考慮高度效應(yīng)的微納米蜂窩面內(nèi)等效剪切模量預測方法

摘要： 得益于微納米技術(shù)的迅速發(fā)展，微納米蜂窩常被應(yīng)用于微電機系統(tǒng)中，準確評估微納米蜂窩的彈性性能對于微電機系統(tǒng)的設(shè)計是必要的。當蜂窩結(jié)構(gòu)尺寸進入微納米尺度后，尺寸效應(yīng)對其力學響應(yīng)的影響變得不可忽略，在評價微納米蜂窩的力學性能時應(yīng)考慮尺寸效應(yīng)的影響。提出了一種計及尺寸效應(yīng)和高度效應(yīng)的微納米蜂窩等效剪切模量計算方法，將單參數(shù)應(yīng)變梯度理論引入本構(gòu)方程，并根據(jù)能量均勻化方法推導出等效剪切模量的解析解。算例表明，計算結(jié)果高于經(jīng)典彈性理論結(jié)果，與實驗觀察到的現(xiàn)象一致，有效地顯示了尺寸效應(yīng)。尺寸效應(yīng)的顯著程度受蜂窩芯層高度和幾何尺寸的影響，芯層高度更小或幾何尺寸更小的微納米蜂窩表現(xiàn)出更為顯著的尺寸效應(yīng)，尺寸效應(yīng)的存在導致等效剪切模量對芯層高度的敏感性降低。隨著蜂窩幾何尺寸的增大，該方法預測的數(shù)值逐漸逼近宏觀尺度蜂窩等效模量值，且具有良好的普適性，可用于宏觀尺度和微納米尺度蜂窩。

關(guān)鍵詞： 微納米蜂窩；等效剪切模量；應(yīng)變梯度理論；尺寸效應(yīng)；高度效應(yīng)

中圖分類號： O343.8 文獻標志碼： A

doi：10.3969/j.issn.2095-1248.2023.01.005

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

FENG Jia-yue1，HE Dan1，2

（1.Key Laboratory of Liaoning Province for Composite Structural Analysis of Aerocraft and Simulation，Shenyang

Aerospace University，Shenyang 110136，China;2.Hunan InnoChina Advanced Material Co.，Ltd.，Yueyang 414000，China）

Abstract： 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.

Key words： micro-nano honeycombs;equivalent shear modulus;strain gradient theory;size effects;height effects

蜂窩芯層結(jié)構(gòu)因其比強度高、比剛度大、隔熱、隔振性能好等優(yōu)異特性，被廣泛應(yīng)用于航空航天、交通和機械工業(yè)等領(lǐng)域［1］。為便捷而準確地評估蜂窩芯層結(jié)構(gòu)在外載荷下的力學響應(yīng)，人們常通過等效均勻化的方法，將離散非均勻的蜂窩等效為均質(zhì)材料，利用其等效模量分析結(jié)構(gòu)力學性能。……