Fibers and Polymers

, Volume 7, Issue 1, pp 42–50 | Cite as

Anisotropic-asymmetric yield criterion and anisotropic hardening law for composite materials: Theory and formulations

  • Ji Hoon Kim
  • Myoung-Gyu Lee
  • Kwansoo Chung
  • Jae Ryoun Youn
  • Tae Jin Kang


In this paper, elasto-plastic constitutive equations for highly anisotropic and asymmetric materials are developed and their numerical implementation is presented. Some engineering materials such as fiber reinforced composites show different material behavior in the different material directions (anisotropy) as well as in tension and compression (asymmetry). Although these materials have mostly been analyzed using the anisotropic elastic constitutive equations, the necessity of consideration of plastic properties has been frequently reported in the previous works. In order to include both the anisotropic and asymmetric properties of composite materials, the Drucker-Prager yield criterion is modified by adding anisotropic parameters and initial components of translation. The implementation procedure for the developed theory and algorithms is presented based on the implicit finite element scheme. The measured data from the previous work are used to validate the present constitutive equations.


Constitutive equations Drucker-Prager yield criterion Anisotropy Asymmetry Fiber reinforced composites 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    W. Lee, J. H. Kim, H.-J. Shin, K. Chung, T. J. Kang, and J. R. Youn,Fibers and Polymers,4, 77 (2003).CrossRefGoogle Scholar
  2. 2.
    M. R. Piggot and B. Harris,J. Mater. Sci.,15, 2523 (1980).CrossRefGoogle Scholar
  3. 3.
    N. L. Hancox,J. Mater. Sci.,10, 234 (1975).CrossRefGoogle Scholar
  4. 4.
    M. G. Lee, K. Chung, C. J. Lee, J. H. Park, J. Kim, T. J. Kang, and J. R. Youn,Composites Science and Technology,61, 2491 (2001).CrossRefGoogle Scholar
  5. 5.
    A. F. Saleeb, T. E. Wilt, N. R. Al-Zoubi, and A. S. Gendy,Composites Part B,34, 21 (2003).CrossRefGoogle Scholar
  6. 6.
    B. D. Agarwal and L. J. Broutman, “Analysis and Performance of Fiber Composites”, John Wiley & Sons, NY, 1980.Google Scholar
  7. 7.
    A. S. Khan and S. Huang, “Continuum Theory of Plasticity”, John Wiley & Sons, NY, 1995.Google Scholar
  8. 8.
    R. Hill, “The Mathematical Theory of Plasticity”, Oxford University Press, NY, 1956.Google Scholar
  9. 9.
    F. Barlat, D. J. Lege, and J. C. Brem,International Journal of Plasticity,7, 693 (1991).CrossRefGoogle Scholar
  10. 10.
    F. Barlat, J. C. Brem, J. W. Yoon, K. Chung, R. E. Dick, S.-H. Choi, F. Pourboghrat, E. Chu, and D. J. Lege,International Journal of Plasticity,19, 1297 (2003).CrossRefGoogle Scholar
  11. 11.
    A. R. Leewood, J. F. Doyle, and C. T. Sun,Comput. Struct.,25, 749 (1987).CrossRefGoogle Scholar
  12. 12.
    L. P. Isupov and Yu. N. Rabotnov,Izv. AN SSSR MTT,1, 121 (1985).Google Scholar
  13. 13.
    B. S. Sarbayev,Computational Materials Science,6, 211 (1991).CrossRefGoogle Scholar
  14. 14.
    M. G. Lee, D. Kim, K. Chung, J. R. Youn, and T. J. Kang,Polymer and Polymer Composites,12, 225 (2004).Google Scholar
  15. 15.
    J. L. Chaboche,International Journal of Plasticity,2, 149 (1986).CrossRefGoogle Scholar
  16. 16.
    R. M. Jones, “Mechanics of Composite Materials”, McGraw-Hill, NY, 1975.Google Scholar
  17. 17.
    K. Chung, M.-G. Lee, D. Kim, C. Kim, M. L. Wenner, and F. Barlat,International Journal of Plasticity,21, 861 (2005).Google Scholar
  18. 18.
    S. W. Tsai and E. M. Wu,J. Comp. Mater.,5, 58 (1971).CrossRefGoogle Scholar
  19. 19.
    J. W. Yoon, D. Y. Yang, and K. Chung,Computer Methods in Applied Mechanics and Engineering,174, 23 (1999).CrossRefGoogle Scholar
  20. 20.
    J. C. Simo and T. J. R. Hughes, “Computational Inelasticity”, Springer-Verlag, N.Y., U.S.A., 1997.Google Scholar
  21. 21.
    Hibbitt, Karlsson and Sorensen, “ABAQUS User’s Manual”, Version 6.2.6., 2001.Google Scholar
  22. 22.
    D. Lee and W. A. Backofen,Trans. Metall. Soc. AIME, 236 (1966).Google Scholar

Copyright information

© The Korean Fiber Society 2006

Authors and Affiliations

  • Ji Hoon Kim
    • 1
  • Myoung-Gyu Lee
    • 1
    • 2
  • Kwansoo Chung
    • 1
  • Jae Ryoun Youn
    • 1
  • Tae Jin Kang
    • 1
  1. 1.School of Materials Science and EngineeringSeoul National UniversitySeoulKorea
  2. 2.Department of Materials Science and EngineeringOhio State UniversityUSA

Personalised recommendations