压电材料椭圆夹杂界面局部脱粘问题的分析  

Analysis of a Partially Debonded Elliptic Inhomogeneity in Piezoelectric Materials

作　　者：仲政[1] 

机构地区：[1]同济大学固体力学教育部重点实验室,上海200092

出　　处：《应用数学和力学》2004年第4期405-416,共12页Applied Mathematics and Mechanics

基　　金：国家杰出青年科学基金资助项目(10125209);国家自然科学基金资助项目(10072041);高等学校优秀青年教师教学科研奖励基金资助项目

摘　　要：　利用复变函数方法,研究在反平面剪切和面内电场共同作用下压电材料椭圆夹杂的界面脱粘问题·　假定夹杂界面脱粘导致了界面电绝缘型裂纹的产生·　通过保角变换和解析延拓,将原问题化为两个黎曼＿希尔伯特问题,获得了夹杂和基体复势的级数解,进而求得应力变形场以及夹杂＿基体界面脱粘的能量释放率的一般表达式·　通过理想粘结的椭圆夹杂、完全脱粘的椭圆夹杂、局部脱粘的刚性导体椭圆夹杂。A generalized solution was obtained for the partially debonded elliptic inhomogeneity problem in piezoelectric materials under antiplane shear and inplane electric loading using the complex variable method. It was assumed that the interfacial debonding induced an electrically impermeable crack at the interface. The principle of conformal transformation and analytical continuation were employed to reduce the formulation into two Riemann-Hilbert problems. This enabled the determination of the complex potentials in the inhomogeneity and the matrix by means of series of expressions. The resulting solution was then used to obtain the electroelastic fields and the energy release rate involving the debonding at the inhomogeneity-matrix interface. The validity and versatility of the current general solution have been demonstrated through some specific examples such as the problems of perfectly bonded elliptic inhomogeneity, totally debonded elliptic inhomogeneity, partially debonded rigid and conducting elliptic inhomogeneity, and partially debonded circular inhomogeneity.

关 键 词：压电材料 椭圆夹杂 脱粘 能量释放率 

分 类 号：O343[理学—固体力学]