Parameter identification and uncertainty propagation of hydrogel coupled diffusion-deformation using POD-based reduced-order modeling

Abstract

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.

Figures (18)

• Figure 1: Illustration of the offline phase workflow for the POD-based ROM's construction.
• Figure 2: Illustration of the simulated problems:a.benchmark: 2D square hydrogel block and b.case study: co-axial printing. Notes:i. The white dashed boxes mark the domains extracted for the simulation setup. ii. The shadowed area in b refers to the neglected part due to the axisymmetric nature of the case study.
• Figure 3: Benchmark: FOM simulation results for primary variables.a. normalized chemical potential and b. displacement magnitude at time steps $T = \{0.01, 0.15, 0.25\}$.
• Figure 4: Benchmark: transient FOM simulation.a. normalized chemical potential, b displacement in x-direction, and b. normalized stresses at different points in the 2D hydrogel block.
• Figure 5: Benchmark: material parameter sampling for the POD and nested-POD-based ROM construction.