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Analyticity and causality of the three-parameter rheological models

Analyticity and causality of the three-parameter rheological models

Makris, Nicos and Kampas, Georgios (2009) Analyticity and causality of the three-parameter rheological models. Rheologica Acta, 48. pp. 815-825. ISSN 0035-4511 (Print), 1435-1528 (Online) (doi:https://doi.org/10.1007/s00397-009-0374-8)

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Abstract

In this paper the basic frequency response and time response functions of the three-parameter Poynting-Thomson solid and Jeffreys fluid are revisited. The two rheological models find application in several areas of rheology, structural mechanics and geophysics. The relation between the analyticity of a frequency response function and the causality of the corresponding time-response function is established by identifying all singularities at ω=0 after applying a partial fraction expansion to the frequency response functions. The strong singularity at ω=0 in the imaginary part of a frequency response function in association with the causality requirement, imposes the addition of a Dirac delta function in the real part in order to make the frequency response function well defined in the complex plane. This external intervention, which was first discovered by P.A.M. Dirac, has not received the attention it deserves in the literature of viscoelasticity and rheology. The addition of the Dirac delta function makes possible the application of time domain techniques that do not suffer from violating the premise of causality.

Item Type: Article
Uncontrolled Keywords: Viscoelasticity; Relaxation modulus; Causality; Hilbert transform; Retardation fluidity; Jeffreys fluid
Subjects: T Technology > TA Engineering (General). Civil engineering (General)
Faculty / Department / Research Group: Faculty of Engineering & Science
Faculty of Engineering & Science > Department of Engineering Science
Last Modified: 28 Mar 2018 08:56
Selected for GREAT 2016: None
Selected for GREAT 2017: None
Selected for GREAT 2018: None
Selected for GREAT 2019: None
URI: http://gala.gre.ac.uk/id/eprint/19468

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