Kirigami, the creative art of paper cutting, is a promising paradigm for mechanical meta-materials . However, to make this 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. This leads to a deterministic hierarchical construction method that yields an efficient topological way to control both the number of connected pieces (T) and the total degrees of freedom (DoF). We then turn to a statistical approach to the question by studying the rigidity and connectivity of kirigami with random cuts , and find that both the T and DoF can be exquisitely controlled by the density of cuts (links) in the neighborhood of percolation transitions in the connectivity and rigidity. All together, our work provides a general framework for the topological and statistical control of rigidity and connectivity in planar kirigami.
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.
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meta-materials
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kirigami-inspired structures
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topological and statistical