Diffusion-induced Swelling of Patterned Shape-Morphing Hydrogels

Hydrogels, a mixture of polymeric network and solvent (water), play a pivotal role in various practical applications due to their ability to undergo substantial deformations when exposed to external stimuli. The interactions between the polymer network and water in patterned hydrogels results in intriguing, non-linear shape-morphing deformations due to transient swelling. To explore these phenomena in complex geometries, we model deformations along with water diffusion by employing a particle-based numerical method. This hybrid Eulerian-Lagrangian material point method [1] overcomes the limitations of standard mesh-based methods in handling mesh distortion in extreme deformations and contact interactions. This model couples the diffusion of water with elasticity, allowing us to model extremely large deformations with constraints and the exchange of water between hydrogels in contact to drive sequential morphing. We demonstrate the bending of patterned hydrogels due to inhomogeneous swelling, the collective behavior of constrained hydrogel particles, and the emerging swelling-induced surface instabilities with self-contacting deformations. This approach establishes a computational foundation for investigating extreme deformations coupled with diffusion in hydrogels, finding valuable applications in diverse domains, ranging from soft robotics to the design of tissue-like materials and advanced sensors.

[1] Madadi, A. A. & Dortdivanlioglu, B. A Subdivision-stabilized B-spline Mixed Material Point Method. Computer Methods in Applied Mechanics and Engineering (2023). In revision