Unified characteristics line theory of spacial axisymmetric plastic problem

  • Yu Maohong
  • Li Jianchun
  • Zhang Yongqiang


The unified strength theory proposed by Yu in 1991 is extended to spacial axisymmetric problem. A unified spacial axismymmetric characteristics line theory based on the unified strength theory is proposed. This theory takes account of different effects of intermediate principal stress on yielding or failure and the SD effect (tensile-compression strength difference) of materials. Various conventional axisymmetric characteristics line theories, which are based on the Haar-von Karman plastic condition, Szczepinski hypothesis, Tresca criterion, von Mises criterion and Mohr-Coulomb theory, are special cases of the new theory. Besides, a series of new spacial axisymmetric characteristics fields for different materials can be introduced. It forms a unified spacial axisymmetric characteristics theory. Two examples are calculated with the new theory, the results are compared with those obtained by the finite element program UEPP and those based on the Mohr-Coulomb strength theory. It is shown that the new theory is reliable and feasible. The economic benefit can be obtained from the engineering application of the new theory.


plastic axisymmetric problem unified strength theory unified characteristics line field theory Haar-von Karman condition 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Johnson, W., Sowerby, R., Venter, R. D., Plane strain Slip Line Fields for Metal Deformation Processes—A Source Book and Bibliography, New York: Pergamon Press, 1982.MATHGoogle Scholar
  2. 2.
    Hill, R., The Mathematical Theory of Plasticity, Oxford: Oxford University Press, 1950.MATHGoogle Scholar
  3. 3.
    Sokolovsky, V. V., Theory of Plasticity (in Russia), Moskow: Nat. Tech. Press, 1950.Google Scholar
  4. 4.
    Kachanov, L. M., Foundations Theory of Plasticity, London: North-Holland, 1975.Google Scholar
  5. 5.
    Shield, R. T., On the plastic flow of metal condition of axial symmetry, Proc. Roy. Soc., 1955, 233A: 267.MathSciNetGoogle Scholar
  6. 6.
    Lippmann, H., IUTAM Symposium on Metal Forming Plasticity, New York: Springer-Verlag, 1979.Google Scholar
  7. 7.
    Spencer, A. J. M., The approximate solution of certain problem of axially-symunetric plastic flow, J. Mech. Phys. Solids, 1964, 12: 231.MATHCrossRefGoogle Scholar
  8. 8.
    Wang, R., Xiong, Z. H., Wang, W. B., Foundation of Plasticity (in Chinese), Beijing: Science Press, 1982.Google Scholar
  9. 9.
    Collins, I. E., Dewhurst, P., A slip line field analysis of asymmetrical hot rolling, International Journal of Mechanical Science, 1975, 17: 643.CrossRefGoogle Scholar
  10. 10.
    Collins, I. F., Slip line field analysis of forming processes in plane strain and axial symmetry, Advanced Technology of Plasticity, 1984, 11: 1074.Google Scholar
  11. 11.
    Yu, M. H., Yang, S. Y., Liu, C. Y. et al., Unified plane-strain slip line field theory system, J. Civil Engineering (in Chinese), 1997, 30(2): 14Google Scholar
  12. 12.
    Simmons, J. A., Hauser, F., Dorn, E., Mathematical Theories of Plastic Deformation Under Impulsive Loading, Berkeley-Los Angeles: University of California Press, 1962.Google Scholar
  13. 13.
    Lin, C. C., On a perturbation theory based on the method of characteristies, J. Math. Phys., 1954, 33: 117–134.MATHGoogle Scholar
  14. 14.
    Hopkins, H. G., The method of characteristics and its applications to the theory of stress waver in solids, in Engineering Plasticity, Cambridge: Combridge University Press, 1968, 277–315.Google Scholar
  15. 15.
    Shield, R. T., The plastic indentation of a layer by a flat punch, Quart. Appl. Math., 1955, 13: 27.MATHMathSciNetGoogle Scholar
  16. 16.
    Haar, A., von Karman, Th., Zur theorie der spanungszustände in plastischen und sandartigen medion, Nachr. Gesellsch. Wissensch., Göttingen, 1909.Google Scholar
  17. 17.
    Szczepinski, W., Introduction to the Mechanics of Plastic Forming of Metals, Netherlands: Sijthoff and Noordhoff, 1979.MATHGoogle Scholar
  18. 18.
    Chen, W. F., Limit Analysis and Soil Plasticity, New York: Elsevier, 1975.MATHGoogle Scholar
  19. 19.
    Yu, M. H., He, L. N., A new model and theory on yield and failure of materials under complex stress state, Mechanical Behaviors of Materials ≈ 6, Oxford: Pergamon Press, 1991, 3: 841–846.Google Scholar
  20. 20.
    Yu, M. H., New System of Strength Theory (in Chinese), Xi'an: Xi'an Jiaotong Universitry Press, 1992.Google Scholar
  21. 21.
    Yu, M. H., He, L. N., Song, L. Y., Twin shear stress theory and its generalization, Scientia Sinica (Science in China), Series A, 1985, 28(11): 1174–1183.Google Scholar
  22. 22.
    Yu, M. H., Yang, S. Y. et al., Unified elasto-plastic associated and non-associated constitutive model and its engineering applications, Computers and Structures, 1999, 71: 627–636.CrossRefGoogle Scholar
  23. 23.
    Ma, G. W., Shoji, I., Plastic limit analysis of circular plates with respect to unified yield criterion, Int. J. Mech. Sci., 1998, 40(10): 963.MATHCrossRefGoogle Scholar
  24. 24.
    Ma, G. W., Hao, H., Unified plastic limit analyses of circular plates under arbitrary load, Journal of Applied Mechanics, ASME, 1999, 66(2): 568.CrossRefGoogle Scholar
  25. 25.
    Qiang, H. F., Lu, N., Liu, B. J., Unified solutions of crack tip plastic zone under small scale yielding, Chinese Journal of Mechanical Engineering, (in Chinese with English abstract), 1999, 35(1): 34–38.Google Scholar
  26. 26.
    Yang, S. Y., Yu, M. H., Constitutive descriptions of multiphase poropus media, Acta Mechanica Sinica (in Chinese with English abstract), 2000, 32(1): 11–24.Google Scholar
  27. 27.
    Yang, S. Y., Yu, M. H., An elasto-plastic damage model for saturated and unsaturated geomaterials, Acta Mechanica Sinica (in Chinese with English abstract), 2000, 32(2): 198–206.Google Scholar
  28. 28.
    Cheng, H. X., Li, J. J., Zhang, G. S. et al., Finite element analysis program system HAJIF(X), Chinese Journal of Computational Mechanics (in Chinese), 1997, 14, 659.Google Scholar
  29. 29.
    Zhao, J. H., Zhang, Y. Q., Li, J. C., Solutions of some plastic plain strain problems based on unified strength theory and unified slip line theory, J. Mechanical Engng. (in Chinese with English abstract), 1999, 35(6): 61–65.Google Scholar
  30. 30.
    Suh, N. P., Lee, R. S., Rogers, C. R., The yielding or truncated solid cones under quasi-static and dynamic loading, J. Mech. Phys. Solids, 1968, 16: 357.CrossRefGoogle Scholar

Copyright information

© Science in China Press 2001

Authors and Affiliations

  • Yu Maohong
    • 1
  • Li Jianchun
    • 1
  • Zhang Yongqiang
    • 1
  1. 1.School of Civil Engineering and MechanicsXi'an Jiaotong UniversityXi'anChina

Personalised recommendations