Scott-Blair models with time-varying viscosity

Abstract

In a recent paper, Zhou et al. [Mech Time-Depend Mater (2017) 21: 151] studied the time-dependent properties of Glass Fiber Reinforced Polymers composites by employing a new rheological model with a time-dependent viscosity coefficient. This rheological model is essentially based on a generalized Scott-Blair body with a time-dependent viscosity coefficient. Motivated by this study, in this note we suggest a different generalization of the Scott-Blair model based on the application of Caputo-type fractional derivatives of a function with respect to another function. This new mathematical approach can be useful in viscoelasticity and diffusion processes in order to model systems with time-dependent features. In this paper we also provide the general solution of the creep experiment for our improved Scott-Blair model together with some explicit examples and illuminating plots.

arXiv comment7 pages, 3 figures, matches the published version

References in corpus (5)

• A Caputo fractional derivative of a function with respect to another function
• Creep, Relaxation and Viscosity Properties for Basic Fractional Models in Rheology
• Numerical evaluation of two and three parameter Mittag-Leffler functions
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Cited by in corpus (5)

• Modeling biological systems with an improved fractional Gompertz law
• A note on a modified fractional Maxwell model
• Existence and uniqueness of mild solutions for a class of psi-Caputo time-fractional systems of order from one to two
• A note on generalized fractional diffusion equations on Poincarè half plane
• On the fractional operators with respect to another function