Zhou Xin, Liang Xi, Liu Zeliang, Tao Chenglin, Li Huijian
School of Civil Engineering and Mechanics, Yanshan University, Qinhuangdao 066004, China.
Hebei Key Laboratory of Mechanical Reliability for Heavy Equipments and Large Structures, Yanshan University, Qinhuangdao 066004, China.
Materials (Basel). 2022 Jul 26;15(15):5180. doi: 10.3390/ma15155180.
A category of metamaterials consisting of chiral cytosolic elements assembled periodically, in which the introduction of a rotatable annular structure gives metamaterials the ability to deform in compression-shear, has been a focus of research in recent years. In this paper, a compression-shear coupling model is developed to predict the compressive deformation behaviour of chiral metamaterials. This behaviour will be analysed by coupling the rotation of the annular node and the bending characteristics of ligament beam, which are obtained as a function of the length of ligament beam and the angle of rotation at the end of the beam. The shape function of the ligament beam under large deformation is obtained based on the elliptic integral theory; the function characterises the potential relationship between key parameters such as displacement and rotation angle at any point on the ligament beam. By simulating the deformation of cells under uniaxial compression, the reasonableness of the large deformation model of the ligament beam is verified. On this basis, a chiral cell-compression mechanical model considering the ductile deformation of the annular node is established. The compression-shear deformation of two-dimensional planar chiral metamaterials and three-dimensional cylindrical-shell chiral metamaterials was predicted; the offset displacements and torsion angles agreed with the experimental and finite element simulation results with an error of less than 10%. The developed compression-shear coupling model provides a theoretical basis for the design of chiral metamaterials, which meet the need for the precise control of shapes and properties.
一类由周期性组装的手性胞质元素组成的超材料近年来一直是研究热点，其中引入可旋转的环形结构使超材料具有在压缩剪切作用下变形的能力。本文建立了一个压缩-剪切耦合模型，以预测手性超材料的压缩变形行为。通过将环形节点的旋转与韧带梁的弯曲特性相耦合对这种行为进行分析，已知其（环形节点的旋转与韧带梁的弯曲特性）是韧带梁长度和梁端部旋转角度的函数。基于椭圆积分理论得到了韧带梁在大变形状态下的形状函数；该函数表征了韧带梁上任意点的位移和旋转角度等关键参数之间的潜在关系。通过模拟细胞在单轴压缩下的变形，验证了韧带梁大变形模型的合理性。在此基础上，建立了考虑环形节点延性变形的手性细胞压缩力学模型。预测了二维平面手性超材料和三维圆柱壳手性超材料的压缩-剪切变形；偏移位移和扭转角与实验和有限元模拟结果相符，误差小于10%。所建立的压缩-剪切耦合模型为手性超材料的设计提供了理论基础，满足了对形状和性能精确控制的需求。
