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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Plasticity-induced origami for assembly of three dimensional metallic structures guided by compressive buckling
Yan Shi,Fan Zhang,Kewang Nan,Xueju Wang,Juntong Wang,Yijie Zhang,Yutong Zhang,Haiwen Luan,Keh Chih Hwang,Yonggang Huang,John A. Rogers,Yihui Zhang +11 more
TL;DR: In this paper, a model system that consists of a 2D precursor in the form of a straight ribbon with reduced widths at certain sections is used to demonstrate the important role of plasticity in the course of folding, in such a manner that dictates the final 3D layouts.
Journal ArticleDOI
Folding to Curved Surfaces: A Generalized Design Method and Mechanics of Origami-based Cylindrical Structures.
TL;DR: An in-plane design method is proposed to approximate curved surfaces of interest with generalized Miura-ori units and generates multiple types of cylindrical structures, extending the design space of mechanical metamaterials and providing a basis for their practical applications in science and engineering.
Journal ArticleDOI
Mechanically Guided Post-Assembly of 3D Electronic Systems
Bong Hoon Kim,Fei Liu,Yongjoon Yu,Hokyung Jang,Zhaoqian Xie,Zhaoqian Xie,Kan Li,Kan Li,Jungyup Lee,Ji Yoon Jeong,Arin Ryu,Yechan Lee,Do Hoon Kim,Xueju Wang,Kun Hyuck Lee,Jong Yoon Lee,Sang Min Won,Nuri Oh,Jeonghyun Kim,Ju Young Kim,Seong Jun Jeong,Kyung In Jang,Seungmin Lee,Yonggang Huang,Yihui Zhang,John A. Rogers +25 more
Journal ArticleDOI
FlexMaps: computational design of flat flexible shells for shaping 3D objects
Luigi Malomo,Jesús Pérez,Emmanuel Iarussi,Nico Pietroni,Eder Miguel,Paolo Cignoni,Bernd Bickel +6 more
TL;DR: This work starts by mapping the 3D surface onto a 2D domain as in traditional UV mapping to design a set of deformable flat panels called FlexMaps, a novel framework for fabricating smooth shapes out of flat, flexible panels with tailored mechanical properties.
Journal ArticleDOI
Decoupling local mechanics from large-scale structure in modular metamaterials
Nan Yang,Jesse L. Silverberg +1 more
TL;DR: A design strategy for constructing 1D, 2D, and 3D mechanical metamaterials inspired by modular origami and kirigami is introduced, to assemble a number of modules into a voxelized large-scale structure, where the module's design has a greater number of mechanical design parameters than the number of constraints imposed by bulk assembly.
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.
Journal ArticleDOI
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.