Model-based analysis and prediction of swelling-induced buckling of hydrogel structures using a finite element method

Abstract Non-linear buckling of hydrogels has been studied across fields from soft robotics to microfluidics. Recently, it was found that swelling of hydrogel partially bonded to a substrate spontaneously forms unique patterns known as telephone-cord buckling, which have since been used for various biological actuators such as for chemical stimulation of cells and biomimetics of peristaltic pumping. However, reliable prediction of these complex buckled structures prior to fabrication remains a challenge due to the non-linear and coupled nature of swelling and buckling. To address this, we propose a physical model of buckling hydrogel based on a finite element method (FEM). The proposed model simplifies the buckling process by representing it as a combination of inelastic deformation caused by swelling and physical contact between the hydrogel and rigid substrate. It is designed to be intuitive and compatible with standard FEM software, making it broadly accessible. We show that it can simulate buckled structures consistent with experimentally observed ones. Furthermore, it enables simulations of buckling in complex geometries and with non-uniform swelling. These results suggest that our framework is a practical computational tool for pre-experimental design of buckled hydrogel systems, with potential impact on soft actuators, programmable materials, and organ-on-a-chip applications.