曲面薄膜结构褶皱失稳力学

徐凡; 杨易凡; 汪婷

doi:10.6052/1000-0992-20-038

曲面薄膜结构褶皱失稳力学

doi: 10.6052/1000-0992-20-038

复旦大学航空航天系力学与工程仿真研究所, 上海 200433

基金项目: 国家自然科学基金(11872150, 11602058, 11772094); 上海市青年科技启明星计划(19QA1400500)资助项目.

详细信息

作者简介:
徐凡, 复旦大学教授、博导. 中国力学学会青年工作委员会委员、中国力学学会软物质力学、微纳米力学工作组组员、上海市力学学会常务理事. 主要从事软物质与柔性结构力学、薄膜力学和智能材料力学研究. 工作以第一/通讯作者发表于《PRL》(封面)《JMPS》《Nature Biomed. Eng.》《Adv. Funct. Mater.》《IJSS》《IJES》《CMAME》《EML》《Sci. China Phys. Mech. Astron.》等国内外学术期刊, 成果被《Nature》《Nature Phys.》和《Nature Comput. Sci.》《Nature Biomed. Eng.》等　　　　　　　　　专题评论报道

通讯作者:
fanxu@fudan.edu.cn

中图分类号: O33, O34, O39
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出版历程
- 收稿日期: 2020-12-26
- 录用日期: 2021-04-19
- 网络出版日期: 2021-05-01
- 刊出日期: 2021-06-25

Curvature-affected instabilities in membranes and surfaces: A review

Institute of Mechanics and Computational Engineering, Department of Aeronautics and Astronautics, Fudan University, Shanghai 200433, China

More Information

Corresponding author: fanxu@fudan.edu.cn

摘要

摘要: 薄膜结构褶皱失稳在微观和宏观尺度会出现相似的形貌, 在过去二十年里引发了学者们极大的研究兴趣. 而几何曲率对薄膜结构的失稳临界、形貌选择和后屈曲演化起着至关重要的作用. 本文回顾近二十年来平面和曲面薄膜结构褶皱失稳力学研究进展, 聚焦曲率影响下的薄膜拉伸和膜基结构在各种激励下的稳定性问题. 有限应变板壳理论模型和数值计算方法的发展推动了对曲率影响下薄膜结构表面形貌多重分岔转变的定量理解、预测和追踪, 不仅推进了对薄膜结构失稳机理的深入理解, 也为抑制褶皱或利用失稳实现多功能表面制造提供了理论基础, 可促进拓扑形貌相关的功能性膜结构的设计及优化.
- 薄膜 /
- 曲率 /
- 褶皱 /
- 分岔 /
- 大变形
Abstract: Instability of soft materials and membrane structures usually shows similar wrinkling patterns across length scales, which has aroused considerable interest in the past twenty years. Curvature and mechanics are intimately connected in thin-film structures, and curvature plays a key role in the critical threshold, mode selection, and post-buckling evolution. Here, we review the advancement of instability mechanics of thin-film structures in the past two decades, from planar to curved geometry, focusing on the curvature-affected instability of stretched membranes and film-substrate systems under various stimuli. Development of the theoretical models and numerical methods of finite strain plate/shell advances fundamental understanding, quantitative prediction, and tracking of multiple bifurcation transitions in morphology and shape of thin-film structures. It not only promotes the in-depth insight into instability mechanism but also guides wrinkle-resistant control and the effective design of morphology-related multifunctional surfaces and membrane structures via harnessing instability.
- thin films /
- curvature /
- wrinkling /
- bifurcation /
- large deformation

HTML全文

图 1 不同尺度下平面构型(a) ~ (e)与曲面构型(f) ~ (j)薄膜结构褶皱形貌对比: (a)石墨烯(Bao et al. 2009), (b)凝胶薄膜, (c)荷叶(Xu et al. 2020a), (d)窗帘(Vandeparre et al. 2011), (e)太阳光帆, (f)弯曲碳纳米管(Poncharal et al. 1999), (g) PDMS微球(Breid & Crosby 2013), (h)百合花瓣(Liang & Mahadevan 2011), (i)袖子(Yang et al. 2018), (j) Google气球

