Coupling deformation analysis of self-morphing bilayers with mismatch strain

Self-morphing bilayers driven by the inner mismatch strain have inspired numerous actuators and soft robots in the four-dimensional (4D) printing field. Analyzing their coupling deformation is crucial for the design of actuators, but current methods face inefficiencies or accuracy issues. This study provides convenient and efficient approaches, from both deformation theory and model aspects, to analyze the coupling deformations of selfmorphing bilayers. First, we derived a simplified energy expression for self-morphing bilayers to reflect their deformation process. This concise form permits direct derivation of some deformation theories for self-morphing bilayers, thereby significantly simplifying the complexity of deformation analysis. Second, we established the deformation simulation model of bilayers by discretizing and minimizing the simplified energy expression. The checkerboard pattern method, a new discrete differential geometric (DDG) approach, was introduced and improved to discretize the derived energy expression. The Levenberg-Marquardt (LM) algorithm was used to establish the deformation simulation model for bilayers by minimizing the discrete energy function. Further, a series of numerical simulations of bending bilayers were conducted. Results validated that the proposed model achieved a faster simulation speed compared to the finite element method (FEM)-based model in our previous work, and was more accurate for finite strain situations. Finally, three bio-inspired bilayers and a bio-inspired gripper (successfully grasped a sphere) were designed using the resulting model, demonstrating its practical application capabilities. These proposed methods hold substantial potential to facilitate the advancement of the design field of 4D printing and actuators.