Fractional rheological models for thermomechanical systems. Dissipation and free energies

Within the fractional derivative framework, we study thermomechanical models with memory and compare them with the classical Volterra theory. The fractional models involve significant differences in the type of kernels and predicts important changes in the behavior of fluids and solids. Moreover, an...

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Bibliographic Details
Published in:Fractional calculus & applied analysis 2014-03, Vol.17 (1), p.206-223
Main Author: Fabrizio, Mauro
Format: Article
Language:English
Subjects:
Abstract Harmonic Analysis
Analysis
Functional Analysis
Integral Transforms
Mathematics
Mathematics and Statistics
Operational Calculus
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Summary:Within the fractional derivative framework, we study thermomechanical models with memory and compare them with the classical Volterra theory. The fractional models involve significant differences in the type of kernels and predicts important changes in the behavior of fluids and solids. Moreover, an analysis of the thermodynamic restrictions provides compatibility conditions on the kernels and allows us to determine certain free energies, which in turn enables the definition of a topology on the history space. Finally, an analogous analysis is carried out for the phenomenon of heat propagation with memory.
ISSN:1311-0454
1314-2224
DOI:10.2478/s13540-014-0163-7