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.

翻译：本文对水凝胶在大变形框架下的几种著名热力学一致模型进行了比较性综述与分类，特别聚焦于溶剂吸收/解吸过程及其对力学变形和网络膨胀的影响。所提出的论述涵盖了模型构建形式、控制方程的一般数学分类，以及基于有限元法的数值实现问题。所有理论均在统一框架下呈现，论证了尽管某些情况下并不明显，但它们均遵循等价的热力学论证。我们进行了详细的数值分析，在空间离散中采用Taylor-Hood单元以满足inf-sup条件并防止数值伪振荡。通过相容变分公式，利用FEniCS平台求解所得离散问题，并同时采用整体求解和交错求解两种策略。针对多种水凝胶结构开展基准测试，结果表明主要差异源于所选择的水凝胶体积响应。该选择的重要性在现有文献中常被低估，但已被证明对最终水凝胶行为具有重大影响。