Abstract
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.
Highlights
Hydrogels swell by the permeation of solvent molecules into polymer networks
Following the linear and finite poroelasticity approach established by Biot [4,5], Hong et al [23] proposed a theoretical framework that enables finite deformations with combination of Flory theory [19] to model the swelling of a polymeric gel
We aim to evaluate the effectiveness of mixed hybrid finite element method (MHFEM) comparing with standard FEM in terms of robustness, accuracy and efficiency the solution method when applied to simulate the finite transient swelling of hydrogels
Summary
Hydrogels swell by the permeation of solvent (water) molecules into polymer networks. The part of a gel that gets in touch with the external solvent earlier increases dramatically its hydraulic permeability This inhomogeneity in the mobility tensor may require special attention in terms of numerical treatment. Inspired by the success of mixed formulations in Darcy flow problems, a mixed hybrid finite element method (MHFEM) was implemented to simulate the transient swelling of a hydrogel in one of our previous works [45]. We aim to evaluate the effectiveness of MHFEM comparing with standard FEM in terms of robustness, accuracy and efficiency the solution method when applied to simulate the finite transient swelling of hydrogels.
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