 10.2140/jomms.2006.1.1115. http://dx.doi.org/10.2140/jomms.2006.1.1115 [Crossref]

  • [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. [Crossref]

  • [5] Chambon, R., D. Caillerie, and N. El Hassan (1998), One dimensional localization studied with a second grade model, Europ. J. Mech. A 17,4, 637–656, DOI: 10.1016/S0997-7538(99)80026-6. http://dx.doi.org/10.1016/S0997-7538(99)80026-6 [Crossref]

  • [6] Charlier, R. (1987), Approche unifiée de quelques problèmes non linéaires de mécanique 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. http://dx.doi.org/10.1061/(ASCE)GM.1943-5622.0000083 [Web of Science] [Crossref]

  • [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 assemblies, Geotechnique 29,1, 47–65, DOI: 10.1680/geot.1979.29.1.47. http://dx.doi.org/10.1680/geot.1979.29.1.47 [Crossref]

  • [10] de 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. http://dx.doi.org/10.1002/nag.234 [Crossref]

  • [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. http://dx.doi.org/10.1016/S0020-7683(02)00177-4 [Crossref]

  • [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. http://dx.doi.org/10.1002/nag.338 [Crossref]

  • [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. http://dx.doi.org/10.1016/S0045-7825(03)00348-7 [Crossref]

  • [15] Feyel, F., and J.-L. Chaboche (2000), FE 2 multiscale approach for modelling the elastoviscoplastic behaviour of long fibre SiC/Ti composite materials, Comput. Meth. Appl. Mech. Eng. 183,3–4, 309–330, DOI: 10.1016/S0045-7825(99)00224-8. http://dx.doi.org/10.1016/S0045-7825(99)00224-8 [Crossref]

  • [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. E 75,1, 011303, 1–26, DOI: 10.1103/Phys-RevE.75.011303. http://dx.doi.org/10.1103/PhysRevE.75.011303 [Web of Science] [Crossref]

  • [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. http://dx.doi.org/10.1007/s004660000212 [Crossref]

  • [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. http://dx.doi.org/10.1002/nme.541 [Crossref]

  • [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. http://dx.doi.org/10.1002/nme.433 [Crossref]

  • [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 tangent operators, Comput. Method. Appl. Mech. Eng. 193,3–5, 225–256, DOI: 10.1016/j.cma.2003.10.004. http://dx.doi.org/10.1016/j.cma.2003.10.004 [Crossref]

  • [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. http://dx.doi.org/10.1002/nme.2875 [Crossref] [Web of Science]

  • [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. http://dx.doi.org/10.1063/1.4812151 [Crossref]

  • [25] Pérez-Foguet, A., A. Rodríguez-Ferran, and A. Huerta (2000), Numerical differentiation for non-trivial consistent tangent matrices: an application to the MRSLade 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. http://dx.doi.org/10.1002/(SICI)1097-0207(20000520)48:2<159::AID-NME871>3.0.CO;2-Y [Crossref]

  • [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 displacement fluctuations in a 2D granular material subjected to shear, Geotech. Lett. 2, 113–118, DOI: 10.1680/geolett.12.00029. http://dx.doi.org/10.1680/geolett.12.00029 [Web of Science] [Crossref]

  • [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. http://dx.doi.org/10.1016/j.powtec.2010.08.017 [Crossref]

  • [29] Weber, J. (1966), Recherches concernant les contraintes intergranulaires dans les milieux pulvérulents, Bull. Liaison des Ponts et Chaussées 20, 1–20.

  • [30] Ypma, T.J. (1995), Historical development of the Newton-Raphson method, SIAM Rev. 37,4, 531–551, DOI: 10.1137/1037125. http://dx.doi.org/10.1137/1037125 [Crossref]

  • [31] Zienkiewicz, O.C. (1979), La Méthode des Éléments Finis: Traduit de “the Finite Element Method”, 3rd ed., McGraw-Hill Inc., Paris (in French).

About the article

Published Online: 2014-08-17

Published in Print: 2014-10-01


Citation Information: Acta Geophysica, ISSN (Online) 1895-7455, DOI: https://doi.org/10.2478/s11600-014-0228-3. Export Citation

© 2013 Institute of Geophysics, Polish Academy of Sciences. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License. (CC BY-NC-ND 3.0)

Citing Articles

Here you can find all Crossref-listed publications in which this article is cited. If you would like to receive automatic email messages as soon as this article is cited in other publications, simply activate the “Citation Alert” on the top of this page.

[1]
[2]
Gaël Combe, Vincent Richefeu, Marta Stasiak, and Allbens P. F. Atman
Physical Review Letters, 2015, Volume 115, Number 23
[4]
Yang Liu, WaiChing Sun, Zifeng Yuan, and Jacob Fish
International Journal for Numerical Methods in Engineering, 2015, Page n/a
[6]
Ning Guo and Jidong Zhao
International Journal for Numerical and Analytical Methods in Geomechanics, 2015, Page n/a

Comments (0)

Please log in or register to comment.
Log in