Prototypical model for tensional wrinkling in thin sheets

被引:185
作者
Davidovitch, Benny [1 ]
Schroll, Robert D. [1 ]
Vella, Dominic [2 ,3 ]
Adda-Bedia, Mokhtar [2 ]
Cerda, Enrique A. [4 ]
机构
[1] Univ Massachusetts, Dept Phys, Amherst, MA 01003 USA
[2] Univ Paris Diderot, Univ Paris 06, Ecole Normale Super, CNRS,Lab Phys Stat, F-75005 Paris, France
[3] Math Inst, Oxford Ctr Collaborat Appl Math, Oxford OX1 3LB, England
[4] Univ Santiago, Dept Fis, Santiago, Chile
基金
美国国家科学基金会;
关键词
pattern formation; thin-film buckling; ELASTIC SHEETS; FILMS; MEMBRANES; POLYMER;
D O I
10.1073/pnas.1108553108
中图分类号
O [数理科学和化学]; P [天文学、地球科学]; Q [生物科学]; N [自然科学总论];
学科分类号
07 ; 0710 ; 09 ;
摘要
The buckling and wrinkling of thin films has recently seen a surge of interest among physicists, biologists, mathematicians, and engineers. This activity has been triggered by the growing interest in developing technologies at ever-decreasing scales and the resulting necessity to control the mechanics of tiny structures, as well as by the realization that morphogenetic processes, such as the tissue-shaping instabilities occurring in animal epithelia or plant leaves, often emerge from mechanical instabilities of cell sheets. Although the most basic buckling instability of uniaxially compressed plates was understood by Euler more than two centuries ago, recent experiments on nanometrically thin (ultrathin) films have shown significant deviations from predictions of standard buckling theory. Motivated by this puzzle, we introduce here a theoretical model that allows for a systematic analysis of wrinkling in sheets far from their instability threshold. We focus on the simplest extension of Euler buckling that exhibits wrinkles of finite length-a sheet under axisymmetric tensile loads. The first study of this geometry, which is attributed to Lame, allows us to construct a phase diagram that demonstrates the dramatic variation of wrinkling patterns from near-threshold to far-from-threshold conditions. Theoretical arguments and comparison to experiments show that the thinner the sheet is, the smaller is the compressive load above which the far-from-threshold regime emerges. This observation emphasizes the relevance of our analysis for nanomechanics applications.
引用
收藏
页码:18227 / 18232
页数:6
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