Stress and induction field of a spheroidal inclusion or a penny-shaped crack in a transversely isotropic piezo-electric material

Kogan, L. I.; Hui, Chung‐Yuen; Molkov, V.

doi:10.1016/0020-7683(95)00182-4

Cited by 99 publications

(39 citation statements)

References 16 publications

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“…[1][2][3][4][5][6] In particular, the effective responses of piezoelectric composites can be used to design smart materials, which have wide applications in ultrasonic transducers, underwater acoustics, biomedical imaging, etc. 2 Due to these applications, the theoretical and experimental investigations of the effective properties of piezoelectric composites become very important.…”

Section: Introductionmentioning

confidence: 99%

Effective properties of spherically anisotropic piezoelectric composites

Wei

Poon

et al. 2007

Phys. Rev. B

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Piezoelectric composites consisting of spherically anisotropic piezoelectric inclusions ͑i.e., piezoceramic material͒ in an infinite nonpiezoelectric matrix under a uniform electric field are theoretically investigated. Analytical solutions for the elastic displacements and the electric potentials are derived exactly. Taking account of the coupling effects of elasticity, permittivity, and piezoelectricity, formulas are derived for the effective dielectric and piezoelectric responses in the dilute limit. A piezoelectric response mechanism is revealed, in which the effective piezoelectric response vanishes irrespective of how much spherically anisotropic piezoelectric inclusions are inside. Moreover, the effective coupled responses of the piezoelectric composites show that the effective dielectric responses decrease ͑increase͒ as the inclusion elastic ͑piezoelectric͒ constants increase.

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Section: Introductionmentioning

confidence: 99%

Effective properties of spherically anisotropic piezoelectric composites

Wei

Poon

et al. 2007

Phys. Rev. B

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“…Then writing Eqs. (1) to (6) in component form and using Voigt two-index notation, we obtain after some manipulation, the three-dimensional field equations of the transversely isotropic piezoelectric medium as:…”

Section: Field Equations Of Piezoelectric Mediamentioning

confidence: 99%

“…The problem of penny-shaped crack in transversely isotropic piezoelectric media was considered by Huang [5], Chen and Shioya [2], Kogan et al [6], etc. But in reality three-dimensional cracks may be better approximated by elliptical cracks.…”

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confidence: 99%

Elliptical crack and punch problems solved by integral equation method for piezoelectric media

Saha¹,

Saha

2011

Arch Appl Mech

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The problem of an elliptical crack embedded in an unbounded transversely isotropic piezoelectric media with the crack-plane parallel to the plane of isotropy of the media and subjected to remote normal mechanical as well as electric loading is considered first. The problem has been successfully reduced to a pair of coupled integral equations that are suitable for the application of an integral equation method developed earlier for three-dimensional problems of LEFM. Solution to the mechanical displacement and electric potentials are obtained for prescribed uniform loadings and expressions for corresponding intensity factors and crack opening displacement are deduced. The above method has further been applied to solve the problem of a rigid flat-ended elliptical punch indenting a transversely isotropic piezoelectric half-space surface with the plane of isotropy parallel to the surface. Solutions to mechanical stress and electric displacement are obtained for prescribed constant normal displacement and constant electric potential interior to the elliptical region and expression for the total force required to maintain a prescribed indentation is deduced.

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“…However, the strength of brittle piezoelectric materials is commonly reduced by the presence of defects such as cracks. The 3D crack problems in piezoelectric bodies have been studied by many researchers [1][2][3][4][5][6][7][8][9][10][11].…”

Section: Introductionmentioning

confidence: 99%

Coulomb traction on a penny-shaped crack in a three dimensional piezoelectric body

Ricoeur

Kuna

2010

Arch Appl Mech

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The axisymmetric problem of a penny-shaped crack embedded in an infinite three-dimensional (3D) piezoelectric body is considered. A general formulation of Coulomb traction on the crack surfaces can be obtained based on thermodynamical considerations of electromechanical systems. Three-dimensional electroelastic solutions are derived by the classical complex potential theory when Coulomb traction is taken into account and the poling direction of piezoelectric body is perpendicular to the crack surfaces. Numerical results show that the magnitude of Coulomb tractions can be large, especially when a large electric field in connection with a small mechanical load is applied. Unlike the traditional traction-free crack model, Coulomb tractions induced by an applied electric field influence the Mode I stress intensity factor for a penny-shaped crack in 3D piezoelectric body. Moreover, compared to the current model, the traditional traction-free crack model always overestimates the effect of the applied electric load on the field intensity factors and energy release rates, which has consequences for 3D piezoelectric fracture mechanics.

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Stress and induction field of a spheroidal inclusion or a penny-shaped crack in a transversely isotropic piezo-electric material

Cited by 99 publications

References 16 publications

Effective properties of spherically anisotropic piezoelectric composites

Effective properties of spherically anisotropic piezoelectric composites

Elliptical crack and punch problems solved by integral equation method for piezoelectric media

Coulomb traction on a penny-shaped crack in a three dimensional piezoelectric body

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