Quantifying the equilibrium swelling responses and swelling-induced snap-through of heterogeneous spherical hydrogels

Abstract

We employ the finite deformation theory to analyze the inhomogeneous large deformation of a heterogeneous spherical hydrogel subjected to chemo-mechanical loadings. The heterogeneous spherical hydrogel is composed of two concentric spherical hydrogel layers with different material properties. The Gent model is employed for the free energy function of the polymer stretching part in order to tackle the effect of the limiting chain extensibility. The heterogeneous spherical hydrogel is assumed to be perfectly bonded at the interface and is traction free at the external surface. At the internal surface, two boundary conditions are considered: one is internally fixed and the other is internally pressurized. Numerical examples are performed to describe the nonlinear behaviors of a heterogeneous spherical hydrogel when subjected to the swelling and mechanical loadings. For internally fixed case, numerical results show that the limiting chain extensibility and the initial swelling ratio have significant effect on the actuation deformation of a heterogeneous spherical hydrogel. For internally pressurized case, we find that the swelling-induced snap-through instability can be triggered under specified conditions. It is shown that the chemo-mechanical behaviors of the heterogeneous spherical hydrogels can be adjusted by tuning the material properties and the initial swelling ratios.