Analysis of Conducting Rigid Inclusion at the Interface of Two Dissimilar Piezoelectric Materials

Abstract

This paper is concerned with the electro-elastic analysis of a conducting rigid line inclusion at the interface of two bonded piezoelectric materials. By combining the analytic function theory and the Stroh formalism, we were able to obtain closed-form expressions for the field variables. Both the mechanical stresses and the electric displacement are shown to have at least one of the following behaviors: (i) traditional square root singularity; (ii) nonsquare root singularity; and (iii) oscillatory singularity, which depend upon the electro-elastic mismatch at the interface. By using the static equilibrium conditions, the rigid rotation vector of the inclusion is determined and the extended stress singularity factors (ESSF) are evaluated.

The study of dynamic behavior of functionally graded piezoelectric materials and an application to a contact problem

“…Most of the work has been done on crack problems, and it is worth mentioning that some work on inclusion problems in piezoelectric medium may be found in references [21]- [24]. In most of the above references, the authors considered the crack problems in functionally graded materials in which non-homogeneity vary perpendicular to the crack and that the non-homogeneity vary in only one direction.…”

Microcrack initiation at the tip of a finite rigid conducting line in piezoelectric media

“…In-plane case. Following the method in [Erdogan et al 1973], we write the discretized forms of Equations (2-8) and (2-9) as 1 4π 2, 3, (3-13) and n r =1W…”

“…Rigid line inclusions (or, for brevity, rigid lines) have been used to model certain materials or flat defects, such as metal precipitates in a piezoelectric solid. For the past decades, many researchers addressed rigid lines by solving the whole field solutions for various configurations; see, for example, [Wang et al 1985[Wang et al , 1986Li and Ting 1989;Ballarini 1990;Fan and Keer 1993;Asundi and Deng 1995]. Recently, rigid lines embedded in piezoelectric solids have been studied in [Shi 1997;Deng and Meguid 1998;Gao and Fan 2001].…”

“…For the past decades, many researchers addressed rigid lines by solving the whole field solutions for various configurations; see, for example, [Wang et al 1985[Wang et al , 1986Li and Ting 1989;Ballarini 1990;Fan and Keer 1993;Asundi and Deng 1995]. Recently, rigid lines embedded in piezoelectric solids have been studied in [Shi 1997;Deng and Meguid 1998;Gao and Fan 2001]. All that the research work has identified is a square root singularity at the rigid line tip, and led to a stress intensity factor similar to that for a crack.…”

Untitled

“…There are numerous contributions to the literature on electro-elastic coupling characteristics of piezoelectric composite materials. To name a few, Pak [1992a] studied the anti-plane problem of a piezoelectric circular inclusion; Meguid and Zhong [1997] provided a general solution for the elliptical inhomogeneity problem in piezoelectric material under anti-plane shear and an in-plane electric field; Kattis et al [1998] investigated the electro-elastic interaction effects of a piezoelectric screw dislocation with circular inclusion in piezoelectric material; Deng and Meguid [1998; considered the interaction between the piezoelectric elliptical inhomogeneity and a screw dislocation located inside inhomogeneity and outside inhomogeneity respectively under anti-plane shear and an in-plane electric field. More recently, Huang and Kuang [2001] evaluated the generalized electro-mechanical force for dislocation located inside, outside and on the interface of elliptical inhomogeneity in an infinite piezoelectric medium.…”