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.

最近已研究了具有各种切割图案的Kirigami，作为将2D表面转换为3D结构的方法，并提供了许多功能。在这项工作中，我们显示了一个单一的Kirigami主题，定义了两个通过铰链连接的内面板，可以产生多种平面外对称和不对称变形模式。当施加远场拉伸载荷时，由局部不稳定性引起的平面外响应在内板处表现出来，表现出一维和二维旋转（倾斜和扭曲）的组合，有效地变形了平面几何形状进入复杂的3D表面。通过进行数值分析和实验，可以确定切削几何形状的变化与面外响应之间的关系。特别是出现了两种类型的不稳定，两个内板的两个重合分叉点（负责二维倾斜）和顺序分叉点，这些分叉点产生具有明显屈曲阈值的一维倾斜。非线性参数有限元分析（FEA）用于探索可能构型的空间，并根据其参数表征结构的行为，揭示各种变形模式和感兴趣的结构响应。使用纸Kirigami和shadowMoiré技术对数值预测进行了实验验证。组合的数值实验方法揭示了具有固有非线性行为的大量可编程和可控变形模式，这些模式由可调节的瑕疵实现，有望影响从光调制到流体流量控制的各种应用。