A phase-field model for fracture in water-containing soft solids

Abstract

In this paper, a phase field model with energy decomposition previously developed for rubber is extended for hydrogel. Predications of the extended model are qualitatively and quantitatively compared with our experimental results. To be consistent with the phase field model for rubber, we first reformulate the free energy of hydrogels with initial swelling that takes into account the initial volume fraction of water. The free energy (for intact hydrogels) is then modified to be suited for phase field modeling by splitting the deformation into isochoric and volumetric parts. The model parameters are calibrated by experimental tests performed under uniform compression without the phase field damage. A typical water-containing soft solid, hydrogel, is fabricated. Compression and three-point bending experiments on hydrogel blocks are carried out under plane strain conditions. The phase field model can capture the experimentally observed sequence of deformation and fracture at finite strains. It is also found that the energy decomposition is a key for the robust modeling of experimental fracture involving the compression. The role of the water played in the toughness of the gel is also revealed.