纳米夹杂复合材料的有效反平面剪切模量研究

基于Gurtin-Murdoch表面/界面理论模型，利用复变函数方法，获得了考虑夹杂界面应力时夹杂/基体/等效介质模型的全场精确解，发展了能够预测纳米夹杂复合材料有效反平面剪切模量的广义自洽方法，给出了复合材料有效反平面剪切模量的封闭形式解。数值结果显示：当夹杂尺寸在纳米量级时，复合材料的有效反平面剪切模量具有尺度相关性，随着夹杂尺寸的增大，本文结果趋近于经典弹性理论的预测值；夹杂尺寸对于有效反平面剪切模量(本文结果)的影响范围要小于其对有效体积模量与剪切模量(各向同性材料)的影响范围；有效反平面剪切模量受夹杂的界面性能和夹杂刚度影响显著。

STUDY ON THE EFFECTIVE ANTI-PLANE SHEAR MODULUS OF NANO INHOMOGENEITY COMPOSITE MATERIALS

Based on the theory of Gurtin-Murdoch surface/interface model, a rigorous whole-field solution is obtained for the inhomogeneity/matrix/equivalent medium model, in terms of which a generalized self-consistent approach is developed for predicting the effective anti-plane shear modulus of nano composites. Closed-form solution of the effective anti-plane shear modulus was presented. The numerical results reveal that the effective anti-plane shear modulus is size dependent when the size of the inhomogeneity is on the order of nanometer. With the increase of the size of the inhomogeneity, the present solution approaches to the classical results obtained in the linear elasticity theory. In comparison to the effective bulk modulus and shear modulus (isotropic materials), the present effective anti-plane shear modulus of the nano composites is influenced by the size of the inhomogeneity at a smaller range. The interface property and the stiffness of the inhomogeneity play an important role in the effective anti-plane shear modulus of the nano composites.