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

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.