A multiscale tensile failure model for double network elastomer composites

Double network elastomer is a class of molecular composites consisting of a brittle filler network and a ductile matrix network. Upon deformation, progressive scission of the filler network dissipates strain energy while the matrix network resists the micro defect propagation, thus enhancing both stiffness and toughness of the composites. Over the past few years, several types of constitutive models have been developed to capture the nonlinear stress-strain relation of double network elastomers, most of which were formulated by taking consideration of network interaction, chain scission and damage evolution. In parallel, despite the abundant macroscopic experiments and microscopic characterizations on the multiscale failure mechanism of double network elastomers, a theoretical prediction for the ultimate strength of the composites is yet to be built up. In this paper, we develop a multiscale model which describes the deformation and tensile failure of double network elastomer composites at the same time. The progressive damage at molecular level is captured by the stretch-induced scission of randomly distributed polymer chains; the propagation of chain-scission-induced defects at microscale is modeled with analogy to cavitation; finally, the macroscopic necking failure is predicted by tracking the stress softening phenomenon. Our model is validated through the comparison between theoretical calculations and experiments, as well as the predictions and analysis of empirical design principles for double network elastomer composites.