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.

翻译：自然界中曲面自变形过程（如花朵与叶片的生长行为）激发了人们对自变形双层结构的研究兴趣，这类结构已被广泛应用于软体机器人与开关器件。然而，现有研究主要聚焦于材料特性或双层结构制备技术，对自变形机理及其演化过程的研究仍显不足。本研究提出一种基于棋盘离散微分几何方法的自变形双层结构变形模拟新方法。与传统有限元方法相比，该方法在保持计算精度的前提下实现了更高效率，并能有效处理复杂有限应变问题。最后，通过模拟模型分别设计了三种仿生自变形双层结构——折纸花、螺旋草与锥形贝壳，进一步验证了所提方法的有效性。本研究为自变形双层结构的变形预测与设计提供了有效方法，并为运用几何方法解决力学问题提供了新视角。