Beyond Grid Kirigami

Abstract

Kirigami metamaterials are engineered materials inspired by the ancient art of paper cutting. To produce them, partial cuts are placed in a base material so that stretching the material causes it to deploy, or change size and shape. Other exotic mechanical properties can emerge as well. These materials are applicable for many engineering settings where controllable structural change is desired. Existing research has focused on how kirigami patterns based on simple square and triangle grids behave when cut into different materials or used in different settings. In this thesis, we seek to understand the space of kirigami patterns beyond those based on grids. How do we find these patterns, what new features could they offer, and what useful information might lie in a pattern’s underlying structure?

First, we find a set of kirigami patterns representing the 17 wallpaper groups, which are symmetry groups characterizing the space of 2D periodic patterns. By studying the graphs representing these initial kirigami patterns’ underlying connectivity, we develop a pattern augmentation method that can 1) produce new kirigami patterns, 2) help us deploy tilings that were previously difficult or impossible to deploy, and 3) produce large and controllable size change in kirigami patterns. We also study how the symmetries of a kirigami pattern change through deployment.

In the second half of our work, we develop kirigami patterns based on aperiodic quasicrystal tilings. Since these tilings never repeat, they require developing more general kirigami design principles based on underlying structure. We introduce three such design methods and develop a computer simulation for verifying their effectiveness. We analyze geometric, mechanical, and topological properties of our methods and show that each method has different properties suitable for different applications. Finally, we show that one of our deployment methods preserves aspects of the unique long-range order of quasicrystal tilings.