2020
DOI: 10.1073/pnas.1909164117
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Deterministic and stochastic control of kirigami topology

Abstract: Kirigami, the creative art of paper cutting, is a promising paradigm for mechanical metamaterials. However, to make kirigami-inspired structures a reality requires controlling the topology of kirigami to achieve connectivity and rigidity. We address this question by deriving the maximum number of cuts (minimum number of links) that still allow us to preserve global rigidity and connectivity of the kirigami. A deterministic hierarchical construction method yields an efficient topological way to control both the… Show more

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Cited by 22 publications
(27 citation statements)
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“…Finally, we study the mechanics of the patterns by considering their infinitesimal rigidity [15,34]. More specifically, we construct a rigidity matrix A using the length and connectivity constraints given by each pattern, which allows us to determine the total internal degrees of freedom…”
Section: (D) Shows a Physical Model Of A Deployablementioning
confidence: 99%
See 1 more Smart Citation

Quasicrystal kirigami

Liu,
Choi,
Mahadevan
2021
Preprint
Self Cite
“…Finally, we study the mechanics of the patterns by considering their infinitesimal rigidity [15,34]. More specifically, we construct a rigidity matrix A using the length and connectivity constraints given by each pattern, which allows us to determine the total internal degrees of freedom…”
Section: (D) Shows a Physical Model Of A Deployablementioning
confidence: 99%
“…The simple idea of introducing cuts in a sheet of material has led to a surprisingly wide range of applications, including the design of super-stretchable materials [1], nanocomposites [2, 3], energy-storing devices [4] and robotics [5]. Numerous works have been devoted to the design of deployable kirigami patterns based on triangles [6], quads [7,8] or even ancient Islamic tiling patterns [9], with recent efforts on generalizing their cut geometry [10][11][12][13][14] and cut topology [15,16].Almost without exception, these prior studies have manipulated the geometry, topology, and mechanics of tiling patterns with translational symmetry, most recently using periodic deployable 1…”
mentioning
confidence: 99%

Quasicrystal kirigami

Liu,
Choi,
Mahadevan
2021
Preprint
Self Cite
“…We note that in the two-dimensional case presented in [20], proving that the theoretical lower bound of the links for rigidification can be achieved requires multiple steps for handling different problem sizes (even number, odd primes, odd prime powers etc.). By contrast, as shown in the proof of theorem 2.1, the optimal lower bound for the three-dimensional case considered in this work can be achieved more directly without involving the complicated cases.…”
Section: Deterministic Control Of Rectangular Prismatic Assembliesmentioning
confidence: 99%
“…Recently, there have been attempts to explore generalizations of the cut geometry (9,10) and cut topology (11) moving away from purely periodic deployable kirigami base patterns. However, it is still unclear how one might explore such base patterns systematically.…”
Section: Introductionmentioning
confidence: 99%

Wallpaper group kirigami

Liu,
Choi,
Mahadevan
2021
Preprint
Self Cite