Model order reduction for transient coupled diffusion-deformation of hydrogels

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.