Computational modelling of poro-visco-hyperelastic effects on time-dependent fatigue crack growth of hydrogels

Abstract

In newly developed hydrogel-based devices, hydrogels are commonly used in load-bearing components subjected to prolonged cyclic deformations. The anti-fatigue capability of hydrogels is crucial for extending the service life of the devices. While recent developments in the synthesis and characterisation of tough hydrogels have facilitated continuous improvements of the fatigue resistance, the underlying mechanisms that dominate the fatigue fracture of hydrogels are still inconclusive. This work aims to model the complex constitutive response and predict the fatigue crack behaviour of hydrogels. The contribution of this work is twofold. (i) A physically-based poro-visco-hyperelastic model is developed within the framework of the Theory of Porous Media (TPM) at finite strains to describe the solid–fluid-coupled material behaviour of hydrogels. The fluid transport in hydrogels is governed by Darcy’s law. The non-equilibrium mechanical response induced by polymer chain rearrangement is considered by introducing internal variables based on a multiplicative decomposition of the solid deformation gradient tensor into elastic and inelastic parts. The time-dependent breaking/reforming kinetics of physical chains is described by a Bell model-based chain evolution law. (ii) An energy-based fatigue crack growth model is proposed to predict the fatigue crack growth of hydrogels. A volume averaging method is used to calculate the elastic energy density surrounding the crack tip as the driving force. In particular, the cyclic evolution of the averaged energy density due to the breaking/reforming kinetics of physical chains is incorporated in the crack growth model for hydrogels with physical networks. The computational results demonstrate that the predicted fatigue crack growth of different hydrogels reasonably agrees with experimental data. Moreover, the effects of fluid transport, time-dependent deformations and chain kinetics on the fatigue fracture behaviour of hydrogels are systematically analysed. The prediction results indicate that these time-dependent mechanisms cannot be ignored in modelling the fatigue behaviour of anti-fatigue hydrogels.