Hereunder discussed is the applicability of integral constitutive equations to some nonlinear and non-steady viscoelastic behaviors of concentrated polymer systems. Two types of models based on Lodge's model are considered. One of them is the generalization of the so-called WJFLMB model and has the after-effect function depending on the invariants of the rate-ofdeformation tensor through both the spectral density and the value of the relaxation time itself. The other is the generalized WKZ model with the after-effect function depending on the invariants of the relative deformation tensor between the excitation and the current times. Both the models can well explain the rate-of-deformation dependences of the viscosity coefficient and of the normal stress differences for steady simple shearing flow. The rate-of-deformation dependent model 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 beginning of flow, and the stress relaxation after stoppage of the flow. The former model is, however, rather difficult to give the deformation dependence of the relaxation modulus in the stress relaxation in the usual sense for large shearing deformation.
