Programming curvature using origami tessellations
TLDR
In this article, scale-independent elementary geometric constructions and constrained optimization algorithms can be used to determine spatially modulated patterns that yield approximations to given surfaces of constant or varying curvature.Abstract:
Origami describes rules for creating folded structures from patterns on a flat sheet, but does not prescribe how patterns can be designed to fit target shapes. Here, starting from the simplest periodic origami pattern that yields one-degree-of-freedom collapsible structures-we show that scale-independent elementary geometric constructions and constrained optimization algorithms can be used to determine spatially modulated patterns that yield approximations to given surfaces of constant or varying curvature. Paper models confirm the feasibility of our calculations. We also assess the difficulty of realizing these geometric structures by quantifying the energetic barrier that separates the metastable flat and folded states. Moreover, we characterize the trade-off between the accuracy to which the pattern conforms to the target surface, and the effort associated with creating finer folds. Our approach enables the tailoring of origami patterns to drape complex surfaces independent of absolute scale, as well as the quantification of the energetic and material cost of doing so.read more
Citations
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Deployment kinematics of axisymmetric Miura origami: Unit cells, tessellations, and stacked metamaterials
TL;DR: In this article , the deployment kinematics of axisymmetric Miura origami from unit cells to single-layer tessellations and multi-layer stacked metamaterials are investigated.
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Response of Graded Miura-Ori Metamaterials to Quasi-Static and Dynamic In-Plane Compression
TL;DR: In this paper , a non-unique relationship between the density and quasi-static strength of Miura-ori metamaterials was explored for graded materials with respect to quasistatic and dynamic in-plane compression.
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Pop-up kirigami for stiff, dome-like structures
TL;DR: In this article, a design for a pop-up kirigami system that achieves symmetric, positive Gaussian curvature by taking advantage of an internal infinitesimal mechanism is presented.
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Harnessing architected stiffeners to manufacture origami-inspired foldable composite structures
TL;DR: In this article, a cost-effective compression molding technique is employed to develop origami-inspired fiber-reinforced foldable-composite structures, which are demonstrated for two typical composite geometries, namely, an origamiinspired triangulated cylinder with a spiral configuration and a single-DOF reverse-folder flat flasher design.
Advanced Manufacturing of Lightweight Porous Carbide Shapes Using Renewable Resources
TL;DR: In this article, a method for synthesis of porous metal carbide material from fibrous biopolymers is presented. But this method requires the fabrication of 3D shapes of porous carbide materials.
References
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Journal ArticleDOI
Spontaneous formation of ordered structures in thin films of metals supported on an elastomeric polymer
TL;DR: In this paper, the authors describe the appearance of complex, ordered structures induced by the buckling of thin metal films owing to thermal contraction of an underlying substrate, and account qualitatively for the size and form of the patterned features in terms of the nonuniform stresses developed in the film near steps on the polymer substrate.
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Using origami design principles to fold reprogrammable mechanical metamaterials
Jesse L. Silverberg,Arthur A. Evans,Lauren McLeod,Ryan C. Hayward,Thomas C. Hull,Christian D. Santangelo,Itai Cohen +6 more
TL;DR: Working with the Miura-ori tessellation, it is found that each unit cell of this crease pattern is mechanically bistable, and by switching between states, the compressive modulus of the overall structure can be rationally and reversibly tuned.
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Geometry of Miura-folded metamaterials
Mark Schenk,Simon D. Guest +1 more
TL;DR: This paper describes two folded metamaterials based on the Miura-ori fold pattern, where the fold pattern provides a negative Poisson’s ratio for in-plane deformations and a positive Poisson's ratio for out-of-plane bending.
Book
Geometric Folding Algorithms: Linkages, Origami, Polyhedra
Erik D. Demaine,Joseph O'Rourke +1 more
TL;DR: Aimed primarily at advanced undergraduate and graduate students in mathematics or computer science, this lavishly illustrated book will fascinate a broad audience, from high school students to researchers.