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Zh. Vychisl. Mat. Mat. Fiz., 2010, Volume 50, Number 8, Pages 1481–1498 (Mi zvmmf4925)  

This article is cited in 15 scientific papers (total in 16 papers)

A thermodynamically consistent nonlinear model of an elastoplastic Maxwell medium

S. K. Godunov, I. M. Peshkov

Sobolev Institute of Mathematics, Siberian Branch, Russian Academy of Sciences, pr. Akademika Koptyuga 4, Novosibirsk, 630090 Russia

Abstract: The paper is devoted to new applications of the ideas underlying Godunov's method that was developed as early as in the 1950s for solving fluid dynamics problems. This paper deals with elastoplastic problems. Based on an elastic model and its modification obtained by introducing the Maxwell viscosity, a method for modeling plastic deformations is proposed.

Key words: mathematical modeling, large deformations of elastoplastic medium, Godunov's finite volume method, numerical algorithm.

Full text: PDF file (512 kB)
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English version:
Computational Mathematics and Mathematical Physics, 2010, 50:8, 1409–1426

Bibliographic databases:

UDC: 519.634
Received: 13.11.2009
Revised: 31.03.2010

Citation: S. K. Godunov, I. M. Peshkov, “A thermodynamically consistent nonlinear model of an elastoplastic Maxwell medium”, Zh. Vychisl. Mat. Mat. Fiz., 50:8 (2010), 1481–1498; Comput. Math. Math. Phys., 50:8 (2010), 1409–1426

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Godunov S.K., “Thermodynamically consistent systems of hyperbolic equations”, Computational Fluid Dynamics 2010, 2011, 31–33  crossref  zmath  isi
    2. Favrie N., Gavrilyuk S., “Mathematical and numerical model for nonlinear viscoplasticity”, Philos. Trans. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci., 369:1947 (2011), 2864–2880  crossref  mathscinet  zmath  adsnasa  isi  scopus
    3. Favrie N., Gavrilyuk S.L., “Diffuse interface model for compressible fluid - Compressible elastic-plastic solid interaction”, J. Comput. Phys., 231:7 (2012), 2695–2723  crossref  zmath  adsnasa  isi  elib  scopus
    4. Peshkov I., Grmela M., Romenski E., “Two-Phase Solid-Fluid Mathematical Model of Yield Stress Fluids”, Proceedings of the Asme Conference on Smart Materials, Adaptive Structures and Intelligent Systems, Vol 2, Amer Soc Mechanical Engineers, 2012, 9–18  isi
    5. S. K. Godunov, S. P. Kiselev, I. M. Kulikov, V. I. Mali, “Numerical and experimental simulation of wave formation during explosion welding”, Proc. Steklov Inst. Math., 281 (2013), 12–26  mathnet  crossref  crossref  mathscinet  isi  elib
    6. S. K. Godunov, I. M. Kulikov, “Computation of discontinuous solutions of fluid dynamics equations with entropy nondecrease guarantee”, Comput. Math. Math. Phys., 54:6 (2014), 1012–1024  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    7. Ndanou S., Favrie N., Gavrilyuk S., “Criterion of Hyperbolicity in Hyperelasticity in the Case of the Stored Energy in Separable Form”, J. Elast., 115:1 (2014), 1–25  crossref  mathscinet  zmath  isi  elib  scopus
    8. V. N. Belykh, K. V. Brushlinskii, V. L. Vaskevich, S. P. Kiselev, A. N. Kraiko, A. G. Kulikovskii, V. I. Mali, V. V. Pukhnachov, E. I. Romensky, V. S. Ryaben'kii, “Sergei Konstantinovich Godunov has turned 85 years old”, Russian Math. Surveys, 70:3 (2015), 561–590  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    9. Peshkov I., Grmela M., Romenski E., “Irreversible Mechanics and Thermodynamics of Two-Phase Continua Experiencing Stress-Induced Solid-Fluid Transitions”, Continuum Mech. Thermodyn., 27:6 (2015), 905–940  crossref  mathscinet  zmath  isi  elib  scopus
    10. Dumbser M., Peshkov I., Romenski E., Zanotti O., “High Order Ader Schemes For a Unified First Order Hyperbolic Formulation of Continuum Mechanics: Viscous Heat-Conducting Fluids and Elastic Solids”, J. Comput. Phys., 314 (2016), 824–862  crossref  mathscinet  zmath  isi  elib  scopus
    11. Peshkov I., Romenski E., “a Hyperbolic Model For Viscous Newtonian Flows”, Continuum Mech. Thermodyn., 28:1-2, SI (2016), 85–104  crossref  mathscinet  zmath  isi  elib  scopus
    12. Boscheri W., Dumbser M., Loubere R., “Cell centered direct Arbitrary-Lagrangian-Eulerian ADER-WENO finite volume schemes for nonlinear hyperelasticity”, Comput. Fluids, 134 (2016), 111–129  crossref  mathscinet  zmath  isi  scopus
    13. Dumbser M., Peshkov I., Romenski E., Zanotti O., “High Order Ader Schemes For a Unified First Order Hyperbolic Formulation of Newtonian Continuum Mechanics Coupled With Electro-Dynamics”, J. Comput. Phys., 348 (2017), 298–342  crossref  mathscinet  isi  scopus
    14. Hank S., Gavrilyuk S., Favrie N., Massoni J., “Impact Simulation By An Eulerian Model For Interaction of Multiple Elastic-Plastic Solids and Fluids”, Int. J. Impact Eng., 109 (2017), 104–111  crossref  isi  scopus
    15. Pavelka M., Klika V., Grmela M., “Multiscale Thermo-Dynamics: Introduction to Generic”, Multiscale Thermo-Dynamics: Introduction to Generic, Walter de Gruyter Gmbh, 2018, 1–279  mathscinet  isi
    16. Peshkova I., Boscheri W., Loubere R., Romenski E., Dumbser M., “Theoretical and Numerical Comparison of Hyperelastic and Hypoelastic Formulations For Eulerian Non-Linear Elastoplasticity”, J. Comput. Phys., 387 (2019), 481–521  crossref  mathscinet  isi  scopus
  • Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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