Skip to main content
Log in

Allowing for the Third Deviatoric Stress Invariant in Analyzing the Deformation of Thin Shells

  • Published:
International Applied Mechanics Aims and scope

A method for numerical analysis of the elastoplastic axisymmetric stress–strain state of thin shells undergoing nonisothermal deformation along paths of small curvature with allowance for secondary plastic strains and the third invariant of stress deviator is elaborated. The stress–strain state of a shell during heating and cooling is analyzed numerically.

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

Access this article

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

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Ya. M. Grigorenko and A. T. Vasilenko, Theory of Shells with Variable Stiffness, Vol. 4 of the five-volume series Methods of Shell Design [in Russian], Naukova Dumka, Kyiv (1981).

  2. L. M. Kachanov, Fundamentals of the Theory of Plasticity, Dover, New York (2004).

  3. V. V. Novozhilov, Thin Shell Theory, Noordhoff, Groningen (1964).

    Book  MATH  Google Scholar 

  4. Yu. N. Rabotnov, Solid Mechanics [in Russian], Nauka, Moscow (1979).

    Google Scholar 

  5. A. Abel and H. Muir, “The Bauschinger effect and discontinuous yielding,” Philosophical Magasine, 26, No. 2, 489–504 (1972).

    Article  ADS  Google Scholar 

  6. M. E. Babeshko, A. Z. Galishin, A. I. Semenets, and Yu. N. Shevchenko, “Influence of the stress mode on the strength of high-pressure vessels,” Int. Appl. Mech., 51, No. 3, 319–325 (2015).

    Article  ADS  MathSciNet  Google Scholar 

  7. M. E. Babeshko and V. G. Savchenko, “Analyzing processes of nonisothermal loading of shells of revolution with allowance for repeated plastic strains,” Int. Appl. Mech., 53, No. 6, 639–646 (2017).

    Article  ADS  MathSciNet  Google Scholar 

  8. M. E. Babeshko, Yu. N. Shevchenko, and N. N. Tormakhov, “Approximate description of the inelastic deformation of an isotropic material with allowance for the stress mode,” Int. Appl. Mech., 46, No. 2, 139–148 (2010).

    Article  ADS  MATH  Google Scholar 

  9. M. E. Babeshko, Yu. N. Shevchenko, and N. N. Tormakhov, “Thermoviscoplasticity theory incorporating the third deviatoric stress invariant,” Int. Appl. Mech., 51, No. 1, 85–91 (2015).

    Article  ADS  MathSciNet  Google Scholar 

  10. J. Bauschinger, Ümber die Veränderung der Elastizitätsgrenze und des Elastizitätsmoduls ferschidener Metalle, Civilingenieur (1881), pp. 289–348.

  11. J. Bauschinger, “Über die Veränderung der Elastizitätsgrenze und der Festigkeit des Eisens und Stahls durch Strecken und Quetschen durch Erwarmen und Abkuhlenund durch oftmals wiederholte Beanspruchung,“ in: Mitteilung XV aus dem Mech., Techn. Labor., München (1886), pp. 1–116.

  12. A. M. Freudental and H. Geiringer, The Mathematical Theories of the Inelastic Continuum, Springer Verlag, Berlin (1958).

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

  14. W. Lode, “Versuche über den Einfluss der mittleren Hauptspannung auf das Fliessen der Metals – Eisen, Kupfer und Nickel,“ Z. Physik, 36, 913–939 (1926).

    Article  ADS  Google Scholar 

  15. R. Mises, “Mechanik der festen Körper im plastisch deformablen Zustand,“ Göttingen Nachrichten, Mathematisch – Physikalisch Klasse, Göttingen, 4, 582–592 (1913).

    MATH  Google Scholar 

  16. Yu. N. Shevchenko and V. G. Savchenko, “Three-dimensional problems of thermoviscoplasticity: Focus on Ukrainian research (review),” Int. Appl. Mech., 52, No. 3, 217–271 (2016).

    Article  ADS  MathSciNet  MATH  Google Scholar 

  17. P. A. Steblyanko and Yu. N. Shevchenko, “Computational methods in stationary and nonstationary thermal-plasticity problems,” in: R. B. Hetnarski (ed.), Encyclopedia of Thermal Stresses, Vol. 2, C-D, Springer, New York–Dordrecht (2014), pp. 507, 623–630 (1084).

  18. M. Ýyczkowski, Combined Loadings in the Theory of Plasticity, PWN, Warszawa (1981).

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to M. E. Babeshko.

Additional information

Translated from Prikladnaya Mekhanika, Vol. 54, No. 2, pp. 51–60, March–April, 2018.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Babeshko, M.E., Savchenko, V.G. Allowing for the Third Deviatoric Stress Invariant in Analyzing the Deformation of Thin Shells. Int Appl Mech 54, 163–171 (2018). https://doi.org/10.1007/s10778-018-0868-0

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10778-018-0868-0

Keywords

Navigation