A Chain Scission-Induced Anisotropic Damage Constitutive Model for Double Network Hydrogels

Abstract

This work develops a chain scission-induced anisotropic damage constitutive model for double network (DN) hydrogels while considering the damage cross effect. A free energy of a single polymer chain comprising the configuration entropy of the polymer chain and the internal energy of persistent segments is proposed to avoid the force singularity caused by chain stretch limit. Then, a distribution function of the initial stretch ratio of polymer chains in DN hydrogels is derived to consider the randomness of chain length. Based on the micro-sphere full-network model and an energy-form fracture criterion of polymer chains, the damage evolution model of polymer chains in a certain orientation is formulated by the critical initial stretch ratio of the polymer chain, showing that only polymer chains with the initial stretch ratio lower than the critical initial stretch ratio survive in a certain chain stretch. The critical initial stretch ratio is determined by the maximum chain stretch and the maximum first invariant of the deformation state by considering the damage cross effect. Using the developed damage constitutive model, we describe the stress softening, strain hardening behavior and the nonmonotonic stress–strain curve of DN hydrogels. It also reveals that the residual strain of DN hydrogels in the loading cycles is caused by the anisotropic damage of polymer chains in DN hydrogels.