Analytical network-averaging of the tube model: Mechanically induced chemiluminescence in elastomers

Mechanically induced chemiluminescence is a phenomenon where broken chemical bonds send out visible light upon stress application. The intensity of the emitted light is correlated to the underlying evolution of chain scission in the polymer. In this contribution, an anisotropic analytical network-averaging concept is utilized to model mechanically induced chemiluminescence, Mullins effect, hysteresis and induced anisotropy in mechano-chemically responsive polymeric materials. We extend the isotropic analytical network-averaging (Khiêm and Itskov, 2016) by considering anisotropic distribution of polymer subnetworks driven by internal variables. Accordingly, the network damage and recovery alter the distribution of molecules in space and consequently change the mean field deformation measures (mesoscopic stretch and tube contraction). The mechanically induced chemiluminescence is elucidated on the basis of microvoid growth. By this means, its characteristics such as the irreversibility and the anisotropy can be captured. Model predictions demonstrate good agreement to experimental data of dioxetane cross-linked and filled elastomers.