Skip to main content
SpringerLink
Log in

Constitutive equations of elastoplastic isotropic materials that allow for the stress mode

  • Published:
International Applied Mechanics Aims and scope

The constitutive equations describing the elastoplastic deformation of an isotropic material and taking into account the stress mode are validated against available experimental data. We propose a method for the approximate determination of the base functions appearing in the constitutive equations and relating the first and second invariants of the stress tensors and the linear components of finite strains. The strain components obtained by this method are compared to experimental data

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. A. A. Il’yushin, Plasticity. Fundamentals of the General Mathematical Theory [in Russian], Izd. AN SSSR, Moscow (1963).

  2. L. M. Kachanov, Fundamentals of Plasticity Theory [in Russian], GIITTL, Moscow (1956).

    Google Scholar 

  3. S. I. Ratner, Strength and Plasticity of Metals [in Russian], Oborongiz, Moscow (1949).

    Google Scholar 

  4. V. G. Savchenko and Yu. N. Shevchenko, “Spatial thermoviscoplastic problems,” Int. Appl. Mech., 36, No. 11, 1399–1433 (2000).

    Article  Google Scholar 

  5. Yu. N. Shevchenko and M. E. Babeshko, “The thermoviscoelastoplastic state of shells of revolution under axisymmetric deformation along various flat paths,” Int. Appl. Mech., 37, No. 8, 967–997 (2001).

    Article  Google Scholar 

  6. Yu. N. Shevchenko, M. E. Babeshko, and R. G. Terekhov, Thermoviscoelastoplastic Processes of Combined Deformation of Structural Members [in Russian], Naukova Dumka, Kyiv (1992).

    Google Scholar 

  7. Yu. N. Shevchenko and R. G. Terekhov, Physical Equations of Thermoviscoplasticity [in Russian], Naukova Dumka, Kyiv (1982).

    Google Scholar 

  8. Yu. N. Shevchenko, N. N. Tormakhov, and R. G. Terekhov, “Specification of scalar functions of the tensor-nonlinear constitutive equations in the theory of plasticity,” Int. Appl. Mech., 36, No. 10, 1329–1338 (2000).

    Article  Google Scholar 

  9. M. E. Babeshko and Yu. N. Shevchenko, “Elastoplastic stress–strain state of flexible layered shells made of isotropic and transversely isotropic materials with different moduli and subjected to axisymmetric loading,” Int. Appl. Mech., 43, No. 11, 1208–1217 (2007).

    Article  Google Scholar 

  10. A. Z. Galishin, “Axisymmetric thermoviscoelastoplastic state of thin flexible shells with damages,” Int. Appl. Mech., 44, No. 2, 158–166 (2008).

    Article  Google Scholar 

  11. A. Z. Galishin, “Axisymmetric thermoviscoelastoplastic state of thin laminated shells made of a damageable material,” Int. Appl. Mech., 44, No. 4, 431–441 (2008).

    Article  Google Scholar 

  12. R. Hill, The Mathematical Theory of Plasticity, Clarendon Press, Oxford (1950).

    MATH  Google Scholar 

  13. Yu. N. Shevchenko, R. G. Terekhov, and N. N. Tormakhov, “Constitutive equations for describing the elastoplastic deformation of elements of a body along small-curvature paths in view of the stress mode,” Int. Appl. Mech., 42, No. 4, 421–430 (2006).

    Article  Google Scholar 

  14. Yu. N. Shevchenko, R. G. Terekhov, and N. N. Tormakhov, “Linear relationship between the first invariants of the stress and strain tensors in theories of plasticity and strain hardening,” Int. Appl. Mech., 43, No. 3, 291–302 (2007).

    Article  Google Scholar 

  15. Yu. N. Shevchenko, R. G. Terekhov, and N. N. Tormakhov, “Elastoplastic deformation of elements of an isotropic solid along paths of small curvature: Constitutive equations incorporating the stress mode,” Int. Appl. Mech., 43, No. 6, 621–630 (2007).

    Article  Google Scholar 

  16. M. Zyczkowskii, Combined Loadings in the Theory of Plasticity, PWN-Polish Scientific Publishers, Warsaw (1981).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. S. P. Timoshenko Institute of Mechanics, National Academy of Sciences of Ukraine, 3 Nesterov St., Kyiv, Ukraine, 03057

    M. E. Babeshko, Yu. N. Shevchenko & N. N. Tormakhov

Authors
  1. M. E. Babeshko
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Yu. N. Shevchenko
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. N. N. Tormakhov
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to M. E. Babeshko.

Additional information

Translated from Prikladnaya Mekhanika, Vol. 45, No. 11, pp. 50–58, November 2009.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Babeshko, M.E., Shevchenko, Y.N. & Tormakhov, N.N. Constitutive equations of elastoplastic isotropic materials that allow for the stress mode. Int Appl Mech 45, 1189–1195 (2009). https://doi.org/10.1007/s10778-010-0258-8

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10778-010-0258-8

Keywords

Search

Navigation