High Packing Efficiency Deployment Method Using Swelling Hydrogels Inspired by Out-of-Plane Biological Deformation

In this study, we developed a deployment method with both high flexibility and packing efficiency by combining high swelling gel (HS gel) and low swelling gel (LS gel) using precisely controlled expansion rate distributions. Out-of-plane deformation is frequently observed in biological systems as a key morphogenetic process, in which flat tissues transform into three-dimensional (3D) curved structures. Such mechanisms have inspired a wide range of applications in soft robotics, programmable matter, and biomimetic manufacturing. However, replicating the large, complex deformations found in nature—characterized by both high packing efficiency and high flexibility—remains a challenge. Existing approaches, such as shape-memory polymers, self-folding sheets, and four-dimensional (4D) printing, have not fully achieved the dynamic and intricate transformations observed in living organisms. To address this challenge, we programmed deformation by assigning an expansion rate distribution corresponding to a target Gaussian curvature—a curvature determined by the product of two principal curvatures. This approach enables the formation of 3D structures by controlling the in-plane expansion of thin materials. Notably, even simple combinations of materials with different swelling properties can induce out-of-plane deformations with either positive or negative Gaussian curvature. Our proposed concept is scalable and customizable, and is expected to contribute to the advancement of 3D manufacturing technologies.