Multi-cycle deformation of supramolecular elastomers: Constitutive modeling and structure-property relations

Supramolecular elastomers are rubber-like polymers with double-network structure formed by chains bridged by covalent and non-covalent bonds. Due to high mobility of temporary bonds, whose rate of recombination is comparable with the strain rate under loading, these materials demonstrate such properties as self-healing and self-recovery at ambient temperature. A constitutive model is developed for the viscoelastic and viscoplastic behavior of supramolecular elastomers. Stress–strain relations and the kinetic equations for plastic deformation are derived from the free energy imbalance inequality for an isothermal three-dimensional deformation. The viscoelastic response reflects breakage and reformation of temporary junctions in an inhomogeneous transient network (transition of chains from their active to dangling state and vice versa). The viscoplastic response reflects slippage of permanent junctions with respect to their reference positions. A junction starts to slide when it becomes unbalanced due to transformation of one of the chains connected by this junction from its active state into the dangling state. The sliding process (plastic flow) proceeds until the junction reaches its new equilibrium state. The model is applied to fit experimental data in tensile relaxation tests, loading-unloading tests, and multi-cycle tests on supramolecular elastomers and triblock copolymers. Numerical simulation shows that the governing equations describe adequately the experimental stress–strain diagrams, the material parameters evolve consistently with chemical composition and experimental conditions, and predictions of the model are in qualitative agreement with observations.