Modeling of the Stress–Birefringence–Stretch Behavior in Rubbers Using the Gent Model

Abstract

In this paper, we discuss the application of different stress–optic laws for rubbers to predict the birefringence evolution and the stress–stretch relationship. The main focus of this work is to propose a new formulation for the stress–birefringence relationship using the Gent theory for rubber elasticity. The Gent constitutive model for the stress–stretch response has been shown to provide a nearly equivalent rubber elastic behavior as that of the widely used eight-chain model. By combining the simpler stress–stretch relationship from the Gent model with a Gaussian network theory for birefringence, we propose a simplified stress–optic relationship. We show that our obtained results are in accord with the existing experimental results at large strains. Our proposed simplified formulation and results allow us to conclude that the Gent theory can be extended to predict optical anisotropy evolution under large strains and that these predictions are nearly equivalent to the more complex formulation based on the eight-chain model.