Network Theory for Nonlinear Viscoelasticity

Abstract

The network theory of Yamamoto (J. Phys. Soc. Japan, 11, 413 (1956)) is briefly reviewed and then applied to concentrated polymer systems in shearing flow, with the assumption that the probability of chain-breakage is proportional to the square of the end-to-end distance in the chain. It is shown that the theory can explain at least qualitatively some of the nonlinear viscoelastic behavior. The shear-rate dependence of the steady viscosity is similar to the frequency dependence of the absolute value of the complex viscosity. The so-called stress overshoot at the beginning of shearing flow, the stress relaxation after the stoppage of flow, the ordinary stress relaxation under large deformation, and the superposition of a small oscillation upon steady shearing flow are treated; the results are in good qualitative agreement with the experiment. The rate-dependent and the deformation-dependent relaxation spectra are derived from the time dependence of the stresses in the two kinds of stress relaxation.