压电复合材料中的Eshelby夹杂问题

通过采用解析延拓和共形映射技术，获得了压电复合材料中有关Eshelby夹杂几个典型问题的精确弹性解答，即横观各向同性压电介质中任意形状的Eshelby夹杂与圆柱异相夹杂间相互作用；一般各向异性压电介质中任意形状的Eshelby夹杂与双压电材料所形成界面的相互作用．成功求解这些问题的关健在于构造一个辅助函数．与Ru所采用的方法不同，所引入的辅助函数在无穷远点不存在极点，从而使得所展开的分析更加自然合理．分析结果清楚地揭示出Eshelby夹杂的存在对压电复合材料机电耦合响应将产生不容被忽视的影响．很典型的一个例于是当一个Eshelby椭圆夹杂与圆柱异相夹杂相互作用时，每个夹杂体内部的应力场和电场都将是不均匀的；另一个例于是位于界面附近的Eshelby夹杂有可能是界面发生损伤的一个重要原因．

ESHELBY'S INCLUSIONS IN PIEZOELECTRIC COMPOSITE MATERIALS

Analytical solutions are obtained for several typical problems concerning Eshelby's inclusions in piezoelectric composite materials by means of analytical continuation and conformal mapping techniques. The Eshelby's inclusion problems discussed in this research are 1) an Eshelby's inclusion of arbitrary shape interacting with a circular inhomogeneity in transversely isotropic piezoelectric materials, 2) an Eshelby's inclusion of arbitrary shape interacting with an anisotropic piezoelectric bimaterial interface. The key to the successful solving of these problems lies in the construction of an auxiliary function. Different from the method adopted by Ru1,2], the auxiliary function introduced here are regular at infinity. Consequently, the analysis will become more reasonable. The results reveal that the existence of the Eshelby inclusion will exert a significant influence on the electromechanical coupling behavior of piezoelectric composite materials. One example is that when an Eshelby's inclusion interacts with a circular inhomogeneity, the stress and electrical fields within both the Eshelby's inclusion and the inhomogeneity will be intrinsically nonuniform. Another example is that an Eshelby's inclusion very near the interface may be an important cause of damage on the interface.