New developments concerning piezoelectric materials with defects

Sosa, Horacio; Khutoryansky, Naum

doi:10.1016/0020-7683(95)00187-5

Cited by 213 publications

(90 citation statements)

References 9 publications

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“…In this subsection, the impermeable assumption is adopted due to the fact that the dielectric constants of piezoelectrics are three orders of magnitude higher than that of air or vacuum inside the void. As suggested by Sosa and Khutoryansky [27], a slender ellipse (e.g. a 0 /b 0 = 100) could be reasonably approximated by the impermeable assumption.…”

Section: Impermeable Elliptical Voidsmentioning

confidence: 98%

“…The two assumptions are the upper and lower limits of the exact electric boundary conditions [27,28]. In this subsection, a special set of Trefftz functions are derived for arbitrarily oriented permeable sharp cracks, see Figure 1(b).…”

Section: Permeable Sharp Cracksmentioning

confidence: 99%

“…In the literature, there are different opinions on the electric boundary condition for internal defects [25][26][27][28]. In this subsection, the impermeable assumption is adopted due to the fact that the dielectric constants of piezoelectrics are three orders of magnitude higher than that of air or vacuum inside the void.…”

Section: Impermeable Elliptical Voidsmentioning

confidence: 99%

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Trefftz solutions for piezoelectricity by Lekhnitskii's formalism and boundary‐collocation method

Sheng

Sze

Cheung

2005

Numerical Meth Engineering

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SUMMARYIn this paper, a solution procedure for plane piezoelectricity is developed by Trefftz boundarycollocation method. Starting with the general plane piezoelectricity solution derived by Lekhnitskii's formalism, the basic sets of Trefftz functions which satisfy the homogeneous governing equations are derived. Moreover, special sets of Trefftz functions are derived for impermeable elliptical voids, impermeable sharp cracks and permeable sharp cracks with arbitrary orientations with respect to the material poling direction. The functions in the special sets satisfy not only the homogeneous governing equations but also the boundary conditions at the peripheries of the pertinent defects. By adopting Trefftz functions as the trial functions, multi-domain Trefftz boundary-collocation method is formulated. Numerical examples are presented to illustrate the efficacy of the formulation.

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Section: Impermeable Elliptical Voidsmentioning

confidence: 98%

Section: Permeable Sharp Cracksmentioning

confidence: 99%

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Trefftz solutions for piezoelectricity by Lekhnitskii's formalism and boundary‐collocation method

Sheng

Sze

Cheung

2005

Numerical Meth Engineering

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“…In previous works, the impermeable boundary condition is assumed. Sosa & Khutoryansky (1996) applied the exact boundary conditions to expand the study developed by Sosa (1991), concluding that the impermeable boundary condition is unacceptable when the elliptic hole tends to a crack. The same conclusion was numerically obtained by Pérez-Aparicio et al (2007), using the finite element method.…”

Section: Piezoelectric Ceramics 76mentioning

confidence: 99%

Characterization of Properties and Damage in Piezoelectrics

Rus¹,

Palma²,

Suárez³

2010

Piezoelectric Ceramics

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“…Cracks with inside electric field. A more refined model for real flaws in electroelastic bodies is that in which an inside electric field is allowed in the cavity (e.g., Sosa and Khutoryansky 1996). In this case, the interface boundary conditions become C + <t>i = u?+u4= u\ …”

Section: Rigid Inclusionsmentioning

confidence: 99%

Uniform asymptotic solutions for lamellar inhomogeneities in piezoelectric solids

Dascalu¹,

Homentcovschi²

2003

Quart. Appl. Math.

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Abstract.We study the problem of a lamellar inhomogeneity of arbitrary shape embedded in a piezoelectric matrix of infinite extent. Uniform asymptotic solutions for the equations of elastostatics and electrostatics on this configuration are obtained. The first order terms, in the inhomogeneity thickness, are explicitly determined for piezoelectric inclusions, rigid inclusions of electric conductor, impermeable cracks, and cracks with inside electric field. We give real-form expressions of mechanical and electric fields at the interface and on the inhomogeneity axis. Detailed first order solutions are obtained for elliptic and lemon-shaped inhomogeneities.It is found that, while for elliptic piezoelectric inclusions the perturbation stresses and electric displacements at the inclusion ends have the same order as those given at infinity, for a lemon-shaped inclusion they are an order-of-magnitude smaller. Intensity factors are calculated for lemon-shaped cavities. It is shown that, when inside electric fields are considered, the stress intensity coefficients are influenced by the material anisotropy.

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New developments concerning piezoelectric materials with defects

Cited by 213 publications

References 9 publications

Trefftz solutions for piezoelectricity by Lekhnitskii's formalism and boundary‐collocation method

Trefftz solutions for piezoelectricity by Lekhnitskii's formalism and boundary‐collocation method

Characterization of Properties and Damage in Piezoelectrics

Uniform asymptotic solutions for lamellar inhomogeneities in piezoelectric solids

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