An Interface Inclusion Between Two Dissimilar Piezoelectric Materials
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摘要: 应用Stroh理论,研究了两压电介质之间的刚性介电线夹杂问题。首先该问题被化为Hilbert问题,然后分别给出了压电介质内的复势函数解、夹杂内的电场解和夹杂尖端场的解析表达式。结果表明,在夹杂尖端附近,所有的场变量均呈现奇异性和振荡性,且其强度取决于介质的材料常数和无限场远处的应变。此外,结果还表明,当从夹杂内部趋近夹杂尖端时,夹杂内的电场也呈现奇异性和振荡性。Abstract: The generalized two-dimensional problem of a dielectric rigid line inclusion,at the interface between two dissimilar piezoelectric media subjected to piecewise uniform loads at infinity,is studied by means of the Stroh formalism.The problem was reduced to a Hilbert problem,and then closed-form expressions were obtained,respectively,for the complex potentials in piezoelectric media,the electric field inside the inclusion and the tip fields near the inclusion.It is shown that in the media,all field variables near the inclusion-tip show square root singularity and oscillatory singularity, the intensity of which is dependent on the material constants and the strains at infinity.In addition,it is found that the electric field inside the inclusion is singular and oscillatory too,when approaching the inclusion-tips from inside the inclusion.
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Key words:
- piezoelectric material /
- interface inclusion /
- complex potential /
- tip field /
- Stroh formalism
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[1] Wang Z Y, Zhang H T, Chou Y T. Characte ristics of the elastic field of a rigid line inhomogeneity[J]. J Appl Mech,1985,52(3):818-822. [2] Wang Z Y, Zhang H T, Chou Y T. Stress singularity at the tip of a rigid line inhomogeneity under anti-plane shear loading[J]. J Appl Mech,19 86,53(2):459-461. [3] Ballarini R. An integral equation approach for rigid line inhomoge neity problems[J]. Int J Fractures,1987,33(1):R23-R26. [4] Li Q, Ting T C T. Line inclusions in anisotropic elastic solids[J]. J Appl Mech,1989,56(3):558-563. [5] Hao T H, Wu Y C. Elastic plane problem of collinear period ical rigid lines[J]. Engng Fracture Mech,1989,33(4):979-981. [6] Jiang C P. The plane problem of collinear rigid lines under arbitrary loads[J]. Engng Fract Mech,1991,39(2):299-308. [7] Chen Y H, Hahn H G. The stress singularity coefficient at a finite rigid flat inclusion in an orthotropic plane elastic body[J]. Engng Fract Mech,1993,44(3):359-362. [8] 蒋持平. 各向异性材料中共线刚性夹杂的纵向剪切问题[J]. 应用数学和力学,1994,15(2):147-154. [9] Ballarini R. A rigid line inclusion at a bimaterial interface[J]. Engng Fract Mech,1990,37(1):1-5. [10] Wu K C. Line inclusion at anisotropic bimaterial interface[J]. Mechanics of Materials,1990,10(2):173-182. [11] Chao C K, Chang R C. Thermoelastic problem of dissimilar anisotropic solids with a rigid line inclusion[J]. J Appl Mech,1994,61(4):978-980. [12] Asundi A, Deeg W. Rigid inclusions on the interface between two bonded anisotropic media[J]. J Mech Phy Solids,1995,13(6): 1045-1058. [13] Liang J, Han J C, Du S Y. Rigid line inclusions and cracks in anisotropic piezoelectric solids[J]. Mech Res Commu,1995,22(1):43-49. [14] Chen S W. Rigid line inclusions under antiplane deformation and inplane electric field in piezoelectric materials[J]. Engng Fract Mech,1997,56(2):265-274. [15] Deng W, Meguid S A. Analysis of conducting rigid inclusion at the interface of two dissimilar piezoelectric materials[J]. J Appl Mech,1998,65(1):76-84. [16] Suo Z, Kuo C M, Barnett D M, et al. Fracture mechanics for piezoelectric ceramics[J]. J Mech Phys Solids,1992,40(4):739-765. [17] Suo Z. Singularities, interfaces and cracks in dissimilar anisotr opic media[J]. Proc R Soc Lond,1990,A427(1873):331-358. [18] Muskhelishvili N I. Some Basic Problems of Mathematical Theory of Elasticity[M]. Leyden: Noordhoof,1975.
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