柔性电子器件在健康医疗、智能工业、航空航天等领域有着广泛的应用前景。力学结构设计是无机柔性电子器件实现可变形能力的关键，薄膜屈曲互联导线被大量采用来实现器件的可拉伸性。研究发现，厚截面互联导线在部分工况下可以提供更好的力学可拉伸性，且同时具有更优异的电学和热学性能。与薄膜屈曲互联导线不同，厚截面互联导线在屈曲前会发生较大的初始变形，所以我们称这类结构为“有限初始变形结构”。本论文系统研究有限初始变形结构的屈曲理论和可拉伸性优化设计，具体如下：

    细长欧拉压杆等结构在屈曲前的变形通常很小，所以传统的屈曲理论和数值方法中通常忽略了屈曲前变形的影响，只考虑了屈曲前应力的作用。而我们发现厚截蛇形面互联导线在屈曲前会发生很大的初始变形，这对屈曲临界载荷的确定至关重要。虽然近一百年来屈曲理论已经取得了很大的进展，但目前还没有考虑屈曲前变形的屈曲理论，为此有必要建立考虑屈曲前变形影响的有限初始变形屈曲理论。本文通过拉伸实验测得了不同厚度蛇形互联导线的屈曲临界位移载荷，澄清了传统屈曲理论和数值方法由于忽略屈曲前变形的影响而引起较大误差（梁截面厚宽比为0.6时，传统屈曲理论会产生超过50%的误差）的原因。系统建立了考虑屈曲前变形的三维空间直梁的有限初始变形屈曲理论，用以分析梁在弯曲、扭转和拉伸/压缩耦合作用下的屈曲行为。求解了梁的三点弯侧向屈曲、纯弯侧向屈曲和欧拉屈曲三个经典问题。结果显示有限初始变形屈曲理论给出了更为精确的结果，而传统屈曲理论和数值方法会产生较大的误差（梁截面厚宽比为0.8时，三点弯侧向屈曲临界力结果误差达70%）。

    弹性基体被广泛应用于柔性电子器件，其在某些工况下同样会产生很大的屈曲前变形。本文系统建立了考虑屈曲前变形影响的块体结构的有限初始变形屈曲理论，求解了半无限大弹性平面屈曲和弹性矩形块体结构屈曲两个经典问题。与分步加载卸载有限元方法得出的精确解相比，有限初始变形屈曲理论给出了准确的结果，而传统屈曲理论和数值方法则会产生较大的误差（半无限大弹性平面屈曲临界力结果误差超过70%）。梁和块体结构的有限初始变形屈曲理论的建立对柔性电子器件可拉伸结构的力学分析、优化设计以及实际应用具有重要的意义。

    本文将预应变策略应用于厚截面蛇形互联导线结构设计，系统研究了厚截面蛇形互联导线在基体释放预应变阶段和基体拉伸阶段的有限变形问题。结果表明，理论分析模型和有限元所得结果一致，证明了将预应变策略应用于厚截面蛇形互联导线可进一步提升整体结构的可拉伸性；较大的预应变、较长的直线段和较小的弧半径设计可以增强厚截面蛇形互联导线的可拉伸性能；但在基体释放预应变后，较大的预应变会导致厚截面蛇形互联导线产生较大的应变。因此，需选择合适的预应变值(厚截面蛇形互联导线在基体释放预应变后不发生破坏)以达到最优的可拉伸性能。

  Flexible electronics have extensive application prospects, such as healthcare, smart industry, aerospace engineering, etc. The realization of the flexibility and stretchability of flexible electronics depends on the mechanical structure design. Based on the mechanism of buckling, plenty of the film interconnects designs are used to achieve stretchability for the electronics. It is found that the interconnects with thick section provide enhanced stretchability, and have superior performances in electrical and thermal properties during several conditions. Different from buckling interconnects with film structures, the interconnects with thick section have large prebuckling deformation, which is defined as “structures finite prebuckling deformation”. This dissertation aims to study the buckling theory and stretchability of structures with finite prebuckling deformation systematically. The main contents are as follows:

  The prebuckling deformation of structures such as slender compressive rod is usually very small, and is always neglected in the conventional buckling theory (CBT) and numerical method (CNM). Only the effect of prebuckling stress/force is considered. We find the serpentine interconnects with thick section, of which the prebuckling deformation becomes large and essential for determining the critical buckling load. Although great progress has been made for the buckling theory in the past hundred years, it is still challenging to analyze the buckling problems with finite prebuckling deformation (FPD buckling) straightforwardly. Therefore, it is necessary to establish the finite prebuckling deformation buckling theory (FPD buckling theory) with consideration of the prebuckling deformation. Here, the experimental stretch of a series of serpentine interconnects was firstly conducted as a representative example to show the inapplicability of the CBT and CNM (The CNM can yield a huge error of 50% on the critical buckling load for the case with thickness-to-width ratio of the section h / b = 0.6). A systematic and straightforward finite prebuckling deformation buckling theory is developed to analyze the FPD buckling behaviors of beams with the coupling of bending, twist and stretch/compression. As a comparison, various theoretical and numerical methods are applied to three classic problems, including lateral buckling of a three-point-bending beam, lateral buckling of a pure bending beam and Euler buckling. It is found that FPD buckling theory for beams is able to give a good prediction, while the CBT and CNM yield unacceptable results (with 70% error for a three-point-bending beam with h / b = 0.8, for example).

  The elastic substrate, which is a structure with finite prebuckling deformation under certain conditions, is widely used in flexible electronics. A systematic and straightforward theory for the FPD buckling of bulk structures is developed. The classic problems, including buckling of an elastic semi-plane solid and buckling of an elastic rectangular solid, are sovled respectively. Compared with the accurate buckling load from a special numerical method named disturbing-loading-unloading method (DLU method), the FPD buckling theory is able to give a good prediction, while the CBT and CNM may yield unacceptable results (with 70% error for the buckling of an elastic semi-plane solid). The establishment of the finite prebuckling deformation buckling theory for beam and bulk structures is of great significance for mechanical analysis, optimal design and applications of flexible electronics.

  The prestrain strategy is combined with the nonbuckling serpentine interconnect design. An analytic finite deformation model is developed for the serpentine interconnects with thick section during the release of the prestrained substrate or stretch of the interconnects. The perfect agreement with FEA validates the accuracy of the analytic results. It is found that the prestrain strategy enhances the stretchability of serpentine interconnects with thick section. Larger prestrain, longer straight segments and smaller arc radii enhance the stretchability of serpentine interconnects with thick section. While a larger prestrain also yields a larger maximum strain after releasing the prestrain, which means an appropriate prestrain (the interconnects will not be destroyed after releasing the prestrain) need to be selected to achieve the optimal stretchability.