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几种经典热力学一致模型进行了比较性评述与分类，重点关注溶剂吸收/脱附过程及其对力学变形和网络溶胀的影响。研究涉及理论构建、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。通过统一的理论框架呈现各理论体系，论证了尽管部分模型在表现形式上有所差异，但均遵循等价的热力学论证逻辑。数值分析采用泰勒-胡德单元进行空间离散以满足inf-sup条件并抑制数值振荡，基于FEniCS平台通过一致变分公式求解离散问题，同时采用整体式与交错式求解策略。针对不同水凝胶结构的基准测试表明，模型差异主要源于所选取的水凝胶体积响应特性。该选择的重要性在当前文献中常被低估，但已被证实对水凝胶行为预测具有实质性影响。