Minimization and saddle-point principles for the phase-field modeling of fracture in hydrogels

Abstract

Material modeling of hydrogels has gained importance over the last years due to their emerging deployment in biomedical applications and as stimuli-responsive functional materials. Their polymer network structure allows hydraulic permeability and can exhibit an extremely broad range of elastic properties. This renders the predictive modeling of failure mechanisms a daunting task for future perspectives of this class of materials. In the present contribution, we propose a phase-field model of hydrogel fracture embedded into a variational framework and its implementation using an algorithm based on operator splits. Saddle-point and minimization principles are outlined, their relation is shown and representative boundary value problems are analyzed for both formulations. Phenomena specific to the slow mass transport in hydrogels are studied by means of a diffusion-driven creep test with crack evolution and crack initiation induced by drying. The latter shows that large volume change not only leads to buckling pattern as often studied in the literature, but also to crack initiation and growth. The proposed model can thus be validated and its significance as a first approach to the modeling of fracture in polymeric hydrogels is shown.