辐射对称金字塔型剪纸的力学行为

Mechanical behaviors of radial symmetric pyramid kirigami

通过在弹性薄板上引入切口,构建了多边形辐射对称金字塔型剪纸结构.利用伽辽金法求解的悬臂梁形变公式和悬臂梁组合的方法,创建了用于解释形变过程的"梁模型",得到n个模块的正N边形金字塔结构的弹性系数与结构参数的关系公式,并求出弹性系数线性阈值的表达式,解释了该结构产生平面外扭曲的原因.利用推导的"梁模型"公式,并通过有限元仿真和实验的方法,系统研究了辐射对称金字塔型剪纸结构的力学响应特征,验证模型的准确性,并用于已有报道的石墨烯剪纸结构的力学特征分析.这项工作系统解释了竖直拉伸的金字塔型剪纸结构的力学响应.

Kirigami,the art of cutting paper,recently emerged as a powerful tool to substantially modify,reconfigure and program the properties of material.The development of kirigami technology provides an effective solution for designing the inorganic flexible electronic devices.Pyramid kirigami,as a kind of kirigami structure,shows a large vertical extension characteristic.It has been widely used to demonstrate versatile applications,such as graphene kirigami spiral spring,three-dimensional stretchable supercapacitor,and wearable flexible sensors.In the present work,we construct a polygonal radial symmetric pyramid kirigami by introducing some cuts in the elastic sheet.The mechanical behavior of pyramid kirigami is investigated based on the cantilever formula solved by Galerkin method.In addition,a"beam model"is proposed to explain deformation process of pyramid kirigami,which consists of several"beam elements"containing two cantilever beams.The formula for the relationship between the elastic coefficient K and the structural parameters of the regular N-sided pyramid kirigami of n modules is obtained by combining several cantilever beams.The formula for the linear threshold of deformation DT is obtained based on the comparison between the approximate curve of small deflection and the theoretical curve of a cantilever beam.When the deformation of the structure exceeds the linear threshold,the structure cannot keep the elastic coefficient K value linear any more,and the mechanical behaviors become nonlinear.The simple geometric relationship of a single module is used to explain the out-of-sheet distortion of the structure.The proposed theoretical model is confirmed by finite element method simulation and experimental methods,and it is used to analyze the mechanical characteristics of graphene krigami reported.The results indicate that the defined parameters can be adjusted to tailor or manipulate the ductility and mechanical behaviors.This work provides theoretical support for the application of pyramid kirigami in the field of flexible devices.In the macroscopic field,the pyramid kirigami structure is expected to be applied to the field of flexible devices as a flexible structure with controllable elastic coefficient.In the microscopic field,it is expected to use two-dimensional materials to make force measurement devices with a simple visual readout and femtonewton force resolution.