曲面构型薄膜－基底系统失稳及后屈曲形貌演化研究

Wrinkles of a thin film on a substrate are widely observed in both nature and daily life. Exploring instabilities of such film–substrate systems can not only guide engineering designs, but also create specified surface patterns and fabricate advanced functional materials with the use of surface instabilities. However, most previous studies were focused on planar systems, yet the buckling characteristics of thin films on curved substrates, especially the wrinkling pattern evolution and transformation during the postbuckling process remain a challenging issue. In this project, systematic theoretical analysis and high efficient numerical simulations will be carried out to study the buckling of films on cylindrical and spherical substrates, focusing on the morphological evolution and transformation during the postbuckling process. More specifically, we will establish a theoretical framework based on the energy method for the buckling of films on curved substrates, which can capture the critical buckling characteristics and the postbuckling behavior. An efficient numerical algorithm via spectral method will also be developed to validate the theoretical results, and simulate the morphological evolution of the curved film–substrate system. Thereafter, we will explore the influences of the curvature and nonlinear constitutive relation of the substrate on the wrinkling patterns of the film. This project is expected to be helpful for not only understanding complicated pattern formations on curved surfaces in nature, but also providing novel route for fabricating and modulating patterns on curved surfaces.

基底上薄膜失稳的现象在自然界以及日常生活中广泛存在，开展薄膜－基底系统失稳的研究不仅可以指导工程结构的设计，而且可以利用失稳产生的特定表面形貌，制备具有先进功能的材料。然而现有的研究大多集中于平面构型，曲面基底上薄膜的失稳尤其是薄膜后屈曲过程中的形貌演化及转变仍然是个具有挑战性的问题。本项目拟通过系统的理论分析和高效的数值计算方法，研究圆柱和圆球两种构型的薄膜－基底系统的失稳行为，重点关注薄膜后屈曲过程中的形貌演化及转变。拟采用能量法建立曲面基底上薄膜失稳的理论模型，求解得到临界特征及薄膜后屈曲行为。拟发展基于谱方法的高效数值计算方法模拟系统的失稳和形貌演化，并与理论结果进行对比。基于理论分析模型和数值计算方法，探讨基底曲率和基底本构非线性对薄膜三维形貌演化的影响。本项目的研究结果不仅有助于理解自然界中曲面上复杂形貌的形成机理，也有望为三维曲面上的形貌制备和调控提供新途径。

基底上薄膜失稳的现象在自然界以及日常生活中广泛存在，开展薄膜－基底系统失稳的研究不仅可以指导工程结构的设计，而且可以利用失稳产生的特定表面形貌，制备具有先进功能的材料。本项目对曲面上薄膜失稳现象进行了系统的研究，对圆柱形薄膜基底结构在受内压、轴向压缩以及组合加载形式下的屈曲行为进行分析，并揭示了后屈曲行为中出现的局部失稳现象的原因，探讨了薄膜的几何非线性和基底的材料非线性对局部失稳的影响。此外，结合基于深度学习的人工智能方法，探讨了薄膜失稳后形貌演化图像与输入载荷之间的变化关系。本项目的研究结果不仅有助于理解自然界中曲面上复杂形貌的形成机理，也有望为三维曲面上的形貌制备和调控提供新途径。