Model-based material functions for SAOS and LAOS analyses

• In general, material functions originate from a constitutive model.
• SAOS and LAOS analyses are based on either the Kelvin–Voigt or the Maxwell model.
• The Jeffreys model is the simplest one that is able to predict the complete spectrum of mechanical behavior.
• The analysis based on the Jeffreys framework is applicable to both SAOS and QL-LAOS data.

In this paper we argue that material functions usually originate from some constitutive model, and demonstrate the importance of determining the model involved in the material function of interest and of evaluating its appropriateness vis-à-vis the material under rheological characterization. In particular, we demonstrate that the usual material functions that arise in the analyses of SAOStrain and LAOStrain experiments are directly related to the Kelvin–Voigt model, while the ones that appear in the analyses of SAOStress and LAOStress experiments are directly related to the Maxwell model. Then we argue that it would be more appropriate to use a framework for data analyses of generic materials that is capable of predicting qualitatively the whole range of mechanical behavior. Finally we demonstrate that the Jeffreys model is the simplest appropriate framework for SAOS and LAOS data analyses. Since this model has three parameters and hence generates three material functions, these are determined with the aid of steady-flow data. The arguments presented in this paper are useful not only for determining the mechanical behavior of general non-Newtonian materials, but can also aid in the prediction of the behavior of these materials in complex flows.