Journal
JOURNAL OF THE MECHANICS AND PHYSICS OF SOLIDS
Volume 58, Issue 12, Pages 2033-2042Publisher
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.jmps.2010.09.011
Keywords
Self-assembly; Capillary force; Folding; Bending rigidity; Thin films
Funding
- NSF [DMR-0504751, CMMI-0906361]
- DARPA [02-130130-00]
- Department of Energy [DE-FG02-07ER46471]
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Self-assembly of complex structures is common in nature. Self-assembly principles provide a promising way to fabricate three-dimensional, micro- or millimeter scale devices. In the present paper, we present a generalized analytical study of the self-folding of thin plates into deterministic 3D shapes through fluid-solid interactions. Based on the beam theory, a mechanics model is developed, incorporating the two competing components-a capillary force promoting folding and the beinding rigidity of the foil that resists folding into a 3D structure. Through an equivalence argument of thin foils of different geometry, an effective folding parameter, which uniquely characterizes the driving force for folding, has been identified. A criterion for spontaneous folding of any shaped 2D patterned foil based on the effective folding parameter is thus established. The model predictions show excellent agreement with experimental measurements made on a variety of materials, indicating that the assumptions used in the analysis are valid. (C) 2010 Elsevier Ltd. All rights reserved.
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