分形桥联结构的屈曲行为及优化设计研究

In recent years, stretchable and flexible electronics based on inorganic materials has attracted a lot of interest from both the electronics industry and the scientific community. From the high-efficiency consideration, some of the stretchable and flexible electronics, such as stretchable photovoltaics, demand a very high areal coverage of the active device. Therefore, for the island-bridge model, one of the key scientific challenges is how to achieve simultaneously high areal coverage of the active device and large elastic stretchability of the entire system via the structural design and optimization of interconnects between islands. In this project, the fractal design concept is introduced into the structural optimization of the freestanding interconnects. By simulating the critical-buckling and post-buckling behaviors of the freestanding interconnects under general loading conditions, we determine the scaling laws for the critical buckling strain and the elastic stretchability, and establish the deformation mechanism of the multi-level buckling induced by the self-similarity of fractal structures, and reveal the coupling effect and competition mechanism between the instability of the local defect and the buckling of the entire structure, and find out the optimum design achieving both high areal coverage of the active device and large elastic reversibility of the entire system.

近年来，基于无机电子材料的可延展柔性电子成为全球电子产业界和学术界共同关注的新焦点。一些可延展柔性电子器件（例如可延展光伏电池）出于效率的考虑而对功能电子组件的表面占有率提出极高的要求。因此，就岛桥结构模型而言，如何充分利用岛间极其有限的空间来对桥联进行力学结构设计和优化，以使电子器件具备尽可能大的柔性和延展性，是目前所面临的关键科学问题之一。本项目将分形设计理念引入到自由式桥联的结构优化之中，通过模拟自由式分形桥联在拉伸、剪切等荷载下作用的临界屈曲及后屈曲行为，归纳出关于临界屈曲应变及弹性延展极限的比例定律，建立起因结构自相似而导致的多级屈曲变形机制，揭示出局部缺陷失稳与整体结构屈曲之间的耦合关系及竞争机制，寻找到兼顾功能组件表面占有率及整体结构各向延展性的最佳设计方案。

近年来，基于无机电子材料的可延展柔性电子成为全球电子产业界和学术界共同关注的新焦点。一些可延展柔性电子器件（例如可延展光伏电池）出于效率的考虑而对功能电子组件的表面占有率提出极高的要求。因此，就岛桥结构模型而言，如何充分利用岛间极其有限的空间来对桥联进行力学结构设计和优化，以使电子器件具备尽可能大的柔性和延展性，是目前所面临的关键科学问题之一。本项目在上述相关问题上取得了如下主要进展：1. 给出了薄膜型直梁在面内承受端部弯矩、剪力、轴力条件下面外临界屈曲问题的精确解，并在此基础上提出了求解平面分形桥联结构弯-扭组合型面外临界屈曲问题的回传射线矩阵法及传递矩阵法列式，从中可得临界屈曲问题的比例定律，也使发展出一种等效或简化理论成为可能。2.发现了两种可进一步提升蜿蜒型分形桥联结构可拉伸性能的新途径，一是利用岛间闲置空间破坏分形结构的周期性和对称性，一是改变分形结构子单元的走向和排列方式，从而使得在给定功能电子组件表面占有率的情况下，器件能够获得尽可能大的可拉伸性能。3.研究了结构缺陷对分形桥联结构弹性延展极限的影响，结果发现缺陷往往会削弱结构的弹性延展极限，应尽量避免。上述研究成果对于分形桥联结构的优化设计具有重要的指导意义。