Hereunder is discussed the applicability of constitutive equations of integral type to some nonlinear non-steady viscoelastic behaviors of concentrated polymer systems. Two types of models based on Lodge's model are considered. One of them is to represent the generalization of the so-called WJFLMB model and has the after-effect function depending on the invariants of the rate-of-deformation tensor at the time of excitation. The other is the generalized WKZ model with the after-effect function depending on the invariants of the relative deformation tensor between the times of excitation and response. Both the models can well explain the rate-of-defomation dependences of the viscosity coefficient and of the normal stress differences for a steady simple shearing flow. The model depending on the rate-of-deformation is simpler and rather good than the relative deformation dependent model in the explanation of some nonlinear non-steady viscoelastic behaviors such as the stress development at the biginning of flow, the stress relaxation after stoppage of the flow, and parallel and orthogonal superpositions of small sinusoidal oscillation on the steady shearing flow. The former model is, however, not efficient enough to give cause to deformation dependence of the relaxation modulus in the stress relaxation in the usual sense for large shearing deformation.
