Authors: Atanacković, Teodor
Janev, Marko 
Pilipović, Stevan
Affiliations: Mechanics 
Mathematical Institute of the Serbian Academy of Sciences and Arts 
Title: Restrictions on parameters in distributed order fractional linear constitutive equations
Journal: Applied Mathematical Modelling
Volume: 110
First page: 99
Last page: 111
Issue Date: 1-Oct-2022
Rank: ~M21a
ISSN: 0307-904X
DOI: 10.1016/j.apm.2022.05.023
We analyze a viscoelastic body in a linear stress state with the distributed order fractional derivative in the constitutive equation. The model was formulated so that it takes into account all derivatives of stress and strain between zero and one. Using a new procedure, we derive restrictions on a model that follow from the Clausius-Duhem inequality under isothermal conditions. Several constitutive equations are derived as special cases of proposed models. We apply our analysis to a creep test, a dynamical creep test and an oscillatory system.
Keywords: constitutive equations | dissipation inequality | fractional derivative
Publisher: Elsevier

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