Design of cut unit geometry in hierarchical kirigami-based auxetic metamaterials for high stretchability and compressibility

Tang, Yichao; Yin, Jie

doi:10.1016/j.eml.2016.07.005

Cited by 197 publications

(144 citation statements)

References 25 publications

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“…etic structures (13,14), super-stretchable sheets (15)(16)(17)(18)(19) etc. However, almost without exception, these studies study the forward problem of understanding the behavior given the topology and geometry of the tessellations.…”

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confidence: 99%

Programming shape using kirigami tessellations

2019

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Kirigami tessellations, regular planar patterns formed by cutting flat, thin sheets, have attracted recent scientific interest for their rich geometries, surprising material properties and promise for technologies. Here we pose and solve the inverse problem of designing the number, size, and orientation of cuts that allows us to convert a closed, compact regular kirigami tessellation of the plane into a deployment that conforms approximately to any prescribed target shape in two and three dimensions. We do this by first identifying the constraints on the lengths and angles of generalized kirigami tessellations which guarantee that their reconfigured face geometries can be contracted from a non-trivial deployed shape to a novel planar cut pattern. We encode these conditions in a flexible constrained optimization framework which allows us to deform the geometry of periodic kirigami tesselations with three, four, and sixfold symmetry, among others, into generalized kirigami patterns that deploy to a wide variety of prescribed boundary target shapes. Physically fabricated models verify our inverse design approach and allow us to determine the tunable material response of the resulting structures. We then extend our 1 arXiv:1812.08644v1 [cond-mat.soft] 20 Dec 2018 framework to create generalized kirigami patterns that deploy to approximate curved surfaces in R 3 . Altogether, this work illustrates a novel framework for designing complex, shape-changing sheets from simple cuts showing the power of kirigami tessellations as flexible mechanical metamaterials.Kirigami is the creative art of paper cutting and folding that originated in Japan. Kirigami tessellations, which are regular planar patterns formed by cuts, have recently emerged as paradigms of mechanical metamaterials. Various studies have focused on their geometry and kinematics (1-3), the mechanics of their deployment (4-9), the mathematics of their constructions (10), and as materials with a range of unusual properties such as topological insulators (11, 12), aux-

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Programming shape using kirigami tessellations

2019

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“…In recent years, origami [1][2][3][4][5][6][7][8][9] and kirigami [10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27] have become emergent tools to design programmable and reconfigurable mechanical metamaterials. Origamiinspired metamaterials are created by folding thin sheets along predefined creases, whereas kirigami allows the practitioner to exploit cuts in addition to folds to achieve large deformations and create 3D objects from a flat sheet.…”

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confidence: 99%

Buckling-Induced Kirigami

2017

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“…With kirigami, the roles of Figure 4: a. Morphing with halftone lithography adapted from [240], b. non-Euclidean plates adapted from [241], c. a monkey saddle, adapted from [242], d. pollen grain isometry of a spherical cap, related to the work in [12], e. 4D printing using shape memory polymer joints, adapted from [243], and f. active printed meshes, adapted from [244]. topology [220] and geometry are once again at the heart of design rules that enable targeted shape changes [221,222,223]. Mechanics enters the picture by enabling these flat sheets to buckle into 3D structures when stretched or compressed beyond a critical point [16,224].…”

Section: Origami and Kirigamimentioning

confidence: 99%