Theorem for the design of deployable kirigami tessellations with different topologies

Dang, Xiangxin; Feng, Fan; Duan, Huiling; Wang, Jianxiang

doi:10.1103/physreve.104.055006

Cited by 8 publications

(7 citation statements)

References 33 publications

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“…To address the former challenge, future research endeavors can explore more intricate kirigami unit-cell prototypes, explore the synergy of kirigami and origami techniques, or consider panel deformation to improve flexibility. Regarding the latter challenge, there is promise in enhancing our method with the integration of a recently proposed geometric theorem 28 concerning the inverse design of kirigami tessellations with varying topologies. Our findings shed light on the crucial role of the interplay between active materials, geometry, and stimuli in achieving physically stable morphologies.…”

Section: Discussionmentioning

confidence: 99%

“…It is important to acknowledge that although optimization-based inverse design methods have been proposed in the literature to achieve geometrical compatibility [26][27][28] , on which our method is built, they are unable to incorporate physical equilibrium requirements into the design process. This is due to the complex interactions among the panels and the strong elastic-magnetic coupling, as demonstrated in Fig.…”

Section: Physics-aware Differentiable Designmentioning

confidence: 99%

“…To further harness kirigami's shapemorphing capabilities for intricate functionalities, a recent inverse design framework has successfully relaxed the periodicity requirement in kirigami, creating optimized aperiodic cutting patterns to realize versatile deployed shapes 26 . This approach has been further extended to encompass various types of kirigami, addressing complex kinematic requirements such as compact reconfigurable designs 27 , and accommodating different topologies 28 . However, to the best of the authors' knowledge, existing inverse design processes for shape-morphing kirigami, including the aforementioned recent works, primarily focus on the design of geometries or kinematics but do not explicitly consider the physics 13,[29][30][31] .…”

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confidence: 99%

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Physics-aware differentiable design of magnetically actuated kirigami for shape morphing

Wang,

Chang,

et al. 2023

Nat Commun

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Shape morphing that transforms morphologies in response to stimuli is crucial for future multifunctional systems. While kirigami holds great promise in enhancing shape-morphing, existing designs primarily focus on kinematics and overlook the underlying physics. This study introduces a differentiable inverse design framework that considers the physical interplay between geometry, materials, and stimuli of active kirigami, made by soft material embedded with magnetic particles, to realize target shape-morphing upon magnetic excitation. We achieve this by combining differentiable kinematics and energy models into a constrained optimization, simultaneously designing the cuts and magnetization orientations to ensure kinematic and physical feasibility. Complex kirigami designs are obtained automatically with unparalleled efficiency, which can be remotely controlled to morph into intricate target shapes and even multiple states. The proposed framework can be extended to accommodate various active systems, bridging geometry and physics to push the frontiers in shape-morphing applications, like flexible electronics and minimally invasive surgery.

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Section: Discussionmentioning

confidence: 99%

Section: Physics-aware Differentiable Designmentioning

confidence: 99%

mentioning

confidence: 99%

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Physics-aware differentiable design of magnetically actuated kirigami for shape morphing

Wang,

Chang,

et al. 2023

Nat Commun

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“…1(A). Moreover, we suggest that this multi-compatibility design method can be extended to transform all over-constrained mechanisms, which are widely present in origami [39] and kirigami [40] tessellations and stackings, into multi-compatible structures. The outline of this paper is following: 1) the basic principle of multi-compatibility for MSTO structures to show the design framework; 2) the typical design cases of MSTO structures to validate the design framework, including two degree-4 single-vertex bi-stable thick origami structures, two degree-6 single-vertex tri-stable structures, and two degree-4 multi-vertex bi-stable structures; 3) the preliminary application, including a deployable tent, a deployable stair, and an impulsive robotic gripper.…”

Section: Introductionmentioning

confidence: 99%

Multi-Stable Origami Structures with Thick Panels

Li,

Wang,

Miao

et al. 2024

Preprint

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Multi-stable morphing structures can be self-locked, easily actuated, and generate impulsive motion, and origami mechanisms with thick panels have the practical combination of morphing ability and load-bearing capacity. In this paper, we combine the two and propose a method to design multi-stable thick-origami (MSTO) structures, where the stable configurations can be arbitrarily prescribed. Bi-stable degree-4 and tri-stable degree-6 vertices with the corresponding tessellations are designed, analyzed, manufactured, and experimentally tested. Compared to the original one-degree-of-freedom thick-origami mechanisms, the multi-stable/multi-compatible version in this paper has a larger design space with more achievable configurations due to the relaxation of compatibility constraints. In addition to the existent multi-stable origami designs, such as Kresling-ori tubes and vertex-inverting locking designs, this work provides a new form of multi-stable origami with 2 to 3 arbitrarily prescribable stable configurations. Preliminary applications like self-locking deployable furniture and an impulsive gripper are demonstrated, which suggest a promising and potential prospect in many engineering fields such as deployable architectures and robotic devices.

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“…Deterministic approaches to kirigami have primarily focused on understanding the geometry and mechanical response of periodic cut patterns, with tiles ranging from simple regular polygons [3] to more general wallpaper group patterns [4][5][6]. Complementing this, the design of non-periodic kirigami patterns modulates the geometry [7][8][9][10][11] and the topology [12][13][14] of the cut patterns to achieve different geometric and mechanical properties.…”

Section: Introductionmentioning

confidence: 99%

Explosive rigidity percolation in kirigami

2023

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Controlling the connectivity and rigidity of kirigami, i.e. the process of cutting paper to deploy it into an articulated system, is critical in the manifestations of kirigami in art, science and technology, as it provides the resulting metamaterial with a range of mechanical and geometric properties. Here, we combine deterministic and stochastic approaches for the control of rigidity in kirigami using the power of k choices, an approach borrowed from the statistical mechanics of explosive percolation transitions. We show that several methods for rigidifying a kirigami system by incrementally changing either the connectivity or the rigidity of individual components allow us to control the nature of the explosive transition by a choice of selection rules. Our results suggest simple lessons for the design of mechanical metamaterials.

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Theorem for the design of deployable kirigami tessellations with different topologies

Cited by 8 publications

References 33 publications

Physics-aware differentiable design of magnetically actuated kirigami for shape morphing

Physics-aware differentiable design of magnetically actuated kirigami for shape morphing

Multi-Stable Origami Structures with Thick Panels

Explosive rigidity percolation in kirigami

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