On the thermodynamics of fractional damping elements
type: Item
instance of: scholarly article
title: On the thermodynamics of fractional damping elements
zbMATH Open document ID: 0914.73013
author: Alexander Lion
published in: Continuum Mechanics and Thermodynamics
publication date: 1999-06-10T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 74A15
Mathematics Subject Classification ID: 74D99
Mathematics Subject Classification ID: 80A10
Mathematics Subject Classification ID: 74A20
zbMATH DE Number: 1034151
zbMATH Keywords: free energy functional
zbMATH Keywords: fractional differential operator
zbMATH Keywords: fractional dashpot
zbMATH Keywords: Clausius-Duhem inequality
reviewed by: Sanda Cleja-Ţigoiu
MaRDI profile type: Publication
full work available at URL: s001610050057
OpenAlex ID: W1996386580
DOI: 10.1007/S001610050057
description: scientific article; zbMATH DE number 1034151