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We propose a kinetics model including extension and anisotropic movement between entangled or branched chains and develop constitutive equations containing the Larson model and the Giesekus model through non-linear parameters. In order to make clear the characteristics of the developed constitutive equations, we examined the predictions of using non-linear parameters and a non-linear stress relaxation modulus. We found that the proposed model shows better predictions of the nonlinear stress relaxation after a double-step shear strain than those of the Larson and the Giesekus models. Furthermore, we found that the proposed model is able to predict the biaxial elongational viscosity and the first planar elongational viscosity comparatively well by fitting the uniaxial elongational viscosity curve.However, the predictions of stress relaxation in the time-strain inseparable region was at most qualitative, and the predictions of the second normal stress difference and the second planar elongational viscosity were lower than experimental results because of the assumptions or crude approximations used in our development.

The Ability of Predictions of Differential Type Viscoelastic Constitutive Equations to Nonlinear Rheological Behaviors