Skip to main content
SpringerLink
Log in

SIMULATION OF VISCOELASTIC-PLASTIC BEHAVIOR OF SHALLOW SHELLS WITH ACCOUNT FOR STRAIN RATE OF MATERIALS

  • Published:
Journal of Applied Mechanics and Technical Physics Aims and scope

Abstract

This paper describes a numerical-analytical model of the viscoelastic-plastic behavior of flexible shallow shells with account for the dependence of plastic properties of their materials on strain rate. The inelastic behavior of materials is described by the theory of flow with isotropic hardening. Loading functions depend on the hardening parameter and strain rate intensity. Viscoelastic behavior is described by linear constitutive equations from a multiconstant body model. Transverse shears of structures during bending deformation are taken into account within the framework of the Ambartsumyan theory, and geometric nonlinearity within the von Karman approximation. A cross-type explicit scheme is used for the numerical integration of the formulated initial boundary value problem. The dynamic deformation of a cylindrical elongated panel made of a polymer material is studied. The structure is transversely loaded by a pressure generated by an air blast wave. It is shown that neglecting the dependence between the plastic properties of the material and the strain rate may cause one to significantly underestimate a maximum deflection in absolute value and the largest strain value during oscillations and cause one to overestimate a maximum residual strain. In addition, residual deflection diagrams obtained by such a calculation do not agree with the diagrams obtained by a calculation that takes the mentioned dependence into account.

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

Fig. 1
Fig. 2
Fig. 3

Similar content being viewed by others

REFERENCES

  1. R. Houlston and C. G. DesRochers, “Nonlinear Structural Response of Ship Panels Subjected to Air Blast Loading," Comput. Structures 26 (1/2), 1–15 (1987).

    Article  Google Scholar 

  2. N. A. Abrosimov and V. G. Bazhenov, Nonlinear Problems of Dynamics of Composite Structures (Izd. Nizhegor. Gos. Univ., Nizhniy Novgorod, 2002) [in Russian].

    Google Scholar 

  3. Z. Kazanci, “Dynamic Response of Composite Sandwich Plates Subjected to Time-Dependent Pressure Pulses," Intern. J. Non-Linear Mech. 46, 807–817 (2011).

    Article  ADS  Google Scholar 

  4. P. M. Nagdi and S. A. Merch, “Mechanical Behavior of Viscoelastic-Plastic Bodies," Prikladnaya Mekhanika. Trudy Amerikanskogo Obshchestva Inzhenerov-Mekhanikov. Ser. E 30 (3), 3–12 (1963).

    Google Scholar 

  5. D. Kolarov, A. Baltov, and N. Boncheva, Mechanics of Plastic Media (Mir, Moscow, 1979) [in Russian].

    Google Scholar 

  6. G. V. Ivanov, Yu. M. Volchkov, I. O. Bogul’skii, et al., Numerical Solution of Dynamic Problems of Elastoplastic Deformation of Solids (Sib. Univ. Izd., Novosibirsk, 2002) [in Russian].

    Google Scholar 

  7. P. Perzyna, “Fundamental Problems in Viscoplasticity", in Advances in Applied Mechanics, Vol. 9 (Academic Press, New York, 1966).

    Google Scholar 

  8. L. A. Igumov, T. D. Karimbaev, and Sh. Mamaev, “Elastoplastic Flow Model at Variable Strain Rate," Vestnik Nizhegorodskogo Universiteta Imeni N. I. Lobachevskogo. Mekhanika, No. 1, 120–129 (2013).

  9. A. P. Yankovskii, “Simulation of Dynamic Elastoplastic Behavior of Flexible Reinforced Shallow Shells," Konstruktsii Iz Kompozitsionnykh Materialov, No. 2, 3–14 (2018).

  10. A. P. Yankovskii, “Modeling the Elasto-Visco-Plastic Bending of Spatially Reinforced Plates Accounting for the Strain-Rate Sensitivity of Composition Components," Prikladnaya Matematika i Mekhanika 83 (4), 660–686 (2019) [Mech. Solids 54 (5), 832–852 (2019)].

    Article  ADS  MATH  Google Scholar 

  11. A. P. Yankovskii, “Viscoelastic-Plastic Deformation of Plates with Spatial Reinforcement Structures," Prikl. Mekh. Tekh. Fiz. 61 (1), 118–132 (2020) [J. of Appl. Mech. Tech. Phys. 61 (1), 101–113 (2020)].

    Article  ADS  MathSciNet  Google Scholar 

  12. A. P. Yankovskii, “A Refined Model of Viscoelastic-Plastic Deformation of Flexible Plates with Spatial Reinforcement Structures," Vychislitel’naya Mekhanika Sploshnykh Sred 13 (1), 5–22 (2020) [J. Appl. Mech. Tech. Phy. 62, 1045–1062 (2021).

    Article  ADS  MathSciNet  MATH  Google Scholar 

  13. J. F. Bell, Mechanics of Solids, Vol. 1: The Experimental Foundations of Solid Mechanics (Springer, 1973).

    Book  Google Scholar 

  14. E. Reissner, “The Effect of Transverse-Shear Deformation on the Bending of Elastic Plates," J. Appl. Mech. 12 (2), 69–77 (1945).

    Article  MathSciNet  MATH  Google Scholar 

  15. A. E. Bogdanovich, Non-Linear Dynamic Problems for Composite Cylindrical Shells (CRC Press, 1993).

    Book  Google Scholar 

  16. S. A. Ambartsumyan, General Theory of Anisotropic Shells (Nauka, Moscow, 1974) [in Russian].

    Google Scholar 

  17. A. M. Freudental and H. Oeiringer, Elastizitat und Plastizitat (Springer Verlag, Berlin-Gottingen-Heidelberg, 1958).

    Google Scholar 

  18. Handbook on Composite Materials, Vol. 1 (Mashinostroenie, Moscow, 1988) [in Russian]

Download references

Author information

Authors and Affiliations

  1. Khristianovich Institute of Theoretical and Applied Mechanics, Siberian Branch, Russian Academy of Sciences, 630090, Novosibirsk, Russia

    A. P. Yankovskii

Authors
  1. A. P. Yankovskii
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to A. P. Yankovskii.

Additional information

Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, 2021, Vol. 63, No. 2, pp. 140-150. https://doi.org/10.15372/PMTF20220213.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Yankovskii, A.P. SIMULATION OF VISCOELASTIC-PLASTIC BEHAVIOR OF SHALLOW SHELLS WITH ACCOUNT FOR STRAIN RATE OF MATERIALS. J Appl Mech Tech Phy 63, 298–307 (2022). https://doi.org/10.1134/S0021894422020134

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S0021894422020134

Keywords

Search

Navigation