基于应变梯度理论的微尺度蜂窝等效模量计算方法

Methodology for calculating the in-plane equivalent modulus of micro-honeycomb core using the strain gradient theory

本文提出了一种新的能够计及尺度效应的微纳米蜂窝等效模量的计算方法。将一种单参数应变梯度理论引入到本构方程当中,并基于能量等效原理推导了蜂窝面内等效模量地计算公式。算例分析表明,本文方法能够有效地计及尺度效应对蜂窝等效模量的影响。尺度效应与胞壁厚度和长度的值都有关,当胞壁厚度较小时,尺度效应显著,本文方法预测的模量会明显高于传统方法;而当胞壁厚度较大时,尺度效应变得微弱乃至可以忽略不计。但如果胞壁的长度/厚度比很大,则面内等效模量会趋近于0,此时是否考虑尺度效应意义不大。

This paper proposes a new method for calculating the equivalent modulus of micro-nano honeycombs in which the scale effect is included.In this method,a single-parameter strain gradient theory is introduced into the constitutive equation,and the equivalent modulus of a honeycomb is derived based on the principle of energy equivalence.An example is given to demonstrate that this method can account for the influence of the scale effect when moduli are calculated.The scale effect is relevant to the thickness and length of the cell wall.When the cell wall is thin,the scale effect is significant.In this case,the modulus predicted by the method in this paper will be significantly higher than that determined by the traditional method.Meanwhile,when the cell wall is a thick plate,the scale effect becomes small or even negligible.However,if the length-thickness ratio of cell wall is large,the in-plane equivalent modulus will approach 0.In this case,there is no need to include the scale effect in the calculation of the modulus.