Acta Mechanica Sinica

, Volume 6, Issue 4, pp 357–366 | Cite as

A multi-dimensional composite model for plastic continua under polyaxial loading condition

  • Liang Naigang
  • Pal G. Bergan
Article

Abstract

By replacing a medium with reinforcing components oriented and distributed uniformly in a multi-dimensional space, a constitutive model is constructed. The components are extended/compressed compatibly with the strain and the resultant of load exerted on them to balance the stress. Their load-elongation relation can be determined from a conventional material test. Each component undergoes different elongation history depending on its own orientation during deformation, so that the model can simulate elasto-plastic behavior of materials under polyaxial loading conditions. The incremental constitutive matrix has been derived for application in numerical analysis and a yield criterion is also introduced. A few subsequent yield surfaces have been predicted and compared with experiments.

Key Words

plasticity constitutive relationship 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    Budiansky, B, Dow, N.F., Peters, R.W. and Shepherd, R.P., Proc. 1st U.S. Nat. Congr. Appl. Mech., (1951), 503.Google Scholar
  2. [2]
    Ivey, H.J.,J. Mech. Eng. Sci.,3, 1 (1961), 15–30.Google Scholar
  3. [3]
    Phillips, A. and Tang, J.L.,Int. J. Solids and Struct. 8 (1972), 463–474.CrossRefGoogle Scholar
  4. [4]
    Phillips, A. et al.,Acta Mech.,20 (1974), 23–29.CrossRefGoogle Scholar
  5. [5]
    Weng, G.J. and Phillips, A.,Int. J. Engr. Sci.,15 (1977), 45–59 and 61–71.MATHCrossRefGoogle Scholar
  6. [6]
    Sanders, Jr., J.L., Proc. Second U.S. Nat. ongr. Appl. Mech. Amer. Soc. mech. Engrs. (1954), 455–460.Google Scholar
  7. [7]
    Christoffersen, J. and Hutchinson, J. W.,J. Mech. Phys. Solids,27, (1979) 464–487.MathSciNetGoogle Scholar
  8. [8]
    Thomas J. R. Hughes and Farzin Shakib,Eng. Comput., 3 (1986), 116–120.Google Scholar
  9. [9]
    Zienkiewicz, O.C., Nayak, G.C. and Owen, D.R.J., Int. Symp. on Foundations of plasticity, Warsa (Sep., 1972), 107.Google Scholar
  10. [10]
    Owen, D. R. J., Prokash, A. and Zienkiewicz, O. C.,Computers & Structures,4 (1974), 1251–1267.CrossRefGoogle Scholar
  11. [11]
    Mroz, Z.,Acta Mech. 7 (1969), 199.MathSciNetCrossRefGoogle Scholar
  12. [12]
    Drucker, D.C., Proc. First U.S. national Cong., of Appl. Mech. ASME (1951), 487–491.Google Scholar
  13. [13]
    Ishlinskii, I. U.,J. Moscow National University, Mechanics, 46 (1944).Google Scholar
  14. [14]
    Yu, M.H.,Int. J. Mech. Sci. 25, 1 (1983), 71–75.CrossRefGoogle Scholar

Copyright information

© Chinese Society of Theoretical and Applied Mechanics 1990

Authors and Affiliations

  • Liang Naigang
    • 1
  • Pal G. Bergan
    • 2
  1. 1.Institute of MechanicsChinese Academy of SciencesBeijingP.R. China
  2. 2.A. S. Veritas ResearchOsloNorway

Personalised recommendations