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1. Control of connectivity and rigidity in prismatic assemblies

   https://doi.org/10.1098/rspa.2020.0485  

   Choi, Gary P. ; Chen, Siheng ; Mahadevan, L. ( December 2020 , Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences)

   null (Ed.)

   How can we manipulate the topological connectivity of a three-dimensional prismatic assembly to control the number of internal degrees of freedom and the number of connected components in it? To answer this question in a deterministic setting, we use ideas from elementary number theory to provide a hierarchical deterministic protocol for the control of rigidity and connectivity. We then show that it is possible to also use a stochastic protocol to achieve the same results via a percolation transition. Together, these approaches provide scale-independent algorithms for the cutting or gluing of three-dimensional prismatic assemblies to control their overall connectivity and rigidity. 

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2. Programmable active kirigami metasheets with more freedom of actuation

   https://doi.org/10.1073/pnas.1906435116  

   Tang, Yichao ; Li, Yanbin ; Hong, Yaoye ; Yang, Shu ; Yin, Jie ( December 2019 , Proceedings of the National Academy of Sciences)

   Kirigami (cutting and/or folding) offers a promising strategy to reconfigure metamaterials. Conventionally, kirigami metamaterials are often composed of passive cut unit cells to be reconfigured under mechanical forces. The constituent stimuli-responsive materials in active kirigami metamaterials instead will enable potential mechanical properties and functionality, arising from the active control of cut unit cells. However, the planar features of hinges in conventional kirigami structures significantly constrain the degrees of freedom (DOFs) in both deformation and actuation of the cut units. To release both constraints, here, we demonstrate a universal design of implementing folds to reconstruct sole-cuts–based metamaterials. We show that the supplemented folds not only enrich the structural reconfiguration beyond sole cuts but also enable more DOFs in actuating the kirigami metasheets into 3 dimensions (3D) in response to environmental temperature. Utilizing the multi-DOF in deformation of unit cells, we demonstrate that planar metasheets with the same cut design can self-fold into programmable 3D kirigami metastructures with distinct mechanical properties. Last, we demonstrate potential applications of programmable kirigami machines and easy-turning soft robots.

    

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3. Rapid Design of Fully Soft Deployable Structures Via Kirigami Cuts and Active Learning

   https://doi.org/10.1002/admt.202301305  

   Ma, Leixin ; Mungekar, Mrunmayi ; Roychowdhury, Vwani ; Jawed, M. K. ( January 2024 , Advanced Materials Technologies)

   Soft deployable structures – unlike conventional piecewise rigid deployables based on hinges and springs – can assume intricate 3‐D shapes, thereby enabling transformative soft robotic and manufacturing technologies. Their virtually infinite degrees of freedom allow precise control over the final shape. The same enabling high dimensionality, however, poses a challenge for solving the inverse problem: fabrication of desired 3D structures requires manufacturing technologies with extensive local actuation and control, and a trial‐and‐error search over a large design space. Both of these shortcomings are addressed by first developing a simplified planar fabrication approach that combines two ingredients: strain mismatch between two layers of a composite shell and kirigami cuts that relieves localized stress. In principle, it is possible to generate targeted 3‐D shapes by designing the appropriate kirigami cuts and the amount of prestretch (without any local control). Second, a data‐driven physics‐guided framework is formulated that reduces the dimensionality of the inverse design problem using autoencoders and efficiently searches through the “latent” parameter space in an active learning approach. The rapid design procedure is demonstrated via a range of target shapes, such as peanuts, pringles, flowers, and pyramids. Experiments and our numerical predictions are found to be in good agreement.

    

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4. 3D Transformable Modular Kirigami Based Programmable Metamaterials

   https://doi.org/10.1002/adfm.202105641  

   Li, Yanbin ; Zhang, Qiuting ; Hong, Yaoye ; Yin, Jie ( July 2021 , Advanced Functional Materials)

   Kirigami, the ancient paper art of cutting, has recently emerged as a new approach to construct metamaterials with novel properties imparted by cuts. However, most studies are limited to thin sheets‐based 2D kirigami metamaterials with specific forms and limited reconfigurability due to planar connection constraints of cut units. Here, 3D modular kirigami is introduced by cutting bulk materials into spatially closed‐loop connected cut cubes to construct a new class of 3D kirigami metamaterials. The module is transformable with multiple degrees of freedom that can transform into versatile distinct daughter building blocks. Their conformable assembly creates a wealth of reconfigurable and disassemblable metamaterials with diverse structures and unique properties, including reconfigurable 1D column‐like materials, 2D lattice‐like metamaterials with phase transition of chirality, as well as 3D frustration‐free multilayered metamaterials with 3D auxetic behaviors and programmable deformation modes. This study largely expands the design space of kirigami metamaterials from 2D to 3D.

    

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5. Explosive rigidity percolation in kirigami

   https://doi.org/10.1098/rspa.2022.0798  

   Choi, Gary P. ; Liu, Lucy ; Mahadevan, L. ( March 2023 , Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences)

   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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