Comparing mixed hybrid finite element method with standard FEM in swelling simulations involving extremely large deformations

Swelling involving (extremely) large deformations simulations have wide range of applications in biomedicine, tissue engineering and hygienic product design. Typically, standard FEM is used in which deformations and chemical potential are chosen to be the prime variables. On the other hand, mixed hybrid finite element method (MHFEM) featuring an additional independent variable field flux possesses local mass conservation property. Such a property has shown its success in Darcy's type equations with heterogeneous permeability. In this work, we perform a full-round comparison between MHFEM and FEM in solving swelling problems involving large deformations. Specifically, based on the permeability distributions, the problems fall into three categories: constant permeability, strain-dependent permeability and permeability with a discontinuous interface. For each category, we compare the two methods in aspects like solution convergence robustness, deformation, chemical potential and flux field accuracy and computational cost. We conclude that MHFEM outperforms standard FEM in terms of solution convergence robustness and the accuracy of all three fields when a swelling problem involves discontinuous interface in permeability.