Date Published:

2020

Abstract:

Kirigami, the creative art of paper cutting, is a promising paradigm for mechanical meta-materials. 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.

Notes:

(*equal contribution)

Publisher's Version