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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Critical slowing down in purely elastic 'snap-through' instabilities
TL;DR: In this article, the dynamics of snap-through instabilities, a widespread phenomenon in their own right, are shown to display critical scaling properties, which are well understood in a wide range of physical systems.
Journal ArticleDOI
Kirigami-Inspired Inflatables with Programmable Shapes
Lishuai Jin,Lishuai Jin,Antonio Forte,Antonio Forte,Bolei Deng,Ahmad Rafsanjani,Katia Bertoldi,Katia Bertoldi +7 more
TL;DR: Kirigami principles are exploited to design inflatables that can mimic target shapes upon pressurization and can selectively manipulate the parameters of the single units to allow the reproduction of features at different scales and ultimately enable a more accurate mimicking of the target.
Journal ArticleDOI
Desolvation Induced Origami of Photocurable Polymers by Digit Light Processing.
Zeang Zhao,Zeang Zhao,Jiangtao Wu,Xiaoming Mu,Haosen Chen,H. Jerry Qi,Daining Fang,Daining Fang +7 more
TL;DR: In this new method, flat polymer sheets can be cured by a light field from a commercial projector with varying intensity, and the self-folding process is triggered by desolvation in water, which can be used for responsive actuators and the fabrication of 3D electronic devices.
Journal ArticleDOI
Multistable inflatable origami structures at the metre scale.
David Melancon,Benjamin Gorissen,Carlos J. García-Mora,Carlos J. García-Mora,Chuck Hoberman,Katia Bertoldi,Katia Bertoldi +6 more
TL;DR: In this paper, a library of foldable origami shapes is created and then combined with a single fluidic pressure input to construct a rigid-walled deployable structure that can lock in place after deployment.
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.
Journal ArticleDOI
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.