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图 2 平面超弹性薄膜拉伸起皱−消皱演化. (a)单轴拉伸实验, 对应拉伸应变分别为$\varepsilon = 0,\;0.05,\; $$ 0.1,\;0.15,\;0.2,\;0.3$; (b)薄膜拉伸失稳分岔图(Li & Healey 2016), 其中点划线、点线、虚线及实线分别表示NH, MR, SVK, FvK模型

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图 3 (a) (b)平展的袖子受拉时出现横向褶皱, 穿起的袖子受拉时表面光滑. (c) (d)曲面薄膜拉伸实验装置及光栅表面形貌测量. (e) ~ (g)相同拉伸应变下增大曲率可抑制褶皱, 且大于临界曲率时薄膜保持光滑. (h)曲率影响下的稳定性边界三维相图. 理论预测的稳定性界面(整体弯曲变形与局部起褶的边界)与实验(散点)一致(Wang et al. 2020)

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图 4 (a)应变−挠度分岔曲线, 当曲率$\kappa \geqslant {\kappa _{{\rm{cr}}}} \sim 0.0013$时, 只出现整体弯曲(无褶). (b)弯曲能−应变演化曲线, 绿色区域表示整体弯曲与局部起褶的耦合行为, 橙色区域表示只发生整体弯曲变形(无褶). (c)经典DMV壳模型无法预报褶皱消失现象. (d)理论计算演化与实验对比(Wang et al. 2020)

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图 5 膜基结构失稳模态演化示意图: (a)基底预压缩: 平整→褶皱→三倍周期→折痕, (b)直接压缩: 平整→褶皱→倍周期→四倍周期→折痕, (c)基底预拉伸(高模量比): 平整→褶皱→凸脊, (d)基底预拉伸(低模量比): 平整→褶皱→多级褶皱(Cheng & Xu 2021)

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图 6 三种典型柱面核壳结构失稳形貌: (a)轴压下轴对称正弦形模态; (b)轴压下非轴对称钻石形模态; (c)热载荷下油条状失稳模态(Xu et al. 2017); (d)(e)为实验(Zhao et al. 2014)分别对应(a)(b)模态; (f)西班牙油条

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图 7 液晶高聚物网络(LCN)柱面核壳结构表面失稳形貌相图. 液晶分子指向矢取向显著影响褶皱失稳形貌选择(Zhao et al. 2021)

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图 8 软壳在圆柱面上滑动受压失稳模态. (a)撸起的袖子上的褶皱. (b) ~ (d)单轴压缩桌面上的一张平坦的纸, 纸面隆起形成单一凸脊. (e)柱面乳胶气球厚度$h_{\rm{f}} = 0.2\;{\rm{mm}}$, 嵌套在半径$R = 3\;{\rm{mm}}$的亚克力圆柱上. 随着右侧压缩的增加, 出现四种不同的状态: (e)初始光滑构型; (f)正弦形褶皱; (g)凸脊; (h)松垂形凸脊. (i) ~ (l)分别对应于(e) ~ (h)的特征示意图(Yang et al. 2018)

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图 9 球面核壳结构表面失稳是一种复杂的跨尺度力学行为: (a) (b)植物果实失水皱缩形貌(Li et al. 2011, Xu & Potier-Ferry 2017); (c) Ag核/SiO₂壳微球结构表面失稳形貌(Cao et al. 2008); (d)不同径厚比下球面核壳结构的失稳模态(Stoop et al. 2015)

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图 10 核壳结构起皱模态相图. 无量纲参数${C_{\rm{s}}}$决定了局部凹陷、巴基球、迷宫和棋盘之间的模态选择. 局部凹陷到巴基球的相变边界为${C_{\rm{s}}} \thickapprox 1.3$, 巴基球到迷宫的相变边界为${C_s}\thickapprox 15$ (Xu et al. 2020b)

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