Deterministic and stochastic control of kirigami topology

TL;DR

This paper develops deterministic and stochastic methods to control the topology, connectivity, and rigidity of kirigami-inspired structures, enabling their practical design and application in mechanical metamaterials.

Contribution

It introduces a maximum cut framework for preserving rigidity and connectivity, along with a hierarchical construction and a percolation-based statistical approach.

Findings

Maximum cuts preserve global rigidity and connectivity.

Hierarchical construction controls connected pieces and degrees of freedom.

Percolation transitions occur as cut density varies.

Abstract

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.