Undulations in tubular origami tessellations: A connection to area-preserving maps
Origami tessellations, whose crease pattern has translational symmetries, have attracted significant attention in designing the mechanical properties of objects. Previous origami-based engineering applications have been designed based on the “uniform-folding” of origami tessellations, where the fold...
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Published in | Chaos (Woodbury, N.Y.) Vol. 33; no. 8 |
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Main Authors | , |
Format | Journal Article |
Language | English |
Published |
United States
01.08.2023
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Online Access | Get full text |
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Summary: | Origami tessellations, whose crease pattern has translational symmetries, have attracted significant attention in designing the mechanical properties of objects. Previous origami-based engineering applications have been designed based on the “uniform-folding” of origami tessellations, where the folding of each unit cell is identical. Although “nonuniform-folding” allows for nonlinear phenomena that are impossible through uniform-folding, there is no universal model for nonuniform-folding, and the underlying mathematics for some observed phenomena remains unclear. Wavy folded states that can be achieved through nonuniform-folding of the tubular origami tessellation called a waterbomb tube are an example. Recently, the authors formulated the kinematic coupled motion of unit cells within a waterbomb tube as the discrete dynamical system and identified a correspondence between its quasiperiodic solutions and wavy folded states. Here, we show that the wavy folded state is a universal phenomenon that can occur in the family of rotationally symmetric tubular origami tessellations. We represent their dynamical system as the composition of the two 2D mappings: taking the intersection of three spheres and crease pattern transformation. We show the universality of the wavy folded state through numerical calculations of phase diagrams and a geometric proof of the system’s conservativeness. Additionally, we present a non-conservative tubular origami tessellation, whose crease pattern includes scaling. The result demonstrates the potential of the dynamical system model as a universal model for nonuniform-folding or a tool for designing metamaterials. |
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ISSN: | 1054-1500 1089-7682 |
DOI: | 10.1063/5.0160803 |