A microstructure-informed continuum model of transversely isotropic, fibre-reinforced hydrogels

Abstract

Fibre-reinforced hydrogels are promising materials for biomedical applications due to their strength, toughness, and tunability. However, it remains unclear how to design fibre-reinforced hydrogels for use in specific applications due to the lack of a robust modelling framework that can predict and hence optimise their behaviour. In this paper, we present a microstructure-informed continuum model for transversely isotropic fibre-reinforced hydrogels that captures the specific geometry of the fibre network. The model accounts for slack (or crimp) in the initial fibre network that is gradually removed upon deformation. The mechanical model for the fibre network is coupled to a nonlinear poroelastic model for the hydrogel matrix that accounts for osmotic stress. We find that slack in the fibre network leads to J-shaped stress–strain curves, as seen in experiments, and a more isotropic swelling of the material. The model is compared to data from time-dependent unconfined compression experiments. Although we find qualitative agreement between model and experiment, the discrepancies suggest that additional physics, such as viscoelasticity and slip between the fibre network and the hydrogel matrix, can play important roles in these materials. We showcase how the model can be used to guide the design of materials for artificial cartilage by exploring how to maximise interstitial fluid pressure. Fluid pressurisation can be increased by using stiffer fibres, removing slack from the fibre network prior to matrix hydration, and reducing the Young’s modulus of the hydrogel matrix. Finally, a high-level and open-source Python package has been developed for simulating unconfined compression experiments using the model.