剪纸拓扑的确定性和随机性控制。
Deterministic and stochastic control of kirigami topology.
机构信息
John A. Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, MA 02138.
John A. Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, MA 02138;
出版信息
Proc Natl Acad Sci U S A. 2020 Mar 3;117(9):4511-4517. doi: 10.1073/pnas.1909164117. Epub 2020 Feb 13.
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.
剪纸艺术，是一种具有创新性的纸艺，它为机械超材料提供了一种很有前途的范例。然而，要将剪纸艺术的结构变为现实，就需要控制剪纸的拓扑结构，以实现连接性和刚性。我们通过推导出在保持全局刚性和连接性的情况下，仍然允许我们进行的最大切割数量（最小连接数）来解决这个问题。一种确定性的层次结构构建方法提供了一种有效的拓扑方法，可以控制连接部件的数量和总自由度。对具有随机切口的剪纸的刚性和连接性的控制的统计方法补充了确定性途径，并表明连接部件的数量和自由度都表现出作为切口密度（连接数）函数的渗流转变。总的来说，这为平面剪纸的刚性和连接性控制提供了一个通用框架。
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