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Mathematical Modelling of Viscoelastic Media Without Bulk Relaxation via Fractional Calculus Approach

Author

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  • Marina V. Shitikova

    (Department of High Mathematics, Institute of Digital Technologies and Modelling in Civil Enfineering, National Research Moscow State University of Civil Engineering, Yaroslavskoye Shosse 26, Moscow 129337, Russia)

  • Konstantin A. Modestov

    (Department of High Mathematics, Institute of Digital Technologies and Modelling in Civil Enfineering, National Research Moscow State University of Civil Engineering, Yaroslavskoye Shosse 26, Moscow 129337, Russia)

Abstract

In the present paper, several viscoelastic models are studied for cases when time-dependent viscoelastic operators of Lamé’s parameters are represented in terms of the fractional derivative Kelvin–Voigt, Scott-Blair, Maxwell, and standard linear solid models. This is practically important since precisely these parameters define the velocities of longitudinal and transverse waves propagating in three-dimensional media. Using the algebra of dimensionless Rabotnov’s fractional exponential functions, time-dependent operators for Poisson’s ratios have been obtained and analysed. It is shown that materials described by some of such models are viscoelastic auxetics because the Poisson’s ratios of such materials are time-dependent operators which could take on both positive and negative magnitudes.

Suggested Citation

  • Marina V. Shitikova & Konstantin A. Modestov, 2025. "Mathematical Modelling of Viscoelastic Media Without Bulk Relaxation via Fractional Calculus Approach," Mathematics, MDPI, vol. 13(3), pages 1-20, January.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:3:p:350-:d:1573801
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