剪切和扭转工况下微纳米薄壁蜂窝的等效剪切模量计算

Equivalent shear modulus of micro-nano thin-walled honeycomb under shear and torsion

分别针对剪切和扭转两种工况给出了微纳米薄壁蜂窝等效剪切模量的解析计算方法。该方法综合考虑了由面板对芯层的约束导致的高度效应和当蜂窝胞壁厚度进入微纳米量级时引起的尺度效应。首先对蜂窝各胞壁选取了可反映面板约束以及受力状态的三角级数位移场,然后在本构关系中引入修正偶应力理论以描述尺度效应,最后应用能量均匀化方法求得蜂窝的等效剪切模量。以典型六边形蜂窝为例,给出了完整的计算过程和结果。与文献中的等效剪切模量结果进行对比,讨论了不同工况下等效剪切模量随芯层高度和胞壁厚度的变化趋势,以及高度效应和尺度效应之间的相互影响。

An analytical methodology to calculate the equivalent shear modulus of micro-nano thin-walled honeycomb under shear and torsion is presented.Height effect caused by constraint of the skin on the core layer and scale effect caused by the thickness of honeycomb cells in micro-nano scale is comprehensively considered.Firstly,a series of trigonometric functions are selected for the displacement of each cell wall,which can reflect the constraint and load condition of the skin.Then the modified couple stress theory is introduced to describe the scale effect.Finally,the equivalent shear modulus of honeycomb is obtained by energy homogenization method.A typical hexagonal honeycomb is taken as the illustrative example to show the whole calculation process.Results are compared with the data from published references.The variation trend of the equivalent shear modulus with core height and cell wall thickness under different load conditions is discussed,and the interaction between height effect and scale effect is discussed as well.