Constitutive modeling for hydrogel composites with arbitrary fiber distribution

Abstract

In this work, a constitutive model is developed to consider the effect of arbitrary fiber distribution on the swelling and tensile deformations of fiber-reinforced hydrogels. In the model, the free energy of total system is divided into two parts, i.e., the hydrogel contribution and fiber phase one. For hydrogel subsystem, we adopt the hydrogel free energy function of Flory-Rehner so that the swelling characteristic of hydrogel can be well captured; for the fiber, a statistical method is used to construct its free energy function. To effectively model the effect of fiber distribution, a principal invariant and dispersion coefficient are introduced so that the quantitative relationship between fiber distribution and anisotropy of material can be well described. Furthermore, through the analytical method or finite element implementation, both the swelling and tensile deformations of hydrogel composites with different fiber distributions are investigated. The modeling results show that the model can not only quantitatively predict the swelling and tensile deformations, but also can capture the effect of fiber distribution on the mechanical response of hydrogel composites. The new model may be helpful to the design and optimization of hydrogel composites.