考虑高度效应的微纳米蜂窝面内等效剪切模量预测方法

Approach for predicting in-Plane equivalent shear modulus of micro-nano honeycombs with height effects Size-dependent analytical model for predicting in plane equivalent shear modulus of micro/nano-honeycombs with height effects

得益于微纳米技术的迅速发展,微纳米蜂窝常被应用于微电机系统中,准确评估微纳米蜂窝的弹性性能对于微电机系统的设计是必要的。当蜂窝结构尺寸进入微纳米尺度后,尺寸效应对其力学响应的影响变得不可忽略,在评价微纳米蜂窝的力学性能时应考虑尺寸效应的影响。提出了一种计及尺寸效应和高度效应的微纳米蜂窝等效剪切模量计算方法,将单参数应变梯度理论引入本构方程,并根据能量均匀化方法推导出等效剪切模量的解析解。算例表明,计算结果高于经典弹性理论结果,与实验观察到的现象一致,有效地显示了尺寸效应。尺寸效应的显著程度受蜂窝芯层高度和几何尺寸的影响,芯层高度更小或几何尺寸更小的微纳米蜂窝表现出更为显著的尺寸效应,尺寸效应的存在导致等效剪切模量对芯层高度的敏感性降低。随着蜂窝几何尺寸的增大,该方法预测的数值逐渐逼近宏观尺度蜂窝等效模量值,且具有良好的普适性,可用于宏观尺度和微纳米尺度蜂窝。

Benefiting from the rapid development of micro-nano technology,micro-nano honeycombs have been applied to micromotor systems.It is necessary to accurately evaluate the elastic properties of micro-nano honeycombs for the design of a micromotor system.When the structural size of the honeycomb enters the micro-nano scale,the influence of size effects on the mechanical responses becomes non-negligible,which should be taken into account when evaluate the mechanical properties of micro-nano honeycombs.Therefore,a novel method for predicting the equivalent elastic moduli of micro-nano honeycombs was proposed in which size effects and height effects were considered.The single-parameter strain gradient model was introduced into the constitutive equations,and the analytical solution of the equivalent moduli was derived according to the energy homogenization method.It is illustrated by the numerical examples that the results of the present method are higher than those of the classical elasticity theory,which is consistent with the phenomena observed in the experiment,effectively showing the size effects.The magnitude of size effects can be influenced by the core height and the geometrical size of the honeycombs.Micro-nano honeycombs with smaller core heights or smaller geometric size show more significant size effects,and the existence of size effects reduces the sensitivity of honeycomb equivalent elastic moduli to core height.With the increase of the geometrical size of the honeycomb,the values predicted by the present method is gradually close to the equivalent moduli values of the macro-scale honeycombs.Hence,the present method has a good universality that can be used in both macro and micro-nano honeycombs.