Journal of Materials Science

, Volume 40, Issue 22, pp 5859–5866 | Cite as

Finite element modeling concepts and linear analyses of 3D regular open cell structures

  • Mathias H. Luxner
  • Juergen Stampfl
  • Heinz E. Pettermann
Mechanical Behavior of Cellular Solids


Various Finite Element modeling concepts and linear analyses of 3D regular cellular solids (lattice structures) with relative densities ranging from 10% to 20% are presented. Continuum element based models and beam element based models are employed, the latter with and without an adaptation of stiffness in the vicinity of the vertices. Space filling unit cell models are used for a constitutive characterization of four different structures in terms of density and directional dependence of their Young's moduli. Finite structure models of different size are simulated for investigating the influence of free surfaces and being compared to results of uniaxial compression tests of samples fabricated by two different Rapid Prototyping techniques.


Free Surface Relative Density Compression Test Uniaxial Compression Open Cell 
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.
    W. Sun, A. Darling, B. Starly and J. Nam, Biotechnol. Appl. Biochem. (2004) 39.Google Scholar
  2. 2.
    L. Gibson and M. Ashby, “Cellular Solids: Structure and Properties,” 2nd ed. (Cambridge University Press, 1997).Google Scholar
  3. 3.
    J. Grenestedt, Int. J. Sol. Struct. (1999) 36.Google Scholar
  4. 4.
    R. Christensen, ibid. (2000) 37.Google Scholar
  5. 5.
    H. Zhu, J. Knott and N. Mills, J. Mech. Phys. Solids (1997) 45.Google Scholar
  6. 6.
    Y. Kwon, R. Cooke and C. Park, J. Mat. Sci. and Eng. (2003) A343.Google Scholar
  7. 7.
    W. Sanders and L. Gibson, ibid. (2003) A352.Google Scholar
  8. 8.
    J. Hohe and W. Becker, Comput. Mat. Sci. (2003) 28.Google Scholar
  9. 9.
    T. Daxner, H. J. Böhm and F. G. Rammerstorfer, in “Metal Foams and Porous Metal Structures,” edited by J. Banhart, M. F. Ashby and N. A. Fleck (Verlag MIT, Bremen, 1999) p. 283.Google Scholar
  10. 10.
    T. Daxner, R. Denzer, H. J. Böhm, F. G. Rammerstorfer and M. Maier, Mater.-Wiss. u. Werkst.-Techn. (2000) 31.Google Scholar
  11. 11.
    T. Daxner, “Multi-Scale Modeling and Simulation of Metallic Foams,” Fortschritts-Berichte VDI, Reihe 18, No. 285 (VDI Verlag, Düsseldorf, 2003).Google Scholar
  12. 12.
    J. Stampfl, M. Seyr, M. H. Luxner, H. E. Pettermann, A. Woesz and P. Fratzl, in Proceedings of 2004 MRS Spring Meeting – Biological and Bioinspired Materials and Devices, edited by J. Aizenberg, C. Orme, W. Landis and R. Wang, (2004) vol. 823.Google Scholar
  13. 13.
    A. Woesz, J. Stampfl and P. Fratzl, Advanced Eng. Mat. (2004) 6.Google Scholar
  14. 14.
    M. H. Luxner, J. Stampfl and H. E. Pettermann, in Proceedings of 2004 ASME International Mechanical Engineering Congress (ASME, New York, 2004).Google Scholar
  15. 15.
    H. Böhm, “Mechanics of Microstructured Materials” (Springer Verlag, Wien, 2004).Google Scholar
  16. 16.
    A. Anthoine, Int. J. Sol. Struct. 2 (1995) 32.Google Scholar
  17. 17.
    P. Jacobs, “Rapid Prototyping and Manufacturing” (Society of Manufacturing Engineers, Dearborn, 1992).Google Scholar
  18. 18.
    A. Gebhardt, “Rapid Prototyping – Werkzeuge für die schnelle Produktentwicklung” second edition (Hanser Fachbuch, München, 2000).Google Scholar
  19. 19.
    R. Liska, F. Schwager, A. Woesz, A. Pisaipan, S. Seidler and J. Stampfl, in Proceedings Radtech 2003, Berlin (2003) p. 93.Google Scholar

Copyright information

© Springer Science + Business Media, Inc 2005

Authors and Affiliations

  • Mathias H. Luxner
    • 1
  • Juergen Stampfl
    • 2
  • Heinz E. Pettermann
    • 1
  1. 1.Institute of Lightweight Design and Structural BiomechanicsVienna University of TechnologyViennaAustria
  2. 2.Institute of Materials Science and TechnologyVienna University of TechnologyViennaAustria

Personalised recommendations