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.
Keywords
Cite
@article{arxiv.1805.08432,
title = {Scott-Blair models with time-varying viscosity},
author = {Ivano Colombaro and Roberto Garra and Andrea Giusti and Francesco Mainardi},
journal= {arXiv preprint arXiv:1805.08432},
year = {2018}
}
Comments
7 pages, 3 figures, matches the published version