https://doi.org/10.1140/epjs/s11734-025-01903-6
Regular Article
Sub-singularities for shaping thin sheets
Department of Physics and the James Franck Institute, The University of Chicago, 60637, Chicago, IL, USA
a
This email address is being protected from spambots. You need JavaScript enabled to view it.
Received:
28
August
2025
Accepted:
1
September
2025
Published online:
10
September
2025
Abstract
The principles behind the sharp, singular structures in a crumpled sheet are well understood. Here we discuss more general ways of exploiting such sharp structures to control the shape of a sheet by deforming or forcing it elsewhere. Often, the induced shape leads to further sharp structures—“sub-singularities.” Though weaker and softer than the primary singularities, they nevertheless provide robust ways of shaping a sheet. In simple cases, we understand the reason for these and their strength. This paper surveys a broad range of other sub-structure phenomena and reports recent progress in understanding some of them.
© The Author(s) 2025
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 licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence 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 licence, visit http://creativecommons.org/licenses/by/4.0/.
