Acta Mechanica Solida Sinica

, Volume 27, Issue 1, pp 73–84 | Cite as

Buckling and Postbuckling Analysis of Elasto-Plastic Fiber Metal Laminates

  • Rengui Bi
  • Yiming Fu
  • Yanping Tian
  • Chao Jiang


The elasto-plastic buckling and postbuckling of fiber metal laminates (FML) are studied in this research. Considering the geometric nonlinearity of the structure and the elasto-plastic deformation of the metal layers, the incremental Von Karman geometric relation of the FML with initial deflection is established. Moreover, an incremental elasto-plastic constitutive relation adopting the mixed hardening rule is introduced to depict the stress-strain relationship of the metal layers. Subsequently, the incremental nonlinear governing equations of the FML subjected to in-plane compressive loads are derived, and the whole problem is solved by the iterative method according to the finite difference method. In numerical examples, the effects of the initial deflection, the loading state, and the geometric parameters on the elasto-plastic buckling and postbuckling of FML are investigated, respectively.

Key Words

fiber metal laminates elasto-plastic buckling postbuckling 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Khalili, S.M.R., Mittal, R.K. and Kalibar, G., A study of the mechanical properties of steel/aluminum/GRP laminates. Materials Science and Engineering, 2005, 412: 137–140.CrossRefGoogle Scholar
  2. 2.
    Vogelesang, L., Schijve, J. and Fredell, R., Fibre-metal laminates: damage tolerant aerospace materials. In: Case Studies in Manufacturing with Advanced Materials, Elsevier, 1995, 2: 259–260.Google Scholar
  3. 3.
    Vlot, A. and Vogelesang, L.B., Towards application of fibre metal laminates in large aircraft. Aircraft Engineering and Aerospace Technology, 1999, 71(6): 558–570.CrossRefGoogle Scholar
  4. 4.
    Vermeern, C.A., An historic overview of the development of fiber metal laminates. Applied Composite Materials, 2003, 10: 189–205.CrossRefGoogle Scholar
  5. 5.
    Vogelesang, L.B. and Vlot, A., Development of metal laminates for advanced aerospace structures. Journal of Materials Processing Technology, 2000, 103: 1–5.CrossRefGoogle Scholar
  6. 6.
    Remmers, J.J.C. and Borst, R., Delamination buckling of fibre-metal laminates. Composites Science and Technology, 2001, 61: 2207–2213.CrossRefGoogle Scholar
  7. 7.
    Vlot, A. and Gunnink, J.W., Fiber Metal Laminates—An Introduction. Netherlands: Kluwer Academic Publishers, 2001.CrossRefGoogle Scholar
  8. 8.
    Wittenberg, T.C., van Baten, T.J. and de Boer, A., Design of fibre metal laminate shear panels for ultra-high capacity aircraft. Aircraft Design, 2001, 4: 99–113.CrossRefGoogle Scholar
  9. 9.
    Chen, J.L. and Sun, C.T., Modeling of orthotropic elastic-plastic properties of ARALL laminates. Composites Science and Technology, 1989, 36: 321–337.CrossRefGoogle Scholar
  10. 10.
    Wu, G.C. and Yang, J.M., Analytical modeling and numerical simulation of the nonlinear deformation of hybrid fibre-metal laminates. Modelling and Simulation in Materials Science and Engineering, 2005, 13: 413–425.CrossRefGoogle Scholar
  11. 11.
    Homan, J.J., Fatigue initiation in fibre metal laminates. International Journal of Fatigue, 2006, 28: 366–374.CrossRefGoogle Scholar
  12. 12.
    Morrison, A.M., Braunlich, C.G., Kamaruddin, N., Cai, L.A., Hashagen, E., Schellekens, J.C.J., de Borst, R. and Parisch, H., Finite element procedure for modelling fibre metal laminates. Composite Structures, 1995, 32: 255–264.CrossRefGoogle Scholar
  13. 13.
    Kawai, M., Morishita, M., Tomura, S. and Takumida, K., Inelastic behavior and strength of fiber metal hybrid composite-glare. International Journal of Mechanics Science, 1998, 40: 183–198.CrossRefGoogle Scholar
  14. 14.
    Shanley, F.R., Inelastic column theory. Journal of the Aeronautical Sciences, 1947, 14: 261–268.CrossRefGoogle Scholar
  15. 15.
    Wang, C.M., Xiang, Y. and Chakrabarty, J., Elastic/plastic buckling of thick plates. International Journal of Solids and Structures, 2001, 38: 8617–8640.CrossRefGoogle Scholar
  16. 16.
    Alexander, V.I., Comparison of different isotropic elastoplastic models at finite strains used in numerical analysis. Computer Methods Applied Mechanics and Engineering, 2003, 192: 4659–4674.CrossRefGoogle Scholar
  17. 17.
    Hutchinson, J.W., Post-bifurcation behavior in the plastic range. Journal of the Mechanics and Physics of Solids, 1973, 21(3): 163–190.CrossRefGoogle Scholar
  18. 18.
    Hutchinson, J.W., Plastic buckling. Advances in Applied Mechanics, 1974, 14: 67–141.CrossRefGoogle Scholar
  19. 19.
    Needleman, A. and Tvergaard, V., An analysis of the imperfection sensitivity of square elastic-plastic plates under axial compression. International Journal of Solids and Structures, 1976, 12(3): 185–201.CrossRefGoogle Scholar
  20. 20.
    Cimetière, A. and Léger, A., Some problems about elastic-plastic post-buckling. International Journal of Solids and Structures, 1996, 30(10): 1519–1533.CrossRefGoogle Scholar
  21. 21.
    Pi, Y.L. and Bradford, M.A., Elasto-plastic buckling and postbuckling of arches subjected to a central load. Computers and Structures, 2003, 81(18–19): 1811–1825.CrossRefGoogle Scholar
  22. 22.
    Chia, C.Y., Nonlinear Analysis of Plates. New York: McGraw-Hill International Book Company, 1980.Google Scholar

Copyright information

© The Chinese Society of Theoretical and Applied Mechanics and Technology 2014

Authors and Affiliations

  • Rengui Bi
    • 1
    • 2
  • Yiming Fu
    • 1
    • 2
  • Yanping Tian
    • 3
  • Chao Jiang
    • 1
    • 2
  1. 1.State Key Laboratory of Advanced Design and Manufacturing for Vehicle BodyHunan UniversityChangshaChina
  2. 2.College of Mechanical and Vehicle EngineeringHunan UniversityChangshaChina
  3. 3.School of Mechanical EngineeringHangzhou Dianzi University310018China

Personalised recommendations