Internal Variable Theory in Viscoelasticity: Fractional Generalizations and Thermodynamical Restrictions

Teodor M. Atanackovic, Cemal Dolicanin and Enes Kacapor
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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

Mathematics, 2022, vol. 10, issue 10, 1-13

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.

Keywords: fractional calculus; internal variables; thermodynamical admissibility (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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