A symplectic analytical method for fracture analysis of hydrogels under chemo-mechanical coupled loading

This study presents a Hamiltonian-based symplectic methodology for investigating swelling-induced fracture in hydrogels caused by water absorption. A constitutive model for hydrogels, incorporating chemical coupling effects, is established through perturbation analysis rooted in a physically rigorous theoretical framework. Within the Hamiltonian system, the dual equation governing plane fracture in hydrogels is directly solved using the method of separation of variables. Analytical expressions for the generalized stress/displacement fields are explicitly derived based on eigenvalues and eigensolutions, thereby obviating the need for trial functions. Moreover, critical fracture parameters (including stress intensity factors (SIFs) and J -integral), as well as the crack initiation angle are accurately quantified. Finally, the influence of chemical potential on these fracture parameters and initiation angle is systematically examined. These findings offer a robust theoretical basis for the practical engineering applications of hydrogel materials.