Explosive rigidity percolation in kirigami

Abstract

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 and control of mechanical metamaterials.

References in corpus (7)

• Bistable Auxetic Mechanical Metamaterials Inspired by Ancient Geometric Motifs
• Explosive percolation in scale-free networks
• Explosive percolation via control of the largest cluster
• Compact reconfigurable kirigami
• Wallpaper group kirigami
• Quasicrystal kirigami
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Cited by in corpus (1)

• Explosive rigidity percolation in origami