Vulcanization and the mechanical response of rubber

Hyperelastic models are widely used to describe the mechanical response of rubber. However, purely mechanical models cannot account for changes in the material due to chemical reactions such as those that take place during vulcanization. Here, we present a model developed within a thermodynamic framework accounting for chemical reactions. A mixture theory approach that allows for the existence of multiple species and their interconversion is followed. The existence of a Helmholtz potential and a rate of entropy production function for the mixture as a whole are posited. Following the multiple natural configuration approach, the rate of entropy production is maximized to obtain constitutive equations. The viscoelastic model is then specialized to the elastic case. The model is calibrated using data available in the literature for rubber. A simulation of the stress–strain curve of rubber as vulcanization progresses is presented.