Shape-morphing structures based on perforated kirigami

TL;DR

This paper introduces a novel perforated kirigami approach with uniform thickness and variable porosity to design shape-morphing structures, validated through simulations and experiments, enabling easier fabrication of complex 3D forms.

Contribution

It proposes a new perforated kirigami strategy with uniform thickness and calculated porosity for shape morphing, simplifying manufacturing compared to previous tapered thickness methods.

Findings

Theoretical model accurately predicts porosity distribution for desired shapes.

Finite element simulations match physical experiments in shape transformation.

Morphed structures demonstrate significant load-bearing capacity.

Abstract

Shape-morphing structures, which are able to change their shapes from one state to another, are important in a wide range of engineering applications. A popular scenario is morphing from an initial two-dimensional (2D) shape that is flat to a three-dimensional (3D) target shape. One of the exciting manufacturing paradigms is transforming flat 2D sheets with prescribed cuts (i.e. kirigami) into 3D structures. By employing the formalism of the 'tapered elastica' equation, we develop an inverse design framework to predict the shape of the 2D cut pattern that would generate a desired axisymmetric 3D shape. Our previous work has shown that tessellated 3D structures can be achieved by designing both the width and thickness of the cut 2D sheet to have particular tapered designs. However, the fabrication of a sample with variable thickness is quite challenging. Here we propose a new strategy -- perforating the cut sheet with tapered width but uniform thickness to introduce a distribution of porosity. We refer to this strategy as perforated kirigami and show how the porosity function can be calculated from our theoretical model. The porosity distribution can easily be realized by laser cutting and modifies the bending stiffness of the sheet to yield a desired elastic deformation upon buckling. To verify our theoretical approach, we conduct finite element simulations and physical experiments. We also examine the loading-bearing capacity of morphed structures via indentation tests in both FEM simulations and experiments. As an example, the relationship between the measured geometric rigidity of morphed half-ellipsoids and their aspect ratio is investigated in details.