The process of self-morphing in curved surfaces found in nature, such as with the growth of flowers and leaves, has generated interest in the study of self-morphing bilayers, which has been used in many soft robots or switchers. However, previous research has primarily focused on materials or bilayer fabrication technologies. The self-morphing mechanism and process have been rarely investigated, despite their importance. This study proposed a new deformation simulation method for self-morphing bilayers based on a checkerboard-based discrete differential geometry approach. This new method achieved higher efficiency than traditional finite element methods while still maintaining accuracy. It was also effective in handling complex finite strain situations. Finally, the simulation model was used to design three self-morphing bilayers inspired by folding flowers, spiral grass, and conical seashells. These designs further prove the effectiveness of the proposed method. The results of this study propose a good method for predicting deformation and designing self-morphing bilayers and provide a useful viewpoint for using geometrical methods to solve mechanical problems.

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