Exactly solvable flat-foldable quadrilateral origami tilings
Exactly solvable flat-foldable quadrilateral origami tilings
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精确可解的可平折四边形折纸瓷砖
DOI：
10.1103/physreve.98.032112
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发表时间：
2017
影响因子：
2.4
通讯作者：
M. Assis
中科院分区：
文献类型：
--
作者：
M. Assis
我们考虑几个四边形折纸平铺，包括三浦ori折痕图案，允许折痕反转缺陷以上的基态保持当地的平面折叠。使用完全可解的模型，我们表明，这些折纸平铺可以有相变的折痕状态变量的函数，作为一个函数的折痕周围的顶点的安排，并作为一个函数的局部层排序的相邻面。我们使用交错奇数8顶点模型的精确解决的情况下，以及巴克斯特的精确解决的正方形格子上的3-着色问题来研究这些折纸平铺。通过将折痕反转缺陷视为晶格气体，我们找到了它们的密度的精确解析表达式，这与折纸材料的弹性模量直接相关。密度和相变分析对使用这些折纸瓦片作为可调超材料有影响;例如，我们的分析表明，Miura-ori的密度比Barreto的Mars更可调。我们还发现，有一个更广泛的可调谐性作为分层缺陷的密度的函数相比，作为一个函数的折痕顺序缺陷的密度在相变点之前达到的功能;材料和机械性能，取决于局部层排序属性将有更大的可调谐性。另一方面，Barreto's Mars的缺陷密度可以在不经过相变点的情况下增加直到饱和。我们进一步考虑放松的要求，局部平面折叠映射到一个可解的情况下，16顶点模型，证明了不同的相变点，这种情况下。
We consider several quadrilateral origami tilings, including the Miura-ori crease pattern, allowing for crease-reversal defects above the ground state which maintain local flat-foldability. Using exactly solvable models, we show that these origami tilings can have phase transitions as a function of crease state variables, as a function of the arrangement of creases around vertices, and as a function of local layer orderings of neighboring faces. We use the exactly solved cases of the staggered odd 8-vertex model as well as Baxter's exactly solved 3-coloring problem on the square lattice to study these origami tilings. By treating the crease-reversal defects as a lattice gas, we find exact analytic expressions for their density, which is directly related to the origami material's elastic modulus. The density and phase transition analysis has implications for the use of these origami tilings as tunable metamaterials; our analysis shows that Miura-ori's density is more tunable than Barreto's Mars, for example. We also find that there is a broader range of tunability as a function of the density of layering defects compared to as a function of the density of crease order defects before the phase transition point is reached; material and mechanical properties that depend on local layer ordering properties will have a greater amount of tunability. The defect density of Barreto's Mars, on the other hand, can be increased until saturation without passing through a phase transition point. We further consider relaxing the requirement of local flat-foldability by mapping to a solvable case of the 16-vertex model, demonstrating a different phase transition point for this case.
影响因子：
17.3
作者：
Randall, Christina L.;Gultepe, Evin;Gracias, David H.
通讯作者：
Gracias, David H.
影响因子：
16.1
作者：
Fernandes, Rohan;Gracias, David H.
通讯作者：
Gracias, David H.
影响因子：
4.1
作者：
Mulakkal, Manu C.;Seddon, Annela M.;Trask, Richard S.
通讯作者：
Trask, Richard S.