Modelos Viscoelásticos Fracionários Aplicados em Reologia de Polimeros fundidos

Polymeric materials are complex, and, very often originate counterintuitive phenomena such as normal stress differences, the Weissenberg effect, extrudate swell, elastic retraction, etc. In the last decades, several models were proposed in the literature with the aim of predicting such complex behaviors. These classical models allow a good fit to part of the experimental data, but, when the complexity is high, the models simplicity cannot provide reliable information. For example, some of the models cannot predict normal stress differences, or, they are only valid for small deformations, etc. More recently, fractional derivatives and integrals became a hot topic, with application in every field of engineering. These fractional operators allow the use of non-integer orders for derivatives and integrals, and, it seems that this can be helpful in the modeling of physical processes where memory plays a major role, such as the case of viscoelastic fluids. People started using and developing these models since 1921, and one the simplest models is given as an infinite combination of springs and dashpots, generalizing in this way the classical “spring-dashpot” model proposed by Maxwell. In most of the cases, the generalized fractional models are just a generalized model with no true connection with the underlying physics and chemistry. Since this is a recent theory, it is therefore needed to explore these models in detail, so that a good understanding of the theory can be achieved. The aims of this work were to obtain a detailed state of the art about fractional viscoelastic models, assessing their application to model the behavior of viscoelastic fluids, to build a pedagogical tool that allow the fit of fractional models to real experimental data and to fit some experimental data found in literature and compare final results. vi It was concluded that the FMM and SFOV fluid in 1D have an excellent performance of adjustment and thus the quality is modified by the number of model parameters.