Lattice modes of periodic origami tessellations with voids

IF 1.9 4区 工程技术 Q3 MECHANICS
Anandaroop Lahiri, Phanisri P. Pratapa
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Abstract

Elastic modes of origami lattices are of scientific value in the context of metamaterial applications. Miura-ori is a well-studied origami pattern, especially in engineering. A deeper understanding of spatially homogeneous deformations can be useful to homogenization-based material characterization. Miura-ori with rigid parallelogram panels deforms exclusively through crease-folding as a single degree of freedom (DOF) system. Substituting parallelograms with rigid triangular panels introduces two additional DOFs per vertex and could admit a rich space of lattice deformations. In this paper, we investigate the lattice modes of rigid triangulated Miura-ori (RTM) with enclosed voided regions within the tessellations. We use two widely adopted approaches — the bar and hinge framework (BHF) and a folding-angle framework (FAF), that are typically used for the analysis of origami lattices. Unlike the 2D RTM lattice without voids, we find that for the origami lattices with voids, the compatibility constraints based on the crease folding-angles alone are insufficient to capture the admissible deformation modes. Additional loop-closure constraints, based on Denavit–Hartenberg analysis of spatial linkages, must be imposed on creases around each enclosed void. We observe that the homogeneous modes with accumulation of deformations across the lattice are exclusive to the space of Bloch-wave modes within the FAF approach and are not straightforwardly obtained using BHF approach of modeling origami lattices. The 2D RTM lattices with voids, irrespective of the size and aspect ratio of enclosed voids, are found to exhibit exactly six such exclusive FAF modes which can be further characterized using intuitively defined relations between crease angle perturbations.

带空洞的周期折纸镶嵌的晶格模式
折纸晶格的弹性模态在超材料应用中具有重要的科学价值。Miura-ori是一种经过充分研究的折纸图案,尤其是在工程领域。更深入地了解空间均匀变形可以用于均匀化为基础的材料表征。具有刚性平行四边形面板的Miura-ori仅通过折痕折叠作为单自由度(DOF)系统进行变形。用刚性三角形面板代替平行四边形,每个顶点引入了两个额外的自由度,并且可以允许丰富的晶格变形空间。在本文中,我们研究了具有封闭空区域的刚性三角化Miura-ori (RTM)的点阵模式。我们使用了两种广泛采用的方法-杆铰框架(BHF)和折叠角框架(FAF),这两种方法通常用于分析折纸晶格。与无孔洞的二维RTM折纸晶格不同,我们发现对于有孔洞的折纸晶格,仅基于折痕折叠角的相容性约束不足以捕获允许的变形模式。基于空间连杆机构的Denavit-Hartenberg分析,必须对每个封闭空隙周围的折痕施加额外的闭环约束。我们观察到,具有变形累积的均匀模态是FAF方法中布洛赫波模态空间所独有的,并且不能直接使用BHF方法建模折纸晶格。无论封闭空洞的大小和纵横比如何,具有空洞的二维RTM晶格都显示出六种这样的专属FAF模式,这些模式可以使用直观定义的折痕角扰动之间的关系进一步表征。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
CiteScore
4.10
自引率
4.20%
发文量
114
审稿时长
9 months
期刊介绍: Mechanics Research Communications publishes, as rapidly as possible, peer-reviewed manuscripts of high standards but restricted length. It aims to provide: • a fast means of communication • an exchange of ideas among workers in mechanics • an effective method of bringing new results quickly to the public • an informal vehicle for the discussion • of ideas that may still be in the formative stages The field of Mechanics will be understood to encompass the behavior of continua, fluids, solids, particles and their mixtures. Submissions must contain a strong, novel contribution to the field of mechanics, and ideally should be focused on current issues in the field involving theoretical, experimental and/or applied research, preferably within the broad expertise encompassed by the Board of Associate Editors. Deviations from these areas should be discussed in advance with the Editor-in-Chief.
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