This study explores reduced-order modeling for analyzing the time-dependent diffusion-deformation of hydrogels. The full-order model 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. We employ proper orthogonal decomposition as a model order reduction approach. The reduced-order model performance is tested through a benchmark problem on hydrogel swelling and a case study simulating co-axial printing. Then, we embed the reduced-order model into an optimization loop to efficiently identify the coupled problem's material parameters using full-field data. Finally, a study is conducted on the uncertainty propagation of the material parameter.

翻译：本研究探索采用降阶模型分析水凝胶随时间变化的扩散-变形行为。描述水凝胶瞬态行为的全阶模型由化学势与位移相互耦合的偏微分方程组构成。该方程组采用整体式表述，并通过有限元方法进行求解。我们采用本征正交分解作为模型降阶方法，通过水凝胶溶胀基准问题及模拟同轴打印的案例研究验证降阶模型的性能。随后，将降阶模型嵌入优化循环中，利用全场数据高效辨识耦合问题的材料参数。最后，对材料参数的不确定性传播进行了系统性研究。