基于二维组装的三维力学超材料设计

3D mechanical metamaterial design technology based on 2D assembly

针对力学超材料设计中缺乏统一模型和仿真预测困难等问题,建立了正、负泊松比力学超材料的统一数学模型,采用参数化方法设计了一种由负泊松比向正泊松比连续变化的二维力学超材料单元族,基于拉伸实验和仿真结果构建了该类二维力学超材料本构模型,建立了组元构造参数和等效力学属性间的关系。三维力学超材料组元由离散装配的二维组元构建而成,根据力学超材料二维-三维组元空间拓扑关系构建三维组元本构模型。通过多组拉伸(压缩)实验对二维、三维力学超材料本构模型进行验证,结果显示,二维组元等效力学属性预测值与试验值分布趋势一致,二维组元和三维组元的等效力学属性预测值与试验值的误差均小于15%。

A unified mathematical model of positive and negative Poisson's ratio mechanical metamaterials is established to address the lack of a unified model and the difficulty of simulation prediction in the design of mechanical metamaterials.A family of 2D mechanical metamaterials that continuously changes from negative Poisson's ratio to positive Poisson's ratio is designed by parametric method.Based on the tensile experiments and simulation results,a constitutive model of this kind of 2D mechanical metamaterials is constructed,and the relationship between the structural parameters of the components and the equivalent mechanical properties is established.3D mechanical metamaterial components are constructed from discretely assembled 2D components,and the 3D component constitutive model is built according to the 2D-3D component space topology relationship of mechanical metamaterials.Several sets of verification experiments are carried out to verify the constitutive models of 2D and 3D mechanical metamaterials.The results show that the predicted values of the equivalent mechanical properties of the 2D components are consistent with the distribution trends of the experimental values,and the relative error between the predicted and experimental values of the equivalent mechanical properties of the 2D and assembled 3D components are both less than 15%.