Constitutive behaviors of tough physical hydrogels with dynamic metal-coordinated bonds

Metal-coordination mediated physical hydrogels exhibit high strength/toughness and intriguing mechanical behaviors with the pronounced rate-dependent viscoelasticity and loading-path dependent strain softening. Also, the stress of the reloaded gels increases with more waiting time, indicating a self-healing effect. This paper aims to develop a constitutive model to capture these complex mechanical behaviors of the metal-coordination mediated physical hydrogels. The theoretical framework incorporates two main physical mechanisms: the microscopic kinetic dissociation/association of cross-links and inelastic conformational changes of gel networks. The model predictions agree well with the experimental data of gel responses under different scenarios, which simultaneously capture the time-dependent stress response, relaxation, hysteresis , self-healing behavior, as well as ultimate failure. The present work can provide theoretical guidance and methodological support for the design and practical applications of tough hydrogels mediated by metal-coordinated bonds as load-bearing materials.