A large deformation viscoelastic model for double-network hydrogels

We present a large deformation viscoelasticity model for recently synthesized double network hydrogels which consist of a covalently-crosslinked polyacrylamide network with long chains, and an ionically-crosslinked alginate network with short chains. Such double-network gels are highly stretchable and at the same time tough, because when stretched the crosslinks in the ionically-crosslinked alginate network rupture which results in distributed internal micro damage which dissipates a substantial amount of energy, while the configurational entropy of the covalently-crosslinked polyacrylamide network allows the gel to return to its original configuration after deformation. In addition to the large hysteresis during loading and unloading, these double network hydrogels also exhibit a substantial rate-sensitive response during loading, but exhibit almost no rate-sensitivity during unloading. These features of large hysteresis and asymmetric rate-sensitivity are quite different from the response of conventional hydrogels. We limit our attention to modeling the complex viscoelastic response of such hydrogels under isothermal conditions. Our model is restricted in the sense that we have limited our attention to conditions under which one might neglect any diffusion of the water in the hydrogel as might occur when the gel has a uniform initial value of the concentration of water, and the mobility of the water molecules in the gel is low relative to the time scale of the mechanical deformation. We also do not attempt to model the final fracture of such double-network hydrogels.