An investigation into the three-dimensional stress-birefringence-strain relationship in elastomers

Abstract

The statistical theory of the birefringence of an individual non-Gaussian elastomer chain is used together with a chain network description of rubber elasticity to develop a relationship among the strain, birefringence, and stress in elastomers, valid for large deformations under generalized strain states. The result is a fully three-dimensional internal variable based constitutive model of rubber elasticity in which measurement of the elastomeric birefringence during straining in one deformation state characterizes the optically anisotropic response of the elastomer. Simultaneous measurement of the stress vs. strain response provides the rubbery modulus and limiting network extensibility properties needed to completely characterize the mechanical anisotropy of the material. Once characterized using the single, large deformation experiment, the birefringence and stress responses of the elastomer in other deformation states may then be predicted without adjusting any model parameters. The theory is compared to experimental studies from the literature of large strain deformations of elastomers in uniaxial tension and compression for which the exhibited birefringence and stress responses of deforming elastomers have been simultaneously recorded.