A comparative analysis of transient finite-strain coupled diffusion-deformation theories for hydrogels

TL;DR

This paper compares various thermodynamically consistent models of hydrogel behavior under large deformations, focusing on solvent interaction, mathematical classification, numerical implementation, and the impact of volumetric response choices.

Contribution

It provides a unified framework for different hydrogel models, highlighting the importance of volumetric response in predicting hydrogel behavior.

Findings

Major differences depend on volumetric response assumptions

Finite element implementation ensures numerical stability

Benchmark tests reveal significant model behavior variations

Abstract

This work presents a comparative review and classification between some well-known thermodynamically consistent models of hydrogel behavior in a large deformation setting, specifically focusing on solvent absorption/desorption and its impact on mechanical deformation and network swelling. The proposed discussion addresses formulation aspects, general mathematical classification of the governing equations, and numerical implementation issues based on the finite element method. The theories are presented in a unified framework demonstrating that, despite not being evident in some cases, all of them follow equivalent thermodynamic arguments. A detailed numerical analysis is carried out where Taylor-Hood elements are employed in the spatial discretization to satisfy the inf-sup condition and to prevent spurious numerical oscillations. The resulting discrete problems are solved using the FEniCS platform through consistent variational formulations, employing both monolithic and staggered approaches. We conduct benchmark tests on various hydrogel structures, demonstrating that major differences arise from the chosen volumetric response of the hydrogel. The significance of this choice is frequently underestimated in the state-of-the-art literature but has been shown to have substantial implications on the resulting hydrogel behavior.