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Quantitative analogies between the linear and non‐linear viscoelastic functions
Author(s) -
Hlavacek B.,
Seyer F. A.,
Stanislav I.
Publication year - 1973
Publication title -
the canadian journal of chemical engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.404
H-Index - 67
eISSN - 1939-019X
pISSN - 0008-4034
DOI - 10.1002/cjce.5450510404
Subject(s) - viscoelasticity , mathematics , function (biology) , constitutive equation , mathematical analysis , stress (linguistics) , linear model , deformation (meteorology) , linear equation , physics , finite element method , thermodynamics , statistics , linguistics , philosophy , evolutionary biology , meteorology , biology
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 P 11 ‐ P 22 and η(γ) assuming that linear viscoelastic function (ω) is known. Alternatively from the function P 11 ‐ P 22 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 P 12 , and is dependent on the square of the deformation for the first normal stress difference, P 11 ‐ P 22 . 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.