A theory of nonlinear viscoelasticity based on a temporarily cross-linked network model

Abstract

Abstract Two kinds of relaxation processes are introduced for the theory of nonlinear viscoelasticity of temporarily crosslinked network structures. One is the chain slip process and the other is the change in number of chains as function of time. The following assumptions are made for this theory: (1) chains are Gaussian; (2) the slip process is characterized by single relaxation time; (3)the chain breakage coefficient is proportional to the absolute value of the average force acting on a chain; (4) the rate of chain generation is constant; (5) the reformed chains have the same strain as that of unbroken chains. The results obtained by the application of this theory are as follows. Stress growth at the onset of shear flow shows the stress overshoot. Stress growth at the onset of elongational flow is monotonic. Stress relaxation at a large deformation is nonlinear. The storage modulus of periodic deformation superposed in parallel on a steady shear flow vanishes at a low frequency but not the loss modulus.