A Constitutive Model for Alginate-Based Double Network Hydrogels Cross-Linked by Mono-, Di-, and Trivalent Cations

In this contribution, a micro-mechanically based constitutive model is proposed to describe the nonlinear inelastic rubber-like features of alginate-based double network hydrogel cross-linked via various counterions. To this end, the lengthening of the polysaccharide polymer chain after a fully stretched state is characterized. A polymer chain is firstly considered behaving entropically up to the fully stretched state. Then, enthalpic behavior is accounted for concerning the following lengthening. To calculate enthalpic behavior, the macroscopic material properties, such as elastic modulus, are integrated into the proposed model. Thus, a new energy concept for a polymer chain is proposed. The model is constituted by the proposed energy concept, the network decomposition model, the Arruda–Boyce eight chain model and the network alteration theory. The model is compared against the cyclic tensile test data of alginate-based double network hydrogels cross-linked via mono-, di-, and trivalent cations. Good agreement between the model and experiments is obtained.