FE2-Simulation of Microheterogeneous Steels Based on Statistically Similar RVEs

  • D. BalzaniEmail author
  • J. Schröder
  • D. Brands
Conference paper
Part of the IUTAM Bookseries book series (IUTAMBOOK, volume 21)


A main problem of direct homogenization methods is the high computational cost, when we have to deal with large random microstructures. This leads to a large number of history variables which needs a large amount of memory, and moreover a high computation time. We focus on random microstructures consisting of a continuous matrix phase with a high number of embedded inclusions. In this contribution a method is presented for the construction of statistically similar representative volume elements (SSRVEs) which are characterized by a much less complexity than usual random RVEs in order to obtain an efficient simulation tool. The basic idea of the underlying procedure is to find a simplified SSRVE, whose selected statistical measures under consideration are as close as possible to the ones of the original microstructure.


Spectral Density Representative Volume Element Target Structure Inclusion Phase Real Microstructure 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    D. Balzani and J. Schröder, Some basic ideas for the reconstruction of statistically similar microstructures for multiscale simulations, Proceedings of Applied Mathematics and Mechanics 8, 2008, 10533–10534.CrossRefGoogle Scholar
  2. 2.
    M. Beran, Statistical Continuum Theories, Wiley, 1968.zbMATHGoogle Scholar
  3. 3.
    R. Hill, Elastic properties of reinforced solids: some theoretical principles, Journal of the Mechanics and Physics of Solids 11, 1963, 357–372.zbMATHCrossRefGoogle Scholar
  4. 4.
    C. Miehe, J. Schröder and J. Schotte, Computational homogenization analysis in finite plasticity. Simulation of texture development in polycrystalline materials, Computer Methods in Applied Mechanics and Engineering 171, 1999, 387–418.zbMATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    J. Ohser and F. Mücklich, Statistical Analysis of Microstructures in Materials Science, J. Wiley & Sons, 2000.zbMATHGoogle Scholar
  6. 6.
    E. Parzen, Stochastic Processes. Holden-Day, San Francisco, CA, 1992.Google Scholar
  7. 7.
    G.L. Povirk. Incorporation of microstructural information into models of two-phase materials, Acta Metallurgica et Materialia 43(8), 1995, 3199–3206.CrossRefGoogle Scholar
  8. 8.
    J. Schröder, Homogenisierungsmethoden der nichtlinearen Kontinuumsmechanik unter Beachtung von Stabilitätsproblemen, Habilitationsschrift, Institut für Mechanik (Bauwesen), Lehrstuhl I, Universität Stuttgart, 2000.Google Scholar
  9. 9.
    J. Schröder, D. Balzani, H. Richter, H.P. Schmitz and L. Kessler, Simulation of microheterogeneous steels based on a discrete multiscale approach, in Proceedings of the 7th International Conference and Workshop on Numerical Simulation of 3D Sheet Metal Forming Processes, P. Hora (Ed.), 2008, pp. 379–383.Google Scholar
  10. 10.
    R.J.M. Smit, W.A.M. Brekelmans and H.E.H. Meijer, Prediction of the mechanical behavior of nonlinear heterogeneous systems by multi-level finite element modeling, Computer Methods in Applied Mechanics and Engineering 155, 1998, 181–192.zbMATHCrossRefGoogle Scholar
  11. 11.
    S. Torquato, Random Heterogeneous Materials. Microstructure and Macroscopic Properties, Springer, 2002.zbMATHGoogle Scholar

Copyright information

© Springer Science+Business Media B.V. 2010

Authors and Affiliations

  1. 1.Institute of Mechanics, Faculty of Engineering SciencesUniversity of Duisburg-EssenEssenGermany

Personalised recommendations