Acta Mechanica

, Volume 126, Issue 1–4, pp 19–35 | Cite as

A plasticity model for multiaxial cyclic loading and ratchetting

  • G. Z. Voyiadjis
  • I. N. Basuroychowdhury
Original Papers


The nonlinear behavior of metals when subjected to monotonic and cyclic non-proportional loading is modeled using the proposed hardening rule. The model is based on the Chaboche [1], [2] and Voyiadjis and Sivakumar [3], [4] models incorporating the bounding surface concept. The evolution of the backstress is governed by the deviatoric stress rate direction, the plastic strain rate, the backstress, and the proximity of the yield surface from the bounding surface. In order to ensure uniqueness of the solution, nesting of the yield surface with the bounding surface is ensured. The prediction of the model in uniaxial cyclic loading is compared with the experimental results obtained by Chaboche [1], [2]. The behavior of the model in multiaxial stress space is tested by comparing it with the experimental results in axial and torsional loadings performed by Shiratori et al. [5] for different stress trajectories. The amount of hardening of the material is tested for different complex stress paths. The model gives a very satisfactory result under uniaxial, cyclic and biaxial non-proportional loadings. Ratchetting is also illustrated using a non-proportional loading history.


Cyclic Loading Yield Surface Deviatoric Stress Hardening Rule Stress Path 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    Chaboche, J. L.: Constitutive equations for cyclic plasticity and cyclic viscoplasticity. Int. J. Plasticity5, 247–302 (1989).Google Scholar
  2. [2]
    Chaboche, J. L.: On some modifcations of kinematic hardening to improve the description of ratchetting effects. Int. J. Plasticity7, 661–678 (1991).Google Scholar
  3. [3]
    Voyiadjis, G. Z., Sivakumar, S. M.: A robust kinematic hardening rule with ratchetting effects: Part I. Theoretical formulation. Acta Mech.90, 105–123 (1991).Google Scholar
  4. [4]
    Voyiadjis, G. Z., Sivakumar, S. M.: A robust kinematic hardening rule with ratchetting effects: Part II. Application to nonproportional loading cases. Acta Mech.107, 117–136 (1994).Google Scholar
  5. [5]
    Shiratori, E., Ikegami, K., Yoshida, F.: Analysis of stress-strain relations of use of an anisotropic hardening potential. J. Mech. Phys. Solids27, 213–229 (1979).Google Scholar
  6. [6]
    Tseng, N. T., Lee, G. C.: Simple plasticity model of the two-surface type. ASCE J. Engng Mech.109, 795–810 (1983).Google Scholar
  7. [7]
    Phillips, A., Tang, J. L., Ricciuti, M.: Some new observations on yield surfaces. Acta Mech.20, 23–39 (1974).Google Scholar
  8. [8]
    McDowell, D. L.: An evaluation of recent developments in hardening and flow rules for rate-independent cyclic plasticity. J. Appl. Mech.54, 323–334 (1987).Google Scholar
  9. [9]
    Dafalias, Y. F.: The concept and application of the bounding surface in plasticity theory. In: Physical nonlinearities in structural analysis, (Hult, J., Lamaitre, J., eds.). pp. 56–63. IUTAM Symposium, Senlis, France. Berlin Heidelberg New York: Springer 1981.Google Scholar
  10. [10]
    Armstrong, P. J. Frederick, C. O.: A mathematical representation of the multiaxial Bauschinger effect. CEGB Report RD/B/N/731, Berkeley Nuclear Laboratories (1966).Google Scholar
  11. [11]
    Ohno, N.: A constitutive model of cyclic plasticity with a non-hardening strain region. ASME J. Appl. Mech.49, 721–727 (1982).Google Scholar
  12. [12]
    Ohno, N., Wang, J. D.: Two equivalent forms of nonlinear kinematic hardening: application to nonisothermal plasticity. Int. J. Plasticity7, 637–650 (1991).Google Scholar
  13. [13]
    Ohno, N., Wang, J. D.: Kinematic hardening rules with critical state of dynamci recovery. Part I: Formulation and basic features for ratchetting behavior. Int. J. Plasticity9, 375–390 (1993).Google Scholar
  14. [14]
    Ohno, N., Wang, J. D. Kinematic hardening rules with critical state of dynamci recovery, Part II: Application to experiments of ratchetting behavior. Int. J. Plasticity9, 391–403 (1993).Google Scholar
  15. [15]
    Ohno, N., Wang, J. D.: Kinematic hardening rules for simulation of ratchetting behavior. Eur. J. Mech.13, 519–531 (1994).Google Scholar
  16. [16]
    Mroz, Z.: On the description of anisotropic workhardening. J. Mech. Phys. Solids15, 163 (1967).Google Scholar
  17. [17]
    Mroz, Z.: An attempt to describe the behavior of metals under cyclic loads using a more general workhardening model. Acta Mech.7, 199–212 (1969).Google Scholar
  18. [18]
    Ilyushin, A. A.: An relationship between stress and small strain in continuum mechanics. Prikl. Mate. Mech.18, 641–666 (1954) (in Russian).Google Scholar
  19. [19]
    Voyiadjis, G. Z., Foroozesh, M.: Anisotropic distortional yield model. ASME J. Appl. Mech.57, 537–547 (1990).Google Scholar
  20. [20]
    Voyiadjis, G. Z., Thiagarajan, G., Petarkis, E.: Constitutive modelling for granular media using an isotropic distortional model. Acta Mech.110, 151–171 (1995).Google Scholar

Copyright information

© Springer-Verlag 1998

Authors and Affiliations

  • G. Z. Voyiadjis
    • 1
  • I. N. Basuroychowdhury
    • 1
  1. 1.Department of Civil and Environmental EngineeringLouisiana State UniversityBaton RougeUSA

Personalised recommendations