Freeform quad-based kirigami

Jiang, Caigui; Rist, Florian; Pottmann, Helmut; Wallner, Johannes

doi:10.1145/3414685.3417844

Cited by 23 publications

(8 citation statements)

References 29 publications

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“…One way to easily construct spatial shapes from flat sheets is by appropriately folding paper [Dudte et al 2016;Massarwi et al 2007], which is inherently related to the Japanese art of Origami. Also Kirigami, a technique to cut patterns into planar sheets to allow solid faces to rotate about each other, deforming in three dimensions while remaining planar has been explored for deployable surfaces [Jiang et al 2020;Liu et al 2020] and recently also bi-stable structures .…”

Section: Related Workmentioning

confidence: 99%

Generalized deployable elastic geodesic grids

Pillwein

Weiss²

2021

ACM Trans. Graph.

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Given a designer created free-form surface in 3d space, our method computes a grid composed of elastic elements which are completely planar and straight. Only by fixing the ends of the planar elements to appropriate locations, the 2d grid bends and approximates the given 3d surface. Our method is based purely on the notions from differential geometry of curves and surfaces and avoids any physical simulations. In particular, we introduce a well-defined elastic grid energy functional that allows identifying networks of curves that minimize the bending energy and at the same time nestle to the provided input surface well. Further, we generalize the concept of such grids to cases where the surface boundary does not need to be convex, which allows for the creation of sophisticated and visually pleasing shapes. The algorithm finally ensures that the 2d grid is perfectly planar, making the resulting gridshells inexpensive, easy to fabricate, transport, assemble, and finally also to deploy. Additionally, since the whole structure is pre-strained, it also comes with load-bearing capabilities. We evaluate our method using physical simulation and we also provide a full fabrication pipeline for desktop-size models and present multiple examples of surfaces with elliptic and hyperbolic curvature regions. Our method is meant as a tool for quick prototyping for designers, architects, and engineers since it is very fast and results can be obtained in a matter of seconds.

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Section: Related Workmentioning

confidence: 99%

Generalized deployable elastic geodesic grids

Pillwein

Weiss²

2021

ACM Trans. Graph.

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“…Previous work has demonstrated that the checkerboard kirigami pattern can be used to approximate almost any form of curved surface. [ 43 ] However, its mechanical properties under external loads are still uncovered. Herein, we are primarily interested in both the mechanical strength and shape‐transforming of the checkerboard kirigami.…”

Section: Introductionmentioning

confidence: 99%

Kirigami Design and Modeling for Strong, Lightweight Metamaterials

Zhang

Paik

2022

Adv Funct Materials

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Kirigami is the art of paper cutting, and it is emerging as an elegant design and manufacturing solution in mechanical metamaterials. Currently, the majority of kirigami designs focus on shape-morphing, but there is little attention on the remarkable mechanical properties they can produce: high strength to weight ratio where they can bear thousands of times of their own weight. This paper proposes a kirigami-based, strong, yet lightweight metamaterial, which is created by folding pop-up and pop-down from a checkerboard pattern with blocks. To transform the kirigami metamaterial into arbitrary objects, the challenge lies in how to automatically design the kirigami folding to approximate the outline of the object. Herein, a computational model that is based on deploying discretized objects onto a planar sheet is proposed. Additionally, to achieve high strength, a glue-free connector that can lock the collocated cuts in the folded configuration is designed. The standard compression tests show that the kirigami metamaterial, weighing 12.05 g, can carry 346.4 N payloads. Meanwhile, six examples of curved surfaces are prototyped to verify the shape transforming capability of the proposed kirigami metamaterial. This study paves the way towards using the kirigami technique for weight reduction in industrial applications.

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“…The previous works mostly focus on varying the sizes and orientations of cuts under fixed connections on an intact sheet without defects such as holes or cracks, that is, the topology of the sheet is fixed. The kirigami patterns perforated on flat sheets with flexible topologies are investigated in [20][21][22][23][24], where the deployability is realized by folding to close the cutting holes. Conversely, many other kirigami structures are deployed in the way of opening cuts, among which the quadrilateral tessellations are extensively used to achieve unique properties such as reconfigurability [16,25], high stretchability [26,27], and auxeticity [28,29].…”

Section: Introductionmentioning

confidence: 99%

Theorem for the design of deployable kirigami tessellations with different topologies

Dang,

Feng,

Duan

et al. 2021

Preprint

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The concept of kirigami has been extensively utilized to design deployable structures and reconfigurable metamaterials. Despite heuristic utilization of classical kirigami patterns, the gap between complex kirigami tessellations and systematic design principles still needs to be filled. In this paper, we develop a unified design method for deployable quadrilateral kirigami tessellations perforated on flat sheets with different topologies. This method is based on the parameterization of kirigami patterns formulated as the solution of a linear equation system. The geometric constraints for the deployability of parameterized cutting patterns are given by a unified theorem covering different topologies of the flat sheets. As an application, we employ the design method to achieve desired shapes along the deployment path of kirigami tessellations, while preserving the topological characteristics of the flat sheets. Our approach introduces new perspectives for the topological design of kirigami-inspired structures and metamaterials.

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Freeform quad-based kirigami

Cited by 23 publications

References 29 publications

Generalized deployable elastic geodesic grids

Generalized deployable elastic geodesic grids

Kirigami Design and Modeling for Strong, Lightweight Metamaterials

Theorem for the design of deployable kirigami tessellations with different topologies

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