Programmable 3D structures via Kirigami engineering and controlled stretching

Kirigami with a variety of cut patterns have been recently investigated as means to transform 2D surfaces into 3D structures, offering a number of functionalities. In this work, we show that a single Kirigami motif, defining two inner panels connected by hinges, can generate a rich variety of out-of-plane symmetric and asymmetric deformation modes. The out-of-plane responses, caused by local instabilities when a far field tensile load is applied, manifest themselves at the inner plates, exhibiting a combination of one- and two-dimensional rotations (tilt and twist), effectively morphing the planar geometries into complex 3D surfaces. By conducting numerical analyses and experiments, the relationship between changes in the cut geometry, and out-of-plane responses is identified. In particular, two types of instabilities emerge, coincident bifurcation points for both inner plates, responsible for two-dimensional tilts, and sequential bifurcation points, which produce one-dimensional tilts with distinct buckling thresholds. Nonlinear parametric finite element analysis (FEA) is used to explore the space of possible configurations and characterize the behavior of the structure as a function of its parameters, revealing a variety of deformation modes and structural responses of interest. Numerical predictions are experimentally validated using paper Kirigami and the shadow Moiré technique. The combined numerical–experimental approach reveals a plethora of programmable and controllable deformation modes with intrinsic nonlinear behaviors, enabled by tunable imperfections, which promise to influence a variety of applications ranging from light modulation to fluid flow control.