Two Scale Modeling of Heterogeneous Solid Body by Use of Thick Shell Finite Elements

  • Dalia Čalnerytė
  • Rimantas Barauskas
Part of the Communications in Computer and Information Science book series (CCIS, volume 403)


An elasticity parameters evaluation for homogeneous material is considered in this paper if parameters of consisting materials are known in micro scale. The thick shell formulation for homogeneous orthotropic material is discussed and total Lagrangian formulation for the 4-node thick shell element in implicit and explicit analysis is described. The results of the thick shell model are compared with the results of 3D model and LS-Dyna shell model with the same loading.


Multi-scale modeling Total Lagrangian formulation 4-node thick shell element 


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  1. 1.
    Zienkiewicz, O.C., Taylor, R.L.: The Finite Element Method for Solid and Structural Mechanics. Elsevier, Oxford (2005)zbMATHGoogle Scholar
  2. 2.
    Barbero, E.J.: Finite element analysis of composite materials. CRC Press (2008)Google Scholar
  3. 3.
    Kaw, K.A.: Mechanics of Composite Material. CRC Press (2006)Google Scholar
  4. 4.
    Dvorkin, E.N., Bathe, K.J.: A continuum mechanics based four-node shell element for general nonlinear analysis. Eng. Comput. 1, 77–88 (1984)CrossRefGoogle Scholar
  5. 5.
    Bathe, K.J.: Finite Element Procedures. Prentice Hall (1996)Google Scholar
  6. 6.
    Macneal, R.H., Harder, R.L.: A Proposed Standard Set of Problems to Test Finite Element Accuracy. Finite Element in Analysis and Design 1, 3–20 (1985)CrossRefGoogle Scholar
  7. 7.
    Miller, K., Joldes, G., Lance, D., Wittek, A.: Total Lagrangian explicit dynamics finite element algorithm for computing soft tissue deformation. Communications in Numerical Methods in Engineering 23, 121–134 (2007)MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    Tabiei, A., Tanov, R.: Sandwich shell finite element for dynamic explicit analysis. International Journal for Numerical Methods in Engineering 54, 763–787 (2002)CrossRefzbMATHGoogle Scholar
  9. 9.
    Pinho-da-Cruz, J., Oliveira, J.A., Teixeira-Dias, F.: Asymptotic homogenization in linear elasticity. Part I: Mathematical formulation and finite element modeling. Computational Materials Science 45, 1073–1080 (2009)Google Scholar
  10. 10.
    The, L.H., Clarke, M.J.: Co-rotational and Lagrangian formulations for elastic three-dimensional beam finite elements. Journal of Constructional Steel Research 48, 123–144 (1998)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Dalia Čalnerytė
    • 1
  • Rimantas Barauskas
    • 1
  1. 1.Faculty of InformaticsKaunas University of TechnologyKaunasLithuania

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