蜂窝状薄壁管拉伸时的收缩分析

Analysis of Shrinkage of Honeycomb Thin-Wall Tube During Stretching

关键词:  蜂窝材料  Vertex模型  收缩  变分法  边界效应

Key words:  Honeycomb materials  Vertex model  Shrinkage  Variational method  Boundary effect

摘要:

为研究蜂窝材料拓扑结构与其整体力学性能的关系，从非平面Vertex模型的势能形式出发，结合蜂窝薄壁管拉伸时的轴对称特征，通过变分法得到了管拉伸时母线满足的控制方程，证实了边界效应是蜂窝状薄壁管受拉时产生收缩的原因，并结合控制方程的若干特解，考察了非平面Vertex模型中材料参数对管弯曲程度的影响。结果表明，非平面Vertex模型中表征夹角势强度的参数决定了材料的整体抗弯性，而距离管端最近的3层元胞是管拉伸时的主要收缩区。最后进一步探讨了蜂窝薄壁管曲率与收缩幅度之间的非线性关系，揭示了构型曲率是蜂窝材料泊松比的影响因素之一。

Abstract:

In order to study the relationship between the topology structure of honeycomb materials and its overall mechanical properties， starting from the potential energy form of the non-planar Vertex model， the governing equation for the cable on the tube surface was obtained by the variational method， considered with the axisymmetric characteristics of the honeycomb thin-wall tube. The results reveal that the boundary effect is the cause of the shrinkage when the honeycomb thin-wall tube is pulled. Through several special solutions of the governing equation， the effects of material parameters in non-planar Vertex model on the bending degree of the tube were investigated. The results show that the parameter representing the strength of the face angle potential energy in the non-planar Vertex model determines the overall bending resistance of the material， and the three-layer cells closest to the end of the tube are the main shrinkage region of the tube during stretching. In the end of this paper， the nonlinear relationship between the curvature of the honeycomb thin-wall tube and the degree of the shrinkage is further discussed， and it is revealed that the curvature of the configuration is one of the factors influencing the Poisson’s ratio of the honeycomb material.