Transient swelling of polymeric hydrogels: A new finite element solution framework

The paper presents a new solution framework for the transient swelling of polymeric hydrogels which couples finite deformation and fluid permeation. Based on the kinematic constraint between the mechanical and diffusion fields, a unified constitutive equation incorporating the effects of both mechanical deformation and chemical swelling and a modified fluid balance equation relating the change rate of the volumetric deformation to the fluid diffusion are introduced. Within the modified theoretical framework, a general finite element (FE) procedure is developed to model the transient behaviors in swelling hydrogels. Because the kinematic constraint is satisfied in advance in the FE algorithm, the concentration of the fluid content could be directly calculated from the converged results and the specific element techniques related to the kinematic constraint (such as the F-bar method and the interpolation modes satisfying the Ladyzenskaja-Babuška-Brezzi (LBB) condition) are not needed. A stable convective boundary condition (BC) for the diffusion field is developed which is proved to be an alternative BC to efficiently model the actual swelling process. Four kinds of two- and three-dimensional coupled elements are presented and used to model transient swelling phenomena with various kinds of BCs, geometries and material distributions, which demonstrate the accuracy, convergence and robustness of the FE algorithm.