Programming curvature using origami tessellations.

By Levi H. Dudte, Etienne Vouga, Tomohiro Tachi, L. Mahadevan. Nature Materials, 2016

475 citations recorded by the source corpus.

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.

Subfields: Biomedical Engineering, Mechanical Engineering, Human-Computer Interaction

View Paper: https://www.semanticscholar.org/paper/474a0f972a1f02097c67324c81e38202fd02863e

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Citations in the corpus

Critical slowing down in purely elastic ‘snap-through’ instabilities (2016, background): “Many elastic structures have two possible equilibrium states [1]: from umbrellas that become inverted in a sudden gust of wind, to nanoelectromechanical switches [2, 3], origami patterns [4, 5] and the hopper popper, which jumps after being turned inside-out [6].”
Harnessing Interpretable Machine Learning for Origami Feature Design and Pattern Selection (2022, methodology): “So far, most research on origami inverse design focuses on kinematical shape fitting (e.g. (12, 13, 15)).”
Mechanical metamaterials: a state of the art (2019, methodology): “A remarkable example of a metamaterial inspired by origami is provided by the Miura-ori tessellated structure, which is shown in Figure 1c in [94].”
Bar and hinge models for scalable analysis of origami (2017, methodology): “The energy approach has been modified and has been used to provide fundamental studies on origami (Silverberg et al., 2014; Dudte et al., 2016).”
Bistable Auxetic Mechanical Metamaterials Inspired by Ancient Geometric Motifs (2016, methodology): “Moreover, origami [27, 28, 29] and kirigami [30, 31, 32], respectively known as the arts of folding and cutting of paper, provide an alternative tool for designing auxetic metamaterials.”