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Multistable structures have widespread applications in the design of deployable aerospace systems, mechanical metamaterials, flexible electronics, and multimodal soft robotics due to their capability of shape reconfiguration between multiple stable states. Recently, the snap-folding of rings, often in the form of circles or polygons, has shown the capability of inducing diverse stable configurations. The natural curvature of the rod segment (curvature in its stress-free state) plays an important role in the elastic stability of these rings, determining the number and form of their stable configurations during folding. Here, we develop a general theoretical framework for the elastic stability analysis of segmented rings (e.g., polygons) based on an energy variational approach. Combining this framework with finite element simulations, we map out all planar stable configurations of various segmented rings and determine the natural curvature ranges of their multistable states. The theoretical and numerical results are validated through experiments, which demonstrate that a segmented ring with a rectangular cross-section can show up to six distinct planar stable states. The results also reveal that, by rationally designing the segment number and natural curvature of the segmented ring, its one- or multiloop configuration can store more strain energy than a circular ring of the same total length. We envision that the proposed strategy for achieving multistability in the current work will aid in the design of multifunctional, reconfigurable, and deployable structures.
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This content will become publicly available on June 22, 2027
Physics‐Informed Neural Network‐Enabled Forward Prediction and Inverse Design of Ring Origami
ABSTRACT Ring origami, consisting of closed‐loop rods, can realize diverse shape‐morphing behaviors, including 2D‐to‐1D, 2D‐to‐2D, and 2D‐to‐3D transformations, by harnessing snap‐buckling instability. To broaden its application potential in areas such as deployable aerospace structures, soft robotics, and reconfigurable metamaterials, a programmable design framework is highly desired. In this work, we develop a unified framework for the forward prediction and inverse design of ring origami by integrating Kirchhoff rod theory with a physics‐informed neural network. The framework can identify the stable states of various segmented rings (e.g., square and hexagonal rings) composed of rod segments with prescribed constant or varying natural curvature (i.e., curvature in the stress‐free state). By introducing an additional shape‐matching loss, the framework can also determine the natural curvature profile of segmented rings required to achieve stable configurations that can be confined within a target spatial domain or conform to a target curved surface. Its generality and robustness are further demonstrated by extending it to 3D rod systems. This work establishes a powerful strategy for the programmable design of elastic rod systems exemplified by ring origami and opens new opportunities for functional applications that demand shape‐morphing structures with simple geometries, high packing capability, and prescribed stable configurations.
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- PAR ID:
- 10703077
- Publisher / Repository:
- Wiley
- Date Published:
- Journal Name:
- Advanced Science
- ISSN:
- 2198-3844
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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