Mechanics of single-network hydrogels with network imperfection

Polymer network is a crucial component of hydrogels, and network imperfection is a prominent feature of polymer networks, significantly influencing the performance of hydrogels. Two essential features of network imperfection are unequal chain lengths and dangling chains, both of which have a significant impact on the mechanical properties of single-network (SN) hydrogels. However, a theoretical framework considering network imperfection in SN hydrogels is still lacking. Here, we propose a theoretical model for SN hydrogels with network imperfection to study the damage behavior during deformation, in which we adopt different chain length distributions to accurately depict the real physical characteristics of the polymer network and incorporate the normalized critical chain force for a more precise measurement of network damage. To verify our theory, we discuss the effects of model parameters on the stress-stretch responses of SN hydrogels and predict the results of uniaxial loading-unloading tests of SN hydrogels, which agree well with experimentally measured stress-stretch behaviors. Finally, we implement the constitutive model into ABAQUS as a user subroutine to study the inhomogeneous deformation of hydrogels.