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1. Current-Dependent Dynamics of Bidirectional Self-Folding for Multi-Layer Polymers Using Local Resistive Heating

   https://doi.org/10.1115/1.4049588  

   Elsisy, Moataz; Poska, Evan; Abdulhafez, Moataz; Bedewy, Mostafa (July 2021, Journal of Engineering Materials and Technology)

   null (Ed.)

   Abstract The purpose of this paper is to characterize the dynamics and direction of self-folding of pre-strained polystyrene (PSPS) and non-pre-strained styrene (NPS), which results from local shrinkage using a new process of directed self-folding of polymer sheets based on a resistively heated ribbon that is in contact with the sheets. A temperature gradient across the thickness of this shape memory polymer (SMP) sheet induces folding along the line of contact with the heating ribbon. Varying the electric current changes the degree of folding and the extent of local material flow. This method can be used to create practical three-dimensional (3D) structures. Sheets of PSPS and NPS were cut to 10 × 20 mm samples, and their folding angles were plotted with respect to time, as obtained from in situ videography. In addition, the use of polyimide tape (Kapton) was investigated for controlling the direction of self-folding. Results show that folding happens on the opposite side of the sample with respect to the tape, regardless of which side the heating ribbon is on, or whether gravity is opposing the folding direction. The results are quantitatively explained using a viscoelastic finite element model capable of describing bidirectional folds arising from the interplay between viscoelastic relaxation and strain mismatch between polystyrene and polyimide. Given the tunability of fold times and the extent of local material flow, resistive-heat-assisted folding is a promising approach for manufacturing complex 3D lightweight structures by origami engineering. 

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2. 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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3. Creating Linkage Permutations to Prevent Self-Intersection and Enable Deployable Networks of Thick-Origami

   https://doi.org/10.1038/s41598-018-31180-4  

   Yellowhorse, Alden; Lang, Robert J.; Tolman, Kyler; Howell, Larry L. (August 2018, Scientific Reports)

   Abstract Origami concepts show promise for creating complex deployable systems. However, translating origami to thick (non-paper) materials introduces challenges, including that thick panels do not flex to facilitate folding and the chances for self-intersection of components increase. This work introduces methods for creating permutations of linkage-based, origami-inspired mechanisms that retain desired kinematics but avoid self-intersection and enable their connection into deployable networks. Methods for reconfiguring overconstrained linkages and implementing them as modified origami-inspired mechanisms are proved and demonstrated for multiple linkage examples. Equations are derived describing the folding behavior of these implementations. An approach for designing networks of linkage-based origami vertices is demonstrated and applications for tessellations are described. The results offer the opportunity to exploit origami principles to create deployable systems not previously feasible. 

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4. Architected Origami Materials: How Folding Creates Sophisticated Mechanical Properties

   https://doi.org/10.1002/adma.201805282  

   Li, Suyi; Fang, Hongbin; Sadeghi, Sahand; Bhovad, Priyanka; Wang, Kon‐Well (December 2018, Advanced Materials)

   Abstract Origami, the ancient Japanese art of paper folding, is not only an inspiring technique to create sophisticated shapes, but also a surprisingly powerful method to induce nonlinear mechanical properties. Over the last decade, advances in crease design, mechanics modeling, and scalable fabrication have fostered the rapid emergence of architected origami materials. These materials typically consist of folded origami sheets or modules with intricate 3D geometries, and feature many unique and desirable material properties like auxetics, tunable nonlinear stiffness, multistability, and impact absorption. Rich designs in origami offer great freedom to design the performance of such origami materials, and folding offers a unique opportunity to efficiently fabricate these materials at vastly different sizes. Here, recent studies on the different aspects of origami materials—geometric design, mechanics analysis, achieved properties, and fabrication techniques—are highlighted and the challenges ahead discussed. The synergies between these different aspects will continue to mature and flourish this promising field. 

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5. Variational Level Set Method for Topology Optimization of Origami Fold Patterns

   https://doi.org/10.1115/1.4053925  

   Ye, Qian; Gu, Xianfeng David; Chen, Shikui (August 2022, Journal of Mechanical Design)

   Abstract With specific fold patterns, a 2D flat origami can be converted into a complex 3D structure under an external driving force. Origami inspires the engineering design of many self-assembled and re-configurable devices. This work aims to apply the level set-based topology optimization to the generative design of origami structures. The origami mechanism is simulated using thin shell models where the deformation on the surface and the deformation in the normal direction can be simplified and well captured. Moreover, the fold pattern is implicitly represented by the boundaries of the level set function. The folding topology is optimized by minimizing a new multiobjective function that balances kinematic performance with structural stiffness and geometric requirements. Besides regular straight folds, our proposed model can mimic crease patterns with curved folds. With the folding curves implicitly represented, the curvature flow is utilized to control the complexity of the folds generated. The performance of the proposed method is demonstrated by the computer generation and physical validation of two thin shell origami designs. 

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