This study introduces a reduced-order model (ROM) for analyzing the transient diffusion-deformation of hydrogels. The full-order model (FOM) describing hydrogel transient behavior consists of a coupled system of partial differential equations in which chemical potential and displacements are coupled. This system is formulated in a monolithic fashion and solved using the Finite Element Method (FEM). The ROM employs proper orthogonal decomposition as a model order reduction approach. We test the ROM performance through benchmark tests on hydrogel swelling behavior and a case study simulating co-axial printing. Finally, we embed the ROM into an optimization problem to identify the model material parameters of the coupled problem using full-field data. We verify that the ROM can predict hydrogels' diffusion-deformation evolution and material properties, significantly reducing computation time compared to the FOM. The results demonstrate the ROM's accuracy and computational efficiency. This work paths the way towards advanced practical applications of ROMs, e.g., in the context of feedback error control in hydrogel 3D printing.

翻译：本研究提出了一种用于分析水凝胶瞬态扩散-变形过程的降阶模型（ROM）。描述水凝胶瞬态行为的全阶模型（FOM）由一组耦合偏微分方程构成，其中化学势与位移相互耦合。该方程组采用整体式框架构建，并通过有限元法（FEM）求解。所提出的ROM以本征正交分解作为模型降阶方法。我们通过水凝胶溶胀行为的基准测试及同轴打印模拟案例研究验证了ROM的性能。最后，将ROM嵌入优化问题中，利用全场数据识别耦合问题的模型材料参数。验证结果表明，ROM能够准确预测水凝胶的扩散-变形演化过程及材料特性，且相比FOM大幅缩短了计算时间。本研究展示了ROM的精度与计算效率，为ROM在先进实际应用（如水凝胶三维打印中的反馈误差控制）中奠定了基础。