Piezoelectric solid with an elliptic inclusion or hole

ABSTRACT:The generalized 2D problem in piezoelectric media with collinear cracks is addressed based on Stroh's formulation and the exact electric boundary conditions on the crack faces. Exact solutions axe obtained, respectively, for two special cases: one is that a piezoelectric solid with N collinear cracks is subjected to uniform loads at infinity, and the other is that a piezoelectric solid containing a single crack is subjected to a line load at an arbitrary point. It is shown when uniform loads are applied at infinity or on the crack faces that, the stress intensity factors are the same as those of isotropic materials, while the intensity factor of electric displacement is dependent on the material constants and the applied mechanical loads, but not on the applied electric loads. Moreover, it is found that the electric field inside any crack is not equal to zero, which is related to the material properties and applied mechanical-electric loads.

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“…For this case, A and B are nonsingular, and there is the following orthogonality relation [22] BT .3T B i/ = 0 I…”

Section: Stroh Formulationmentioning

confidence: 98%

Generalized 2D problem of piezoelectric media containing collinear cracks

Gao

Wang

1999

Acta Mech Sinica

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“…Multiplying the two conditions of (2.9) by B T and A T , respectively, and adding the resulting equations, we obtain 10) where use has been made of the following orthogonality relations [33]: on the boundary Γ , we can recast B T u * (y) as…”

Section: Solution Of the Magneto-electro-elastic Inclusion Problem Dumentioning

confidence: 99%

Eshelby's problem of polygonal inclusions with polynomial eigenstrains in an anisotropic magneto-electro-elastic full plane

2015

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This paper presents a closed-form solution for the arbitrary polygonal inclusion problem with polynomial eigenstrains of arbitrary order in an anisotropic magneto-electro-elastic full plane. The additional displacements or eigendisplacements, instead of the eigenstrains, are assumed to be a polynomial with general terms of order M + N. By virtue of the extended Stroh formulism, the induced fields are expressed in terms of a group of basic functions which involve boundary integrals of the inclusion domain. For the special case of polygonal inclusions, the boundary integrals are carried out explicitly, and their averages over the inclusion are also obtained. The induced fields under quadratic eigenstrains are mostly analysed in terms of figures and tables, as well as those under the linear and cubic eigenstrains. The