KAUST Grant NumberKUK-C1-013-04
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AbstractThe 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 Lamé, 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.
CitationDavidovitch B, Schroll RD, Vella D, Adda-Bedia M, Cerda EA (2011) Prototypical model for tensional wrinkling in thin sheets. Proceedings of the National Academy of Sciences 108: 18227–18232. Available: http://dx.doi.org/10.1073/pnas.1108553108.
SponsorsWe thank P. Bella, R. Kohn, and N. Menon for useful discussions. We thank the Aspen Center for Physics for hospitality during the final stages of this work. We acknowledge support by the Petroleum Research Fund of American Chemical Society (B.D.) and National Science Foundation-Materials Research Science and Engineering Center at University of Massachusetts (R.D.S.). This publication is based on work supported in part by Grant KUK-C1-013-04 made by King Abdullah University of Science and Technology (D.V.). M.A.-B. and E.A.C. acknowledge the support of Centre National de la Recherche Scientifique-Conicyt 2008. E.A.C. is thankful for Fondecyt project 1095112 and Anillo Act 95.
PubMed Central IDPMC3215074
CollectionsPublications Acknowledging KAUST Support
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