中文摘要：

出现起皱，一部电影在一个预先拉紧的弹性体的底层罐头上结合了形式周期的起皱的模式，在每天的普通现象生活。在存在理论模型，这部电影比的薄得多底层以便底层罐头被认为与无限的厚度弹性体。在这份报纸，有限底层厚度的效果为免费边界状况理论上被分析盒子。基于最小的势能原则，一个理论模型被建立，并且起皱的波长和振幅模式被获得。当底层的厚度是时，超过 200 预定比这部电影的厚度大，这的结果学习同意很好，结果为无限的底层厚度从以前的模型获得了。为薄底层，然而，有限底层厚度的效果变得重要。精确地在这份报纸给的模型描述有限底层厚度的效果，提供为未来 thin-film-on-substrate 的重要设计指南系统象可拉长的电子设备那样。

英文摘要：

Surface wrinkling, a film bonded on a pre-strained elastomeric substrate can form periodic wrinkling patterns, is a common phenomenon in daily life. In existing theoretical models, the film is much thinner than the substrate so that the substrate can be considered to be elastomeric with infinite thickness. In this paper, the effect of finite substrate thickness is analyzed theoretically for free boundary condition cases. Based on the minimum potential energy principle, a theoretical model is established, and the wave length and amplitude of the wrinkling pattern are obtained. When the thickness of the substrate is more than 200 times larger than the thickness of the film, the results of this study agree well with the results obtained from the previous models for infinite substrate thickness. However, for thin substrates, the effect of finite substrate thickness becomes significant. The model given in this paper accurately describes the effect of finite substrate thickness, providing important design guidelines for future thin-film-on-substrate systems such as stretchable electronic devices.