基于界面层模型的双周期纳米夹杂复合材料反平面问题研究

利用复变函数方法并结合双准周期Riemann边值问题理论，获得了含双周期分布非均匀相（夹杂/界面层）的复合材料在远场均匀反平面应力下弹性场的全场解答．该解答可用于对纳米夹杂复合材料的应力进行分析，结合平均场理论也用于预测纳米夹杂复合材料的有效性能．计算结果表明：当夹杂尺度在纳米量级时，应力和有效反平面剪切模量具有明显的尺度依赖性，并且随着夹杂尺寸的增加，趋近于不考虑界面效应时的结果；界面层厚度和性能对应力和有效反平面剪切模量明显变化时所对应的夹杂尺度范围和趋近于无界面效应结果的快慢有显著影响；当界面厚度足够薄时，界面层模型可用于模拟零厚度界面情况．

Study on Composites Containing Doubly Periodic Nano Inhomogeneities under Anti-Plane Shear Based on Interphase Model

By using complex variable method and the theory of doubly quasi-periodic Riemann boundary problem, the elastic field of composites containing doubly periodic array of inhomogeneities (inclusion/interphase) under remote anti-plane shear loading is derived. The present solution can be used to study the stress and the effective property of nano-inhomogeneity composites. The numerical results reveal that the stress and the effective anti-plane shear modulus are size dependent when the size of the inhomogeneity is on the order of nanometer. With the increase of the inhomogeneity size, the present results approach to the results without considering interface effect. The thickness and the property of the interphase have significant influences on the inclusion size range in which the stress and the effective anti-plane shear modulus change significantly, and on the speed approaching to the results without considering interface effect. The present interphase model can simulate the problem with zero-thickness interface when the thickness of the interphase is thin enough.