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 number of connected pieces and the total degrees of freedom. A statistical approach to the control of rigidity and connectivity in kirigami with random cuts complements the deterministic pathway, and shows that both the number of connected pieces and the degrees of freedom show percolation transitions as a function of the density of cuts (links). Together, this provides a general framework for the control of rigidity and connectivity in planar kirigami.

中文翻译：

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剪纸拓扑的确定性和随机控制。


剪纸是一种创造性的剪纸艺术，是机械超材料的一个有前途的范例。然而，要使剪纸结构成为现实，需要控制剪纸的拓扑结构以实现连通性和刚性。我们通过导出最大切割数量（最小链接数量）来解决这个问题，这仍然允许我们保持剪纸的整体刚性和连通性。确定性分层构造方法提供了一种有效的拓扑方法来控制连接件的数量和总自由度。用随机切割来控制剪纸中刚性和连接性的统计方法补充了确定性路径，并表明连接件的数量和自由度都显示出作为切割（链接）密度的函数的渗透过渡。总之，这为控制平面剪纸的刚性和连接性提供了一个通用框架。