Nonlinear photoelasticity of rubber-like soft materials: comparison between theory and experiment

Photoelasticity often refers to the birefringence effect of materials induced by elastic deformation. Recently, many experiments on the photoelasticity of soft materials have been reported. However, the experimental results are mainly qualitative observations and lack any theoretical analysis. In this paper, we revisit Treloar's and Arruda's models of nonlinear photoelasticity for rubber-like materials. Both models establish the intrinsic relationship between stretch and birefringence, based on the statistics of chain polarizability and a network theory. We discuss the difference of the two models and build an experimental setup to measure the birefringence of PDMS samples as a function of stress/stretch. We vary the curing ratio of PDMS to study the effect of chain density on birefringence and compare with Treloar's theory. We further use experimental data of double-network hydrogels in the literature to compare with theory and find that when the deformation is large compared with the limiting stretch of the material, Arruda's model fits the experimental data much better than Treloar's model. This work presents a basis of using the theory of nonlinear photoelasticity to guide the analysis of experiments. In this paper, we review Treloar's and Arruda's models of nonlinear photoelasticity for rubber-like materials and compare the two models with experimental data. We find that when the deformation is large compared with the limiting stretch of the material, Arruda's model (using non-Gaussian chain assumption) fits the experimental data much better than Treloar's model (using Gaussian chain assumption).