Quantitative analogies between the linear and non‐linear viscoelastic functions

Abstract

A method of determination of linear and non‐linear viscoelastic functions is proposed. Through this method it is possible to calculate the non‐linear functions P11 ‐ P22 and η(γ) assuming that linear viscoelastic function (ω) is known. Alternatively from the function P11 ‐ P22 we are able to calculate η(γ) and y'(ω) etc. The method is based on the assumption that the change from linear to non‐linear functions is proportional to a molecular deformation for shear stress components P12, and is dependent on the square of the deformation for the first normal stress difference, P11 ‐ P22. The obtained results suggest straightforward modification of equations of state, this being demonstrated with the White‐Metzner model of the convected Maxwell element. Consideration of available experimental data shows that this theory is capable of predicting the various functions, at least as well as currently available constitutive equations, while requiring less experimental information.