Computational Mechanics

, Volume 52, Issue 1, pp 121–134 | Cite as

Computational homogenization of porous materials of Green type

  • Felix FritzenEmail author
  • Samuel Forest
  • Djimedo Kondo
  • Thomas Böhlke
Original Paper


The constitutive response of porous materials is investigated computationally. For the solid phase elasto- plastic behavior of Green type is considered, i.e. an isotropic compressible yield criterion is assumed. A wide range of material parameters and porosities from 0.1 to 30 % are investigated by means of FEM simulations of periodic ensembles of spherical pores. The dilatation of the pores and of the compressible matrix are evaluated. It is found that a large part of the total dilatation is due to plastic volume changes of the solid phase. The asymptotic stress states of the simulations are compared to analytical predictions by Shen et al. (Comput Mater Sci 62:189–194, 2012). Based on the computational data, an effective constitutive law is proposed and verified by means of additional computations. A three-scale homogenization procedure for double porous materials is proposed that depends only on the micro- and mesoscale porosity and the yield stress of the solid phase.


Computational homogenization Porous materials Three-scale homogenization Plastic compressibility Material of Green type 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Felix Fritzen
    • 1
    Email author
  • Samuel Forest
    • 2
  • Djimedo Kondo
    • 3
  • Thomas Böhlke
    • 4
  1. 1.YIG Computer Aided Material Modeling, Chair for Continuum Mechanics, Karlsruhe Institute of TechnologyKarlsruheGermany
  2. 2.Centre des Matériaux, UMR7633, Ecole des Mines de Paris /CNRSEvry CedexFrance
  3. 3.Institut Jean le Rond d’AlembertUniversité Pierre etMarie CurieParis CedexFrance
  4. 4.Chair for Continuum MechanicsInstitute of Engineering Mechanics, Karlsruhe Institute of TechnologyKarlsruheGermany

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