Time Dependent Behavior of a Dual Cross-Link Self-Healing Gel: Theory and Experiments

Recent experiments have shown that hydrogels with enhanced toughness can be synthesized by incorporating self-healing physical cross-links in a chemically cross-linked gel network. These gels exhibit rate dependent mechanical behavior, suggesting that improved mechanical properties are closely tied to the breaking and reattaching of temporary cross-links in the gel network. In this work, the connection between rate dependent mechanical behavior and kinetics of breaking and reattachment of temporary cross-links is quantified using a three-dimensional finite strain constitutive model. The parameters of the model are fitted using relaxation and constant strain rate tests in uniaxial tension of a model dual-cross-link gel. The stress versus time curves of more complex strain histories, involving loading followed by unloading at different rates, is successfully and quantitatively predicted by our model. Such modeling strategy combining physically based kinetics and three-dimensional large strain mechanics shows great promise for quantitative modeling of soft biological tissues and synthetic counterparts containing dynamic bonds.