Finite element implementation of poroelasticity theory for swelling dynamics of hydrogels

Hydrogel can swell to many times of its dry volume, resulting in large deformation which is vital for its function. The swelling process is regulated by many physical and chemical mechanisms, and can, to some extent, be fairly described by the poroelasticity theory. Implementation of the poroelasticity theory in the framework of finite element method would aid the design and optimization of hydrogel-based soft devices. Choosing chemical potential and displacement as two field variables, we present the implementation of poroelasticity tailored for hydrogel swelling dynamics, detail the normalization of physical parameters and the treatment of boundary conditions. Several examples are presented to demonstrate the feasibility and correctness of the proposed strategy.