Abstract
A critical review is presented on the recent constitutive models for polymer liquids. Among others, the Leonov, the Giesekus and the Larson models are discussed on their fundamental ideas, main assumptions and applicability to some nonlinear viscoelastic phenomena in concentrated polymer systems. These models have fairly wide applicability compared with other models. However, each model has two or three defects or weak points.
Three defects of the Leonov model are: (1) a few phenomenological assumptions made without a firm basis,(2) weak molecular theoretical reasoning of the strain-hardening parameter β, and (3) difficulty in determining the value of β for mixed flows which include shear and extension. Two defects found for the Giesekus model are:(1) lack of the idea of chain contraction and (2) difficulty in extending the model to the case of multiple relaxation times. Three defects of the Larson model are:(1) mathematical approximations made to obtain the constitutive equation,(2) lack of theoretical or experimental justification for the idea of partially extending convection in branched polymers, and (3) inapplicability of the assumed separable form G(t,γ)=G(t)h(γ) to the short-time behavior in stress relaxation.
It is emphasized that future models should be developed based on the molecular theoretical consideration to express correctly the following interrelations; different mode of deformation (shear, uniaxial or biaxial extension)→different extent of orientation and extension of polymer chains↔difference in the stress level.
