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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Journal ArticleDOI
Gauss Map Based Curved Origami Discretization
TL;DR: In this article, the Gauss map is utilized to investigate the normal curvature change of the curved surface, which leads to the curvature discretization of curved surface being transferred to the normal direction discretisation of spherical curves.
Book ChapterDOI
Perspectives of 3D and 4D bioprinting
TL;DR: In this paper , the authors discuss the likely roles of mathematical modeling in the progress of bioprinting, and their envisioned impact on tissue engineering and regenerative medicine, and conclude with a daring outlook on potential applications of 3D and 4D biopprinting.
Posted Content
Parametrizing Flat-Foldable Surfaces with Incomplete Data.
Di Qiu,Ka Chun Lam,Lok Ming Lui +2 more
TL;DR: A novel way of computing surface folding maps via solving a linear PDE, where the crucial quantity that characterizes the geometry occurs as the coefficient of the equation, namely the Beltrami coefficient is proposed.
Origami-based structures with programmable properties
TL;DR: A novel cellular metamaterial constructed from origami building blocks based on Miura-ori fold is presented and an origami “string” is introduced: a slender structure with a programmable trajectory that demonstrates capabilities of the proposed origami strings for robotics application such as a robotic gripper and a biomimetic hand.
Posted Content
Architected kirigami metamorphosis.
Yanbin Li,Jie Yin +1 more
TL;DR: In this article, a new class of three-dimensional modular kirigami by introducing cuts on cuboid-shaped objects, based on which constructing two quasi-three-15 dimensional architected Kirigamis with even-flat structural form.
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.