Mechanics of a Dual Cross-Link Gel with Dynamic Bonds: Steady State Kinetics and Large Deformation Effects

We develop a three-dimensional continuum theory for a dual cross-link gel with permanent and transient-bonds. This theory connects the breaking and re-forming kinetics of the-transient bonds to the large deformation behavior of the gel-Although based on similar principles as our previous theory for the same gel, the new theory addresses a limitation of the previous theory and agrees. equally well with experimental data. Specifically, in the new theory we assume that breaking and re-forming kinetics of transient bonds reaches a steady state. This assumption leads to fewer material parameters and enables the new theory to capture the healing process of the dual cross-link gel. In addition, the steady state assumption also allows the new theory to reduce to classical linear viscoelastic theory in the limit of infinitesimal strains, where the kinetics, of bond breaking and re-formation can be linked directly to the relaxation function. We also extend the theory to account for strain stiffening under very large deformation. The extended theory with strain stiffening agrees well with experimental data for nominal strain up to 400%. Finally, we extend our theory to gels with multiple types of dynamic bond's which has been recently exploited as a strategy to engineer viscoelastic behavior of gels.