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. 2022 Nov 26;13:7294. doi: 10.1038/s41467-022-34844-y

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© The Author(s) 2022

Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/.

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Fig. 3 — a Plastic films peeled from an arcuate surface with a gradually changing peeling angle (ϕ) result in spiral-like structures. Top: schematic showing the peeling process. Bottom: top view (left) and side view (right) photographs of the spiral-like structure. b Plastic films peeled with gradually increasing deviation angle (δ) form cylindrical helices with gradually increasing pitch. Top: schematics showing the peeling process with ϕ of ~180°. Bottom: photographs of the helices. c Plastic films peeled with δ changing from negative to positive (left schematic) form cylindrical helices with different chirality (right photograph). Schematics show top views of the peeling process at ϕ of 180°. In a–c schematics, the dotted outlines and gray arrows indicate the final state of the peeling process. d Films peeled with simultaneously changing ϕ and δ form conical spirals. Top: oblique view schematic of the peeling process, where the plastic film (gray) adhered at an angle to the generatrix of the arcuate substrate. Bottom: side view (left) and top view (right) photographs of the conical spiral films. In a–d, the ϕ-δ phase diagrams indicate the change of ϕ and δ during the peeling process. e Left schematic shows the structure decoding of polygons with a right triangle as an example that the sides and interior angles can be viewed as lines and arcs which correspond to the intervals and widths of the adhesive tapes. Right schematic (top view) shows the arrangement of adhesives (orange, purple and blue strips) for the triangle and peeling direction (red arrow) with ϕ of 180°. Right photographs: triangles, quadrangle, pentagon and hexagon. f Two-step peeling with orthogonal peeling directions results in hyperboloids. Left: top view (top) and side view (bottom) schematics of the two-step peeling process. Parallel red and blue lines indicate the adhesion regions on different sides of the plastic film. The line direction indicates the peeling direction. The white lines mean that these parts were cut into parallel strips. Right: photographs of the hyperboloids. All the scale bars are 10 mm.