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

Авторы: Shitikova Marina V., Modestov Konstantin A.
Журнал: Mathematics
Том: 13
Номер: 3
Год издания: 2025
Издательство: MDPI
Местоположение издательства: Basel, Switzerland
Первая страница: 1
Последняя страница: 19
Номер статьи: 350
DOI: 10.3390/math13030350
Аннотация: 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.
Добавил в систему: Модестов Константин Анатольевич

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