A solid-shell finite element method for the anisotropic swelling of hydrogels with reinforced fibers

Abstract

In this paper, a solid-shell finite element method for the inhomogeneous swelling of anisotropic thin-walled hydrogels with reinforced fibers is developed. In this numerical framework, the anisotropic mechanical deformation of fiber-reinforced hydrogels is driven by solvent diffusion. The solid-shell model including only displacement degree of freedom is developed for anisotropic hydrogels. The model can directly incorporate three-dimensional material laws based on the modified Flory-Rehner theory for anisotropic thin-walled hydrogels and bypass complex update algorithms for the normal vector in conventional shell models. The constitutive relation and the corresponding tangent moduli for anisotropic hydrogels, referring to convected coordinate system, are derived according to the modified material model. The weak form of equilibrium equation is derived based on the three-field variational principle. Moreover, enhanced assumed strain and assumed natural strain methods are adopted to avoid Poisson-thickness locking and shear locking encountered in simulations of thin-walled hydrogels with reinforced fibers, respectively. Finally, two representative examples considering various moduli and initial directions of fibers are presented to verify the validity, accuracy and efficiency of the proposed method. The applications to predict the swelling of flowers demonstrate that the solid-shell based method for anisotropic swelling of soft materials can assist design of bionic devices.