Geometric mechanics of random kirigami

TL;DR

This paper investigates how cuts in thin sheets, known as kirigami, influence their mechanical behavior and shape-changing capabilities, providing a geometric framework and scaling laws for designing functional deployable structures.

Contribution

It introduces a geometric model for kirigami sheets using simple developable units and derives scaling laws and a theorem on geodesics, advancing the understanding of shape control in kirigami.

Findings

Kirigami geometry can be approximated by flats, cylinders, cones, and elasticae.

Scaling laws describe mechanical response in weak and strong deformation regimes.

Control of deployment trajectories enables functional applications like robotic grippers.

Abstract

The presence of cuts in a thin planar sheet can dramatically alter its mechanical and geometrical response to loading, as the cuts allow the sheet to deform strongly in the third dimension. We use numerical experiments to characterize the geometric mechanics of kirigamized sheets as a function of the number, size and orientation of cuts. We show that the geometry of mechanically loaded sheets can be approximated as a composition of simple developable units: flats, cylinders, cones and compressed Elasticae. This geometric construction yields simple scaling laws for the mechanical response of the sheet in both the weak and strongly deformed limit. In the ultimately stretched limit, this further leads to a theorem on the nature and form of geodesics in an arbitrary kirigami pattern, consistent with observations and simulations. By varying the shape and size of the geodesic in a kirigamized sheet, we show that we can control the deployment trajectory of the sheet, and thence its functional properties as a robotic gripper or a soft light window. Overall our study of random kirigami sets the stage for controlling the shape and shielding the stresses in thin sheets using cuts.