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Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.]:
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Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.], 2012, Issue 1(26), Pages 150–156 (Mi vsgtu1068)  

This article is cited in 1 scientific paper (total in 1 paper)

Mechanics of Solids

Mathematical model of viscoelastic softening material with exponential creep kernel

S. V. Gorbunov

Samara State Technical University, Samara, Russia

Abstract: The variant of mathematical model of uniaxial strain for viscoelastic material with exponential creep kernel is proposed. Lyapunov stability of the solution of the model in case of permanent stress is investigated. The stability region of solutions of mathematical model's differential equations, сorresponding to asymptotically restricted creep of material, is established. Instability region of solutions is in accord with appearance of tertiary creep. Relation between stability of solutions by Lyapunov and stability of iterative calculation for numerical solving the system of equations is established. As an illustration the investigation of model problem is quoted.

Keywords: viscoelastic material, Lyapunov stability of solutions, exponential creep kernel, stability region of solutions, tertiary creep, stability of numerical iterative calculation

DOI: https://doi.org/10.14498/vsgtu1068

Full text: PDF file (489 kB) (published under the terms of the Creative Commons Attribution 4.0 International License)
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Bibliographic databases:

UDC: 539.376
MSC: Primary 74G55; Secondary 74Cxx
Original article submitted 02/XI/2011
revision submitted – 13/III/2012

Citation: S. V. Gorbunov, “Mathematical model of viscoelastic softening material with exponential creep kernel”, Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.], 1(26) (2012), 150–156

Citation in format AMSBIB
\Bibitem{Gor12}
\by S.~V.~Gorbunov
\paper Mathematical model of~viscoelastic softening material with~exponential creep kernel
\jour Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.]
\yr 2012
\vol 1(26)
\pages 150--156
\mathnet{http://mi.mathnet.ru/vsgtu1068}
\crossref{https://doi.org/10.14498/vsgtu1068}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. S. V. Gorbunov, “Eksperimentalnaya proverka reologicheskoi modeli razuprochnyayuscheisya vyazkouprugoi sredy s eksponentsialnym yadrom polzuchesti”, Vestn. Sam. gos. tekhn. un-ta. Ser. Fiz.-mat. nauki, 3(28) (2012), 196–198  mathnet  crossref
  • Вестник Самарского государственного технического университета. Серия: Физико-математические науки
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