FEM × DEM Multi-scale Analysis of Boundary Value Problems Involving Strain Localization

  • J. DesruesEmail author
  • T. K. Nguyen
  • G. Combe
  • D. Caillerie
Conference paper
Part of the Springer Series in Geomechanics and Geoengineering book series (SSGG)


The paper presents a FEM × DEM multiscale modeling analysis of boundary value problems involving strain localization in cohesive granular materials. At the microscopic level, a discrete element method (DEM) is used to model the granular structure. At the macroscopic level, the numerical solution of the boundary value problem (BVP) is obtained via a finite element method (FEM) formulation. In order to bridge the gap between micro- and macro-scale, the concept of representative volume element (REV) is applied: the average REV stress and the consistent tangent operators are obtained in each macroscopic integration point as the results of DEM simulation. The numerical constitutive law is determined through the DEM modeling of the microstructure to take into account the discrete nature of granular materials. The computational homogenization method is described and illustrated in the case of a hollow cylinder made of cohesive-frictional granular material, submitted to different internal and external pressures. Strain localization is observed to occur at the macro scale in this simulation.


Finite Element Method Representative Elementary Volume Discrete Element Method Gauss Point Discrete Element Method Simulation 
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This work was carried out as part of GeoBridge research project at 3SR lab, Grenoble, France, which is funded by the French Agence Nationale de la Recherche (ANR).


  1. Chambon R, Caillerie D, Matsushima T (2001) Plastic continuum with microstructure, local second gradient theories for geomaterials: localization studies. Int J Solids Struct 38(46):8503–8527CrossRefzbMATHGoogle Scholar
  2. Combe G, Roux JN (2003) Discrete numerical simulation, quasistatic deformation and the origin of strain in granular materials. In: 3rd international symposium on deformation characteristics of geomaterials, Lyon, France, pp 1071–1078Google Scholar
  3. Cundall PA, Strack ODL (1979) A discrete numerical model for granular assemblies. Geotechnique 29(1):47–65CrossRefGoogle Scholar
  4. Gilabert F, Roux JN, Castellanos A (2007) Computer simulation of model cohesive powders: influence of assembling procedure and contact laws on low consolidation states. Phys Rev E 75:011303CrossRefMathSciNetGoogle Scholar
  5. Guo N, Zhao J (2013) A hierarchical model for cross-scale simulation of granular media. AIP Conf Proc 1542:1222–1225CrossRefGoogle Scholar
  6. Kouznetsova V, Brekelmans WAM, Baaijens FPT (2001) An approach to micro-macro modeling of heterogeneous materials. Comput Mech 27(1):37–48CrossRefzbMATHGoogle Scholar
  7. Matsushima T, Chambon R, Caillerie D (2002) Large strain finite element analysis of a local second gradient model: application to localization. Int J Numer Methods Eng 54(4):499–521CrossRefMathSciNetzbMATHGoogle Scholar
  8. Meier HA, Steinmann P, Kuhl E (2008) Technische Mechanik Band 28. Heft 1:32–42Google Scholar
  9. Miehe C, Dettmar J (2004) A framework for micro–macro transitions in periodic particle aggregates of granular materials. Comput Methods Appl Mech Eng 193(3):225–256Google Scholar
  10. Nguyen TK, Combe G, Caillerie D, Desrues J (2013) Modeling of a cohesive granular materials by a multi-scale approach. AIP Conf Proc 1542:1194–1197CrossRefGoogle Scholar
  11. Nitka M, Bilbie G, Combe G, Dascalu C, Desrues J (2009) A DEM—FEM two scale approach of the behaviour of granular materials. Powders and grains 2009. Golden CO Colorado School of Mines, USA, pp 443–446Google Scholar
  12. Nitka M, Combe G, Dascalu C, Desrues J (2011) Two-scale modeling of granular materials: a DEM-FEM approach. Granular Matter 13(3):277–281CrossRefGoogle Scholar
  13. Radjaï F, Dubois F (2011) Discrete-element modeling of granular materials. Wiley, New York, pp 139–157Google Scholar
  14. Weber J (1966) Recherches concernant les contraintes intergranulaires dans les milieux pulvérulents. Bul. liaison P. et Ch. N°20, juillet–aoûtGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • J. Desrues
    • 1
    Email author
  • T. K. Nguyen
    • 1
  • G. Combe
    • 1
  • D. Caillerie
    • 1
  1. 1.Laboratoire 3SRUJF-Grenoble 1, Grenoble-INP, CNRS UMR 5521Grenoble Cedex 09France

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