Skip to main content
SpringerLink
Log in

Towards Elastoplastic Deformation of a Solid Body by the Hybrid Godunov Method and by the Multidimensional Nodal Method of Characteristics

  • Published:
Journal of Engineering Physics and Thermophysics Aims and scope

The paper presents the hybrid Godunov method designed for numerical calculation of elastoplastic deformation of a solid body within the framework of the Prandtl–Reuss model with a nonbarotropic equation of state. The Mises flow rule (yield creation) was used as a criterion for the transition from an elastic state to a plastic state. In calculating flow variables on the faces of adjacent cells, use was made of a linearized Riemann solver whose algorithm employs right own vectors of the model equation system. For equations written in a divergent form, use is made of finite-volume formulas, and for others that are not reducible to a divergent form, finite difference relationships are employed. Also, a description is given of a multidimensional nodal method of characteristics based on a coordinate splitting of the original system of equations into a number of one-dimensional subsystems with their subsequent integration with the help of a one-dimensional nodal method of characteristics. Using the proposed methods, a number of model problems has been calculated.

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. S. K. Godunov, A. V. Zabrodin, M. Ya. Ivanov, A. N. Kraiko, and G. P. Prokopov, Numerical Solution of Multidimensional Problems of Gas Dynamics [in Russian], Nauka, Moscow (1976).

  2. M. Kh. Abuzyarov, V. G. Bazhenov, V. L. Kotov, A. V. Kochetkov, S. V. Krylov, and V. R. Fel’dgun, Method of disintegration of discontinuities in the dynamics of elastoplastic media, Zh. Vychisl. Mat. Mat. Fiz., 40, No. 5, 940–953 (2000).

    MATH  Google Scholar 

  3. A. A. Aganin and N. A. Khismatullina, Calculation of waves in an elastoplastic body, Trans. Kazan Univ., Ser.: Fiz. Mat. Nauki, 160, No. 3, 435–447 (2018).

  4. I. S. Men’shov, A. V. Mishchenko, and A. A. Serezhkin, Numerical simulation of elastoplastic flows by the Godunov method on moving Euler grids, Mat. Model., 25, No. 8, 89–108 (2013).

    Google Scholar 

  5. V. S. Surov, Towards calculation of flows of a heat-conducting steam–gas droplets mixture, Sib. Zh. Vych. Mat., 23, No. 2, 201–217 (2020).

    MathSciNet  Google Scholar 

  6. V. S. Surov, The Godunov method for calculating multidimensional flows of a one-velocity multicomponent mixture, J. Eng. Phys. Thermophys., 89, No. 5, 1227–1240 (2016).

    Article  Google Scholar 

  7. V. S. Surov, Hyperbolic model of a one-velocity heat-conducting mixture with account for interfraction heat transfer, Teplofiz. Vys. Temp., 56, No. 6, 975–985 (2018).

    Google Scholar 

  8. E. F. Toro, Riemann solvers with evolved initial condition, Int. J. Numer. Methods Fluids, 52, 433–453 (2006).

    Article  MathSciNet  Google Scholar 

  9. V. V. Rusanov, Characteristics of general equations of gas dynamics, Zh. Vychisl. Mat. Mat. Fiz., 3, No. 3, 508–527 (1963).

    MathSciNet  Google Scholar 

  10. I. S. Berezin and N. P. Zhidkov, Methods of Computing [in Russian], Vol. 2, Fizmatgiz, Moscow (1962).

  11. V. Yu. Gidaspov and N. S. Severina, Elementary Models and Computational Algorithms of Physical Gas Dynamics. One-Dimensional Unsteady Flows [in Russian], Faktorial, Moscow (2015).

  12. V. S. Surov, Model method of characteristics in multifluid hydrodynamics, J. Eng. Phys. Thermophys., 86, No. 5, 1151–1159 (2013).

    Article  Google Scholar 

  13. R. Sauer, Nichstationare Probleme der Gasdynamik, Springer Verlag, Berlin-Heidelberg-New York (1966).

    Book  Google Scholar 

  14. H. Sauerwein, Numerical calculations of multidimensional and unsteady flows by the method of characteristics, J. Comput. Phys., 1, 406–432 (1967).

    Article  Google Scholar 

  15. N. N. Yanenko, Fractional Step Method of Solving Multidimensional Problems of Mathematical Physics [in Russian], Nauka, Novosibirsk (1967).

  16. V. S. Surov, Multidimensional nodal method of characteristics for hyperbolic systems, Komp. Issled. Model., 13, No. 1, 19–31 (2021).

    Google Scholar 

  17. A. N. Ishchenko, S. A. Afanas’eva, N. N. Belov, V. V. Burkin, K. S. Rogaev, M. V. Khabibullin, A. V. Chupashev, and N. T. Yugov, Experimental and mathematical modeling of high-velocity collision of a conical striker with various barriers, J. Eng. Phys. Thermophys., 90, No. 4, 971–977 (2017).

    Article  Google Scholar 

  18. M. L. Wilkins, Calculation of elastic-plastic flow, in: Methods in Computational Physics, Vol. 3, Academic Press, New York (1964), pp. 211−263.

  19. A. G. Kulikovskii, N. V. Pogorelov, and A. Yu. Semenov, Mathematical Problems of Numerical Solution of Hyperbolic Systems of Equations [in Russian], Fizmatlit, Moscow (2012).

  20. V. S. Surov, Glancing collision of metal plates, Fiz. Goreniya Vzryva, 24, No. 6, 115–120 (1988).

    Google Scholar 

  21. V. S. Surov, Simulation of High-Velocity Interaction of Liquid Droplets (Jets) with Barriers, Air Shock Waves, Candidate’s Dissertation in Physics and Mathematics, ITPM SO RAN, Novosibirsk (1993).

  22. V. S. Surov, Interaction of shock waves with bubble liquid droplets, Zh. Tekh. Fiz., 71, No. 6, 7–22 (2001).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. South Ural State University (National Research University), 76 Lenin Ave, Chelyabinsk, 454080, Russia

    V. S. Surov

Authors
  1. V. S. Surov
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to V. S. Surov.

Additional information

Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 95, No. 3, pp. 844–859, May–June, 2022.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Surov, V.S. Towards Elastoplastic Deformation of a Solid Body by the Hybrid Godunov Method and by the Multidimensional Nodal Method of Characteristics. J Eng Phys Thermophy 95, 830–845 (2022). https://doi.org/10.1007/s10891-022-02541-8

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10891-022-02541-8

Keywords

Search

Navigation