In treating the nonlinear viscoelasticity of temporarily crosslinked network structure, two kinds of relaxation processes are introduced. One is the concept of chain-slip and the other is the change in number of chains. The assumptions in the theory are as follows. 1) The relaxation process of chain-slip is a linear process characterized by a single relaxation time. 2) The increase of the coefficient of chain-breakage induced by deformation is proportional to the speed of chain- slip. The theory is applied on some typical kinds of deformations: 1) In the steady shear flow, the non-Newtonian viscosity is predicted, in which the molecular weight versus viscosity relation deviates from the 3.5th power law of molecular weight. 2) The stress growth after the start of a shear flow with a constant shear rate shows the stress overshoot, which appears more easily as the shear rate increases. 3) The stress relaxation under a large constant deformation shows an apparent nonlinear relation in the time ranges not so long and a linear relaxation tendency in the sufficiently long time ranges. 4) The stress relaxation after the stop of shear flow shows a nonlinear relation, which is clear in the early stages. The nonlinearity mainly results from the change in number of chains. The investigation of the relation between the present theory and the phenomenological constitutive equation gives a new type of constitutive equation in which the memory function is a function of the invariants of the internal strain contained in the equation of chain-slip.
A molecular network theory developed by the author (Takano, Y., Polymer J., 6, 61 (1974)) is applicable to qualitative description of various nonlinear viscoelastic phenomena of concentrated polymer systems. The theory is applied to the calculation of the elastic recoil and the tensile viscosity of the systems. The result of the elastic recoil is expressed by an integral equation. The value of tensile viscosity gradually decreases with the rate of stretching. The Trouton's formula is satisfied in the limit of zero values of the shear and the stretching rates.