Source-linked AI summary
Programming shape using kirigami tessellations
Gary P. T. Choi, Levi H. Dudte, L. Mahadevan
TL;DR
The paper addresses how to design kirigami tessellations that deploy into prescribed shapes rather than merely analyze behavior from a given topology. It develops a framework for shape programming, including curved surfaces in R3, with configurations matching shapes such as circles and eggs, while facing an accuracy–effort trade-off.
Problem
The paper asks how kirigami tessellations can be deployed into prescribed final shapes in two or three dimensions, extending beyond studies of behavior given the topology.
Method
The framework uses generalized kirigami patterns and boundary-layer and gap-area considerations to design shape-changing structures from simple cuts.
Results
The framework creates patterns that approximate curved surfaces in R3, with configurations effectively matching either a circle or an egg.
Takeaways & Limitations
Kirigami tessellations provide a framework for designing complex, shape-changing sheets from simple cuts.
Takeaways & Limitations
Approximating a prescribed shape involves an accuracy–effort trade-off, and the resulting solution may be rough with large gradients.
Abstract
from arXiv · showhide
Kirigami tessellations, regular planar patterns formed by cutting flat, thin sheets, have attracted recent scientific interest for their rich geometries, surprising material properties and promise for technologies. Here we pose and solve the inverse problem of designing the number, size, and orientation of cuts that allows us to convert a closed, compact regular kirigami tessellation of the plane into a deployment that conforms approximately to any prescribed target shape in two and three dimensions. We do this by first identifying the constraints on the lengths and angles of generalized kirigami tessellations which guarantee that their reconfigured face geometries can be contracted from a non-trivial deployed shape to a novel planar cut pattern. We encode these conditions in a flexible constrained optimization framework which allows us to deform the geometry of periodic kirigami tesselations with three, four, and sixfold symmetry, among others, into generalized kirigami patterns that deploy to a wide variety of prescribed boundary target shapes. Physically fabricated models verify our inverse design approach and allow us to determine the tunable material response of the resulting structures. We then extend our framework to create generalized kirigami patterns that deploy to approximate curved surfaces in $\mathbb{R}^3$. Altogether, this work illustrates a novel framework for designing complex, shape-changing sheets from simple cuts showing the power of kirigami tessellations as flexible mechanical metamaterials.