Lithographically defined interconnects with filamentary, serpentine configurations have been widely used in various forms of stretchable electronic devices, owing to the ultra-high stretchability that can be achieved and the relative simple geometry that facilitates the design and fabrication. Theoretical models of serpentine interconnects developed previously for predicting the performance of stretchability were mainly based on the theory of infinitesimal deformation. This assumption, however, does not hold for the interconnects that undergo large levels of deformations before the structural failure. Here, an analytic model of serpentine interconnects is developed starting from the finite deformation theory of planar, curved beams. Finite element analyses (FEA) of the serpentine interconnects with a wide range of geometric parameters were performed to validate the developed model. Comparisons of the predicted stretchability to the estimations of linear models provide quantitative insights into the effect of finite deformation. Both the theoretical and numerical results indicate that a considerable overestimation (e.g., > 50% relatively) of the stretchability can be induced by the linear model for many representative shapes of serpentine interconnects. Furthermore, a simplified analytic solution of the stretchability is obtained by using an approximate model to characterize the nonlinear effect. The developed models can be used to facilitate the designs of serpentine interconnects in future applications.

中文翻译：

---

可拉伸电子器件平面蛇形互连的有限变形模型

由于可以实现超高的拉伸性以及有利于设计和制造的相对简单的几何形状，具有丝状、蛇形结构的光刻限定互连已广泛用于各种形式的可拉伸电子器件。先前开发的用于预测可拉伸性能的蛇形互连的理论模型主要基于无穷小变形理论。然而，这种假设对于在结构失效之前经历大量变形的互连并不成立。这里，从平面曲梁的有限变形理论出发，开发了蛇形互连的解析模型。对具有各种几何参数的蛇形互连进行有限元分析 (FEA)，以验证所开发的模型。预测的拉伸性与线性模型的估计的比较提供了对有限变形影响的定量见解。理论和数值结果都表明，对于蛇形互连的许多代表性形状，线性模型可能会导致对可拉伸性的相当大的高估（例如，相对> 50%）。此外，通过使用近似模型来表征非线性效应，获得了拉伸性的简化解析解。开发的模型可用于促进未来应用中蛇形互连的设计。