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1. Origami frustration and its influence on energy landscapes of origami assemblies

   https://doi.org/10.1073/pnas.2426790122  

   Zang, Shixi; Zhao, Tuo; Misseroni, Diego; Paulino, Glaucio H (September 2025, Proceedings of the National Academy of Sciences)

   Harnessing instabilities of multicomponent multistable structural assemblies can potentially lead to scalable and reversible functionalities, which can be enhanced by exploring frustration. For instance, standard Kresling origami cells exhibit nontunable intrinsic energy landscapes determined by their geometry and material properties, limiting their adaptability after fabrication. To overcome this limitation, we introduce frustration to enable fine-tuning of the energy landscape and resulting deformation states. By prestressing the Kresling cell by means of special springs with individual control, we induce either global or localized (i.e., crease level) frustration, which allows changing the energy barrier (cell or assembly). We investigate the mechanical behavior of frustrated Kresling assemblies, both theoretically and experimentally, under various loading and boundary conditions. Our findings reveal that changing the frustration state leads to precise control of folding sequences, enabling previously inaccessible folding paths. The proposed concept paves the way for applications in mechanical metamaterials and other fields requiring highly programmable and reconfigurable systems – e.g., prosthetic limbs. 

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2. Origami engineering

   https://doi.org/10.1038/s43586-024-00313-7  

   Misseroni, Diego; Pratapa, Phanisri P; Liu, Ke; Kresling, Biruta; Chen, Yan; Daraio, Chiara; Paulino, Glaucio H (December 2024, Nature Reviews Methods Primers)
3. Robust folding of elastic origami

   https://doi.org/10.1039/D2SM00369D  

   Lee-Trimble, M. E.; Kang, Ji-Hwan; Hayward, Ryan C.; Santangelo, Christian D. (August 2022, Soft Matter)

   Self-folding origami, structures that are engineered flat to fold into targeted, three-dimensional shapes, have many potential engineering applications. Though significant effort in recent years has been devoted to designing fold patterns that can achieve a variety of target shapes, recent work has also made clear that many origami structures exhibit multiple folding pathways, with a proliferation of geometric folding pathways as the origami structure becomes complex. The competition between these pathways can lead to structures that are programmed for one shape, yet fold incorrectly. To disentangle the features that lead to misfolding, we introduce a model of self-folding origami that accounts for the finite stretching rigidity of the origami faces and allows the computation of energy landscapes that lead to misfolding. We find that, in addition to the geometrical features of the origami, the finite elasticity of the nearly-flat origami configurations regulates the proliferation of potential misfolded states through a series of saddle-node bifurcations. We apply our model to one of the most common origami motifs, the symmetric “bird's foot,” a single vertex with four folds. We show that though even a small error in programmed fold angles induces metastability in rigid origami, elasticity allows one to tune resilience to misfolding. In a more complex design, the “Randlett flapping bird,” which has thousands of potential competing states, we further show that the number of actual observed minima is strongly determined by the structure's elasticity. In general, we show that elastic origami with both stiffer folds and less bendable faces self-folds better. 

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4. Dynamics of Kresling origami deployment

   https://doi.org/10.1103/PhysRevE.101.063003  

   Kidambi, N.; Wang, K. W. (June 2020, Physical Review E)

   null (Ed.)
5. Topological kinematics of origami metamaterials

   https://doi.org/10.1038/s41567-018-0150-8  

   Liu, Bin; Silverberg, Jesse L.; Evans, Arthur A.; Santangelo, Christian D.; Lang, Robert J.; Hull, Thomas C.; Cohen, Itai (May 2018, Nature Physics)

   A variety of electronic phases in solid-state systems can be understood by abstracting away microscopic details and refocusing on how Fermi surface topology interacts with band structure to define available electron states1. In fact, topological concepts are broadly applicable to non-electronic materials and can be used to understand a variety of seemingly unrelated phenomena2,3,4,5,6. Here, we apply topological principles to origami-inspired mechanical metamaterials7,8,9,10,11,12, and demonstrate how to guide bulk kinematics by tailoring the crease configuration-space topology. Specifically, we show that by simply changing the crease angles, we modify the configuration-space topology, and drive origami structures to dramatically change their kinematics from being smoothly and continuously deformable to mechanically bistable and rigid. In addition, we examine how a topologically disjointed configuration space can be used to constrain the locally accessible deformations of a single folded sheet. While analyses of origami structures are typically dependent on the energetics of constitutive relations11,12,13,14, the topological abstractions introduced here are a separate and independent consideration that we use to analyse, understand and design these metamaterials. 

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