含刚性导电椭圆夹杂的压电材料反平面裂纹问题的研究

ANTI-PLANE INTERFACIAL CRACK BETWEEN RIGID-CONDUCTIVE INCLUSION AND PIEZOELECTRIC MATERIAL

用复变函数及其保角映射、解析延展方法 ,建立了含刚性导电椭圆夹杂的压电材料反平面界面裂纹问题的解析方程 ,通过求解Hilbert方程得到了问题的封闭解和耦合场的强度因子。结果表明 ,耦合场在裂纹尖端有 1 / 2阶的奇异性 ,应力和电位移强度因子均与材料常数无关。

Some formulas for solving the problems of the anti plane interfacial crack between rigid conductive inclusion and piezoelectric material were establlshed by using the theory of the complex variables as well as the conformal mapping and continuation techniques for complex functions and by solving Hilbert problems. The closed solution and intensity factors in coupling fields of the problems are obtained. The solutions show that the coupling fields have a square root singularity at the crack tips, and the stress and electric displacement intensity factors are independent of the piezoelectric material constant. The equations for calculating stress and electric displacement intensity factors of some particular cases of the elliptical inclusion, such as the circular inclusion and line inclusion, are given.