Rheological Burgers–Faraday Models and Rheological Dynamical Systems with Fractional Derivatives and Their Application in Biomechanics
Two rheological Burgers–Faraday models and rheological dynamical systems were created by using two new rheological models: Kelvin–Voigt–Faraday fractional-type model and Maxwell–Faraday fractional-type model. The Burgers–Faraday models described in the paper are new models that examine the dynamical...
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MDPI AG
2024-12-01
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| Series: | Fractal and Fractional |
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| author | Katica R. (Stevanović) Hedrih Andjelka N. Hedrih |
| author_facet | Katica R. (Stevanović) Hedrih Andjelka N. Hedrih |
| author_sort | Katica R. (Stevanović) Hedrih |
| collection | DOAJ |
| description | Two rheological Burgers–Faraday models and rheological dynamical systems were created by using two new rheological models: Kelvin–Voigt–Faraday fractional-type model and Maxwell–Faraday fractional-type model. The Burgers–Faraday models described in the paper are new models that examine the dynamical behavior of materials with coupled fields: mechanical stress and strain and the electric field of polarization through the Faraday element. The analysis of the constitutive relation of the fractional order for Burgers–Faraday models is given. Two Burgers–Faraday fractional-type dynamical systems were created under certain approximations. Both rheological Burgers-Faraday dynamic systems have two internal degrees of freedom, which are introduced into the system by each standard light Burgers-Faraday bonding element. It is shown that the sequence of bonding elements in the structure of the standard light Burgers-Faraday bonding element changes the dynamic properties of the rheological dynamic system, so that in one case the system behaves as a fractional-type oscillator, while in the other case, it exhibits a creeping or pulsating behavior under the influence of an external periodic force. These models of rheological dynamic systems can be used to model new natural and synthetic biomaterials that possess both viscoelastic/viscoplastic and piezoelectric properties and have dynamical properties of stress relaxation. |
| format | Article |
| id | doaj-art-4e4581ea61d849fc9055da9a2eb49575 |
| institution | DOAJ |
| issn | 2504-3110 |
| language | English |
| publishDate | 2024-12-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Fractal and Fractional |
| spelling | doaj-art-4e4581ea61d849fc9055da9a2eb495752025-08-20T02:53:35ZengMDPI AGFractal and Fractional2504-31102024-12-0181274210.3390/fractalfract8120742Rheological Burgers–Faraday Models and Rheological Dynamical Systems with Fractional Derivatives and Their Application in BiomechanicsKatica R. (Stevanović) Hedrih0Andjelka N. Hedrih1Department of Mechanics, Mathematical Institute of Serbian Academy of Science and Arts, 11000 Belgrade, SerbiaDepartment of Mechanics, Mathematical Institute of Serbian Academy of Science and Arts, 11000 Belgrade, SerbiaTwo rheological Burgers–Faraday models and rheological dynamical systems were created by using two new rheological models: Kelvin–Voigt–Faraday fractional-type model and Maxwell–Faraday fractional-type model. The Burgers–Faraday models described in the paper are new models that examine the dynamical behavior of materials with coupled fields: mechanical stress and strain and the electric field of polarization through the Faraday element. The analysis of the constitutive relation of the fractional order for Burgers–Faraday models is given. Two Burgers–Faraday fractional-type dynamical systems were created under certain approximations. Both rheological Burgers-Faraday dynamic systems have two internal degrees of freedom, which are introduced into the system by each standard light Burgers-Faraday bonding element. It is shown that the sequence of bonding elements in the structure of the standard light Burgers-Faraday bonding element changes the dynamic properties of the rheological dynamic system, so that in one case the system behaves as a fractional-type oscillator, while in the other case, it exhibits a creeping or pulsating behavior under the influence of an external periodic force. These models of rheological dynamic systems can be used to model new natural and synthetic biomaterials that possess both viscoelastic/viscoplastic and piezoelectric properties and have dynamical properties of stress relaxation.https://www.mdpi.com/2504-3110/8/12/742rheological models of fractional type with piezo-electrical propertiesviscous fluidBurgers–Faraday fractional-type modelrheological Burgers–Faraday dynamical systemoscillator of fractional type with piezoelectric propertiescreeper of fractional type with piezoelectric properties |
| spellingShingle | Katica R. (Stevanović) Hedrih Andjelka N. Hedrih Rheological Burgers–Faraday Models and Rheological Dynamical Systems with Fractional Derivatives and Their Application in Biomechanics Fractal and Fractional rheological models of fractional type with piezo-electrical properties viscous fluid Burgers–Faraday fractional-type model rheological Burgers–Faraday dynamical system oscillator of fractional type with piezoelectric properties creeper of fractional type with piezoelectric properties |
| title | Rheological Burgers–Faraday Models and Rheological Dynamical Systems with Fractional Derivatives and Their Application in Biomechanics |
| title_full | Rheological Burgers–Faraday Models and Rheological Dynamical Systems with Fractional Derivatives and Their Application in Biomechanics |
| title_fullStr | Rheological Burgers–Faraday Models and Rheological Dynamical Systems with Fractional Derivatives and Their Application in Biomechanics |
| title_full_unstemmed | Rheological Burgers–Faraday Models and Rheological Dynamical Systems with Fractional Derivatives and Their Application in Biomechanics |
| title_short | Rheological Burgers–Faraday Models and Rheological Dynamical Systems with Fractional Derivatives and Their Application in Biomechanics |
| title_sort | rheological burgers faraday models and rheological dynamical systems with fractional derivatives and their application in biomechanics |
| topic | rheological models of fractional type with piezo-electrical properties viscous fluid Burgers–Faraday fractional-type model rheological Burgers–Faraday dynamical system oscillator of fractional type with piezoelectric properties creeper of fractional type with piezoelectric properties |
| url | https://www.mdpi.com/2504-3110/8/12/742 |
| work_keys_str_mv | AT katicarstevanovichedrih rheologicalburgersfaradaymodelsandrheologicaldynamicalsystemswithfractionalderivativesandtheirapplicationinbiomechanics AT andjelkanhedrih rheologicalburgersfaradaymodelsandrheologicaldynamicalsystemswithfractionalderivativesandtheirapplicationinbiomechanics |