Scott-Blair models with time-varying viscosity

TL;DR

This paper introduces a novel generalization of the Scott-Blair viscoelastic model using Caputo-type fractional derivatives to better capture systems with time-dependent properties, providing solutions and examples.

Contribution

It proposes a new fractional derivative-based generalization of the Scott-Blair model for viscoelasticity with time-varying viscosity, expanding modeling capabilities.

Findings

Derived the general solution for the creep experiment in the new model

Provided explicit examples and illustrative plots

Demonstrated the model's applicability to systems with time-dependent features

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.