曲面膜基系统表面失稳与后屈曲分岔的多尺度研究

Wrinkling of a thin layer bonded to a curved substrate has been widely observed in nature such as wrinkles of hornbeam leaf and human skin. Besides, in modern industry, such structures have been widely applied in large area, ranging from the micro/nano-fabrication of flexibly stretchable electronic devices with controlled morphological patterns, the coating of optical lens, to the design of advanced functional materials. Most previous works have been mainly constrained to study the occurrence and development of surface wrinkles in planar film/substrate systems under external loading. However, the formation and evolution of surface patterns in curved film/substrate systems are still lacking, e.g. the mechanism and degree of the Gaussian curvature effect on instability pattern formation. The prediction and control of wrinkling process under curvature constraints become a promising technique for micro/nano-scale surface patterning fabrication. The present multi-scale study aims at quantitatively investigating the whole view of instability pattern formation in curved film/substrate systems, through finite element modelling and advanced nonlinear numerical approaches, on the combination of analytical analyses based on buckling theories, to explore, describe, understand and ultimately to predict the post-buckling evolution, multiple bifurcations and surface mode transitions in curved film/substrate systems. Moreover, the underlying mechanism of curvature effect on pattern selection will be explored. The numerical and theoretical results obtained from this research could be used to guide the design of new functionally layered materials and structures. Furthermore, macroscopic reduced-order models of curved film/substrate systems generated from a Fourier-related multi-scale modelling approach will be developed to provide an efficient way to compute large-scale instability problems with a significant reduction of computational cost.

曲面基底上薄膜的褶皱是自然界中普遍存在的现象如树叶的纹路和皮肤的皱纹；同时在现代工业中也已被广泛应用于可拉伸电子器件的制造、光学镜头的镀膜和功能性材料的设计等。已有的研究主要集中于平面膜基系统在外荷载下表面起皱的发生和发展，对曲面膜基系统表面形貌的演化仍不清楚，比如高斯曲率对失稳起皱的影响机理和影响程度等。预测和控制曲率限制下的起皱过程已逐渐成为现代工业中一种很有前景的技术，例如可应用于微纳米级的表面图案生产。本项目旨在从多尺度角度定量地研究曲面膜基系统的失稳全貌，以有限元建模计算和先进的非线性数值方法为主要手段，屈曲理论分析为辅，来发现、描述、理解和预测曲面几何形貌下膜基系统的后屈曲多重分岔和模态演化，并挖掘其背后所蕴含的力学机理，为设计新型功能性材料提供理论依据和模拟支持。同时，以期对曲面膜基系统建立宏观缩减的多尺度模型来显著地降低计算成本，为大尺度周期性失稳计算提供一种高效的方法。

本项目从多尺度角度定量地研究曲面柔性薄膜结构失稳全貌，来发现、描述、理解和预测曲面几何形貌下后屈曲多重分岔和模态演化，并挖掘其背后所蕴含的力学机理，为设计新型功能性柔性材料/结构/器件提供参考。项目资助下取得的重要成果包括：(1)发展了先进的非线性理论和数值方法，提出了研究软物质薄膜结构失稳问题的系统求解方案，解决了“蛇回”跳变失稳、大变形、多稳态解和多重分岔等强非线性问题定量求解难题，实现了非线性系统后屈曲失稳和形貌演化路径的高效预测及连续追踪；(2)建立了适用于各种超弹性本构的改进冯卡门板模型（面内大应变），可准确预测薄膜起皱-消皱现象（经典冯卡门板模型无法正确预测）；(3)发展了光-热-力场耦合作用下的液晶高聚物板大挠度弯曲/屈曲非线性板模型，揭示了柔性结构多物理场失稳行为的内在机理，对柔性结构力学稳定性理论、多尺度多场耦合建模与计算方法做出了创新性贡献；(4)发现了曲率影响下薄膜结构失稳中的新型分岔行为，揭示了曲率影响下软薄膜的非线性失稳形貌演化机理及动态全景，解决了上世纪60年代前人实验研究轴压下金属薄壳屈曲的模态选择问题，为多功能表面制造的力学调控与设计提供了新思路；(5)首次发现水基影响植物生长形貌及内在力学机理。提出了各向异性生长冯卡门板模型，能准确预测各种植物生长形貌演化，并通过基底或边缘驱动表面失稳来实现仿生可展结构形貌控制的新思路；(6)提出了基于力学设计的柔性电子多级碳纳米管结构（仿生肌肉）纤维传感器，实现了可植入柔性电子传感器与生物组织长期变形协调相容，用于生物医学工程中多种疾病的长期实时在体监测，在生物电子学领域发展出一个新的方向。相关结果以第一/通讯作者在国际权威学术期刊PRL (2篇)、Nature Biomed. Eng. (1篇)、JMPS (2篇)、Adv. Funct. Mater. (1篇)、IJES (1篇)、IJSS (2篇)、EML (2篇)、IJNLM (2篇)、Sci. Rep. (1篇)和IJAM (1篇)上发表SCI论文15篇。成果被《自然∙物理》(Nature Phys. 14, 534)作为Picture Story专题评论报道，被PRL选为编辑推荐(Editors’ Suggestion)并被美国物理学会Physics网站专题报道。