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研究了中空纳米夹杂填充复合材料的反平面问题。基于Gurtin-Murdoch表/界面理论和广义自洽方法,给出了考虑夹杂界面效应时空隙-夹杂-基体-等效介质模型的全场精确解,并推导了中空纳米夹杂填充复合材料有效反平面剪切模量的闭合形式解。由本文结果的特殊情形,可以得到一系列有意义的解。数值结果表明:中空夹杂的尺寸在纳米量级时,复合材料的有效反平面剪切模量受表/界面效应影响显著;表/界面效应的影响随着夹杂尺寸的增大而逐渐减弱;当中空纳米夹杂的体积分数和外半径一定时,壁厚越薄其表/界面效应越大;在相同的夹杂外半径下,中空纳米夹杂填充复合材料的表/界面效应比实心纳米夹杂填充复合材料更加明显;无量纲反平面剪切模量受夹杂的表/界面性能和刚度影响显著,过高的夹杂刚度使得表/界面效应的影响变弱。
The anti-plane problem of hollow nanocomposite filled composites was studied. Based on the Gurtin-Murdoch table / interface theory and the generalized self-consistent method, the exact solution of the full-field solution of the void-inclusion-matrix-equivalent medium model considering the interfacial interfacial effect is given and the effective anti-plane Closed form solution of shear modulus. From the special cases of the results in this paper, we can get a series of meaningful solutions. The numerical results show that the effective anti-plane shear modulus of composites is significantly affected by the surface / interface effect when the size of hollow inclusions is in the order of nanometers. The effect of surface / interface effect decreases gradually with the inclusion size increasing When the volume fraction of empty nano-inclusions and the outer radius are constant, the thinner the wall thickness is, the more the surface / interface effect is. Under the same inclusion radius, the surface / interface effect of the hollow nanocomposite filled composite is higher than that of the solid nanocomposite filled composite More obviously, the dimensionless anti-plane shear modulus is significantly affected by the inclusion / surface properties and stiffness, and the excessively high inclusion stiffness weakens the effect of surface / interface effects.