Issue 9, 2024

Geometry, mechanics and actuation of intrinsically curved folds

Abstract

We combine theory and experiments to explore the kinematics and actuation of intrinsically curved folds (ICFs) in otherwise developable shells. Unlike origami folds, ICFs are not bending isometries of flat sheets, but arise via non-isometric processes (growth/moulding) or by joining sheets along curved boundaries. Experimentally, we implement both, first making joined ICFs from paper, then fabricating flat liquid crystal elastomer (LCE) sheets that morph into ICFs upon heating/swelling via programmed metric changes. Theoretically, an ICF's intrinsic geometry is defined by the geodesic curvatures on either side, κgi. Given these, and a target 3D fold-line, one can construct the entire surface isometrically, and compute the bending energy. This construction shows ICFs are bending mechanisms, with a continuous family of isometries trading fold angle against fold-line curvature. In ICFs with symmetric κgi, straightening the fold-line culminates in a fully-folded flat state that is deployable but weak, while asymmetric ICFs ultimately lock with a mechanically strong finite-angle. When unloaded, freely-hinged ICFs simply adopt the (thickness t independent) isometry that minimizes the bend energy. In contrast, in LCE ICFs a competition between flank and ridge selects a ridge curvature that, unusually, scales as t−1/7. Finally, we demonstrate how multiple ICFs can be combined in one LCE sheet, to create a versatile intrinsically curved gripper that lifts a heavy weight.

Graphical abstract: Geometry, mechanics and actuation of intrinsically curved folds

Supplementary files

Article information

Article type
Paper
Submitted
22 Nov 2023
Accepted
02 Feb 2024
First published
05 Feb 2024
This article is Open Access
Creative Commons BY license

Soft Matter, 2024,20, 2132-2140

Geometry, mechanics and actuation of intrinsically curved folds

F. Feng, K. Dradrach, M. Zmyślony, M. Barnes and J. S. Biggins, Soft Matter, 2024, 20, 2132 DOI: 10.1039/D3SM01584J

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