Explosive rigidity percolation in kirigami

TL;DR

This paper explores how to control the rigidity transition in kirigami-based metamaterials using stochastic methods inspired by explosive percolation, enabling tailored mechanical properties.

Contribution

It introduces a novel application of the $k$ choices approach to manipulate rigidity transitions in kirigami systems, combining deterministic and stochastic strategies.

Findings

Methods can induce explosive rigidity transitions in kirigami.

Selection rules influence the nature of the rigidity transition.

Controlled rigidity transitions can be achieved through incremental modifications.

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.