Constitutive models for the nonlinear viscoelastic response of solid polymers with mechanically induced material clocks

The paper presents a review of constitutive equations for the nonlinear viscoelastic response of solid polymers under isothermal loading with finite strains. We focus on materials which do not possess the separability property. The nonseparability conventionally referred to as mechanically induced rejuvenation of polymers is explained in the framework of the K-BKZ theory by changes in some `internal clock' governing the material behavior. Three approaches are discussed to the design of constitutive equations for viscoelastic media. The first is based on the free volume model, the second uses the Eyring theory of absolute reaction rates, and the third employs the Adam-Gibbs concept of cooperative relaxation. To analyze the viscoelastic behavior of polymers, a model of adaptive links is derived (a version of the theory of temporary polymeric networks). The free volume technique, where the increment of the free volume fraction is proportional to the strain energy density of permanent chains, is employed to predict stresses in tensile tests for amorphous and semicrystalline polymers at strains up to 400%. The Eyring concept is used to model an anomalous stress relaxation in specimens at large extension ratios (up to 600%) and after loading-unloading with a constant rate of strains (the Kitagawa effect). The model of cooperative relaxation is applied to predict a decrease in the loss tangent observed in dynamic tests on stretched specimens.