On the thermodynamics of fractional damping elements
The author analyses the termodynamical properties (at a constant temperature) of rheological model which incorporates fractional damping element, and proposes a method for deriving the free energy functional. The fractional differential operator of a positive order (but less than 1), applied to the deformation process, is utilized by the author to design constitutive models of viscoelasticity. The mechanical behaviour of rheological models incorporating fractional dashpot and standard solid under monotonic loadings are illustrated in strain and stress control. In the paper it is shown that an isolated fractional dashpot and, respectively, a fractional solid model satisfy the Clausius-Duhem inequality. The derivation of the free energy is based on the relation between damping element and an appropriate continuous distribution of Maxwell elements. The fractional one-dimensional solid model is generalized to the three-dimensional case and its compatibility with the Clausius-Duhem inequality is emphasized.
scientific article; zbMATH DE number 1034151