On Scott-Blair model with time-varying viscosity in linear viscoelasticity

TL;DR

This paper introduces a novel generalization of the Scott-Blair viscoelastic model using Caputo fractional derivatives with respect to another function, providing exact solutions for creep experiments and extending modeling capabilities for time-dependent properties.

Contribution

It proposes a new mathematical framework for the Scott-Blair model using Caputo derivatives, enabling better modeling of time-varying viscoelastic properties.

Findings

Exact analytic solution for creep experiment

Comparison with Zhou et al.'s model shows advantages

Framework applicable to diffusion processes

Abstract

In a recent paper, Zhou et al. studied the time-dependent properties of Glass Fiber Reinforced Polymers (GFRP) composites by using a new rheological model with a time-variable viscosity coefficient. This rheology is essentially based on a generalized Scott-Blair model with time-varying viscosity coefficient involving Riemann-Liouville fractional derivatives. Motivated by this study, in this note we suggest a different generalization of the Scott-Blair model based on the application of Caputo 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 consider time-dependent coefficients. We are able to find the exact analytic solution of the creep experiment based on our new approach and we can compare it with the results obtained by Zhou et al.