Authors: Okuka, Aleksandar
Zorica, Dušan 
Affiliations: Mathematical Institute of the Serbian Academy of Sciences and Arts 
Title: Fractional Burgers models in creep and stress relaxation tests
Journal: Applied Mathematical Modelling
Volume: 77
First page: 1894
Last page: 1935
Issue Date: 1-Jan-2020
Rank: M21
ISSN: 0307-904X
DOI: 10.1016/j.apm.2019.09.035
Classical and thermodynamically consistent fractional Burgers models are examined in creep and stress relaxation tests. Using the Laplace transform method, the creep compliance and relaxation modulus are obtained in integral form, that yielded, when compared to the thermodynamical requirements, the narrower range of model parameters in which the creep compliance is a Bernstein function while the relaxation modulus is completely monotonic. Moreover, the relaxation modulus may even be oscillatory function with decreasing amplitude. The asymptotic analysis of the creep compliance and relaxation modulus is performed near the initial time-instant and for large time as well.
Keywords: Bernstein and completely monotonic functions | Creep compliance and relaxation modulus | Thermodynamically consistent fractional Burgers models
Publisher: Elsevier
Project: 174005
Provincial Secretariat for Higher Education and Scientific Research, Grant 142-451-2102/2019

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