中空纳米夹杂填充复合材料的反平面问题

Anti-plane problem of hollow nano inclusion composites

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 effective anti-plane shear modulus was studied for the composites containing hollow nano inclusion. Based on the theory of Gurtin-Murdoch surface/interface theory and the generalized self-consistent method, the rigorous whole-field solution is obtained for the void-inclusion-matrix-equivalent medium model. The closed- form solution of the effective anti-plane shear modulus of the hollow nano inclusion composites is presented. Many significant solutions can be regarded as special or degenerated cases. The numerical results reveal that the effective anti-plane shear modulus is influenced remarkably when the size of the hollow nano inclusion is on the order of nanometer. With the increase of the size of the hollow nano inclusion, the surface/interface effect abates gradually. For the same volume fraction and outer radius of the hollow nano inclusion, the thinner the wall thickness is, the greater of the surface/interface effect is. The surface/interface effect of the hollow nano composites is much larger than that of the solid nano composites for the same outer radius of the inclusion. The effective anti- plane shear modulus of the hollow nano composites depends strongly on the surface/interface property and the stiffness of the inclusion. A very hard inclusion shields the surface/interface effect.