In a recent paper, Zhou et al. (2017) 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.
Colombaro, I., Garra, R., Giusti, A., Mainardi, F. (2018). Scott-Blair models with time-varying viscosity. APPLIED MATHEMATICS LETTERS, 86, 57-63 [10.1016/j.aml.2018.06.022].
Scott-Blair models with time-varying viscosity
Colombaro, Ivano;GARRA, ROBERTO;Giusti, Andrea
;Mainardi, Francesco
2018
Abstract
In a recent paper, Zhou et al. (2017) 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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.