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Internal Variable Theory in Viscoelasticity: Fractional Generalizations and Thermodynamical Restrictions

Author

Listed:
  • Teodor M. Atanackovic

    (Faculty of Technical Sciences, University of Novi Sad, Trg D. Obradovica 6, 21000 Novi Sad, Serbia)

  • Cemal Dolicanin

    (Department of Sciences and Mathematics, State University of Novi Pazar, Vuk Karadzica 9, 36300 Novi Pazar, Serbia)

  • Enes Kacapor

    (Department of Sciences and Mathematics, State University of Novi Pazar, Vuk Karadzica 9, 36300 Novi Pazar, Serbia)

Abstract

Here, we study the internal variable approach to viscoelasticity. First, we generalize the classical approach by introducing a fractional derivative into the equation for time evolution of the internal variables. Next, we derive restrictions on the coefficients that follow from the dissipation inequality (entropy inequality under isothermal conditions). In the example of wave propagation, we show that the restrictions that follow from entropy inequality are sufficient to guarantee the existence of the solution. We present a numerical solution to the wave equation for several values of the parameters.

Suggested Citation

  • Teodor M. Atanackovic & Cemal Dolicanin & Enes Kacapor, 2022. "Internal Variable Theory in Viscoelasticity: Fractional Generalizations and Thermodynamical Restrictions," Mathematics, MDPI, vol. 10(10), pages 1-13, May.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:10:p:1708-:d:816937
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