Closed form solutions for partially debonded circular inclusion in piezoelectric materials

Wei, Deng; Meguid, S. A.

doi:10.1007/bf01179207

Cited by 29 publications

(7 citation statements)

References 14 publications

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“…Explicit series expressions were derived for the field potentials using Laurent series expansion. As pointed out by Deng et al [21], their solution was cumbersome and its convergence depends on the number of terms used in the series. Deng et al [21] reexamined the problem of a partially debonded piezoelectric circular inclusion.…”

Section: Introductionmentioning

confidence: 99%

“…As pointed out by Deng et al [21], their solution was cumbersome and its convergence depends on the number of terms used in the series. Deng et al [21] reexamined the problem of a partially debonded piezoelectric circular inclusion. They obtained closed form solutions by considering the behavior of the complex field potentials at origin and infinity, and also derived explicit formulas for the field intensity factors.…”

Section: Introductionmentioning

confidence: 99%

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Stress field near circular-arc interface crack tip based on electric saturation concept

Dai

Wang

2009

Front. Mech. Eng. China

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Within the framework of nonlinear electroelasticity, the anti-plane problem of a circular-arc interfacial crack between a circular piezoelectric inhomogeneity and an infinite piezoelectric matrix subjected to a far-field uniform loading is investigated by an electrical strip saturation model, the complex variable method, and the method of analytical continuation. Explicit closed form expressions for the complex potentials in both the matrix and the inclusion, and the stress intensity factor at the crack tip are presented. Comparison with some related solutions based on the linear electroelastic theory shows the validity of the present solutions

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Stress field near circular-arc interface crack tip based on electric saturation concept

Dai

Wang

2009

Front. Mech. Eng. China

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“…Among the works on the analytical solution, the representative ones that should be mentioned are those of Nemat-Nasser and Hori (1993), Meguid and Zhong (1997), Deng and Meguid (1999), Zhong and Meguid (1999), Jiang et al (2004), Shtrikman (1962, 1963) and later publications, Budiansky (1965), Eshelby (1957) and later publications, Chen and Lee (2002) as well as Buryachenko (2007). Analytical solutions are either limited to very simple geometries such as elliptical inclusions or require high level of mathematical competence.…”

Section: Introductionmentioning

confidence: 99%

Effective elastic properties of solids with irregularly shaped inclusions

Ping

Chen

2009

Int J Mech Mater Des

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A unit rectangular cell is usually cut out from a medium for investigating fracture mechanism and elastic properties of the medium containing an array of irregularly shaped inclusions. It is desirable to clarify the geometrical parameters controlling the elastic properties of heterogeneous materials because they are usually embedded with randomly distributed particulate. The stress and strain relationship of the rectangular cell is obtained by an ad hoc hybrid-stress finite element method. By matching the boundary condition requirements, the effective elastic properties of composite materials are then calculated, and the effect of shape and arrangement of inclusions on the effective elastic properties is subsequently considered by the application of the ad hoc hybrid-stress finite element method through examining three types of rectangular cell models assuming rectangular arrays of rectangular or diamond inclusions. It is found that the area fraction (the ratio of the inclusion area over the rectangular cell area) is one dominant parameter controlling the effective elastic properties.

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“…Shen et al [8] studied the interaction of a piezoelectric screw dislocation with a nonuniformly coated circular inclusion in an unbounded piezoelectric matrix subjected to remote anti-plane shear and electric fields. Deng and Meguid [9] considered the case of a partially debonded circular inclusion in piezoelectric materials. Gao and Noda [10] studied the anti-plane deformation of an arbitrarilyshaped inclusion embodied in an infinite piezoelectric material using Faber series expanding of complex potentials.…”

Section: Introductionmentioning

confidence: 99%

Interactions between N circular cylindrical inclusions in a piezoelectric matrix

2007

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Summary. This paper studies the interactions between N randomly-distributed cylindrical inclusions in a piezoelectric matrix. The inclusions are assumed to be perfectly bounded to the matrix, which is subjected to an anti-plane shear stress and an in-plane electric field at infinity. Based on the complex variable method, the complex potentials in the matrix and inside the inclusions are first obtained in form of power series, and then approximate solutions for electroelastic fields are derived. Numerical examples are presented to discuss the influences of the inclusion array, inclusion size and inclusion properties on couple fields in the matrix and inclusions. Solutions for the case of an infinite piezoelectric matrix with N circular holes or an infinite elastic matrix containing N circular piezoelectric fibers can also be obtained as special cases of the present work. It is shown that the electroelastic field distribution in a piezoelectric material with multiple inclusions is significantly different from that in the case of a single inclusion.

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Closed form solutions for partially debonded circular inclusion in piezoelectric materials

Cited by 29 publications

References 14 publications

Stress field near circular-arc interface crack tip based on electric saturation concept

Stress field near circular-arc interface crack tip based on electric saturation concept

Effective elastic properties of solids with irregularly shaped inclusions

Interactions between N circular cylindrical inclusions in a piezoelectric matrix

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