Shape-morphing structures based on perforated kirigami

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 can be challenging and limits the materials that can be used. Here we propose a new strategy — changing the local bending stiffness by adding small pores, or perforations, within the structure to give it a varying porosity but maintaining a constant thickness. We refer to this strategy as ‘perforated kirigami’ and show how the porosity function can be calculated from a 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 method (FEM) simulations and physical experiments. We also examine the load-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