Mesoscale modeling of bimodal elastomer networks: Constitutive and optical theories and results

A new micromechanics-based constitutive model for the nonlinear large deformation stress and birefringence responses of bimodal elastomer networks is developed. The elastic constitutive law is derived using the analytical rubrics of composite mechanics, which results in a straightforward implementation in contrast to previous bimodal theories. The model requires fewer adjustable parameters than most existing theories and, given a single set of parameters, is predictive over a wide range of bimodal compositions. Nonaffine deformation of short vs long chains is achieved with the model by satisfying equilibrium, compatibility, and the chain constitutive laws during deformation. The model is shown to agree well with data in the literature for both tensile stress and tensile stress-optic tests on specimens of poly(dimethylsiloxane) (PDMS) cross-linked from linear starting oligomers of various molecular weights. Several mixtures of eight different molecular weight combinations were examined. The model is also examined against our own data on PDMS in uniaxial compression and was shown to also predict that series of data well. Deviations of the model from the literature data are seen in bimodal mixtures which form microstructures that are believed to deviate from the proposed microcomposite arrangement. The model provides a framework for generating a constitutive theory capable of incorporating microstructural changes based solely on changes in composition.