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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,论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(论文结果)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.
Based on the Gurtin-Murdoch surface / interface theory model, the exact solution to the problem of inclusion / matrix / equivalent medium model considering interfacial interfacial stress was obtained by using the complex function method. An effective anti-plane shear The generalized self-consistent method for the modulus gives the closed-form solution of the effective anti-plane shear modulus of the composites. Numerical results show that the effective anti-plane shear modulus of the composites with the size of nano- The results show that the inclusion size affects the effective anti-plane shear modulus (paper result) less than its effective bulk modulus and shear modulus The influence range of shear modulus (isotropic material) is that the effective anti-plane shear modulus is significantly affected by the interfacial properties and inclusion stiffness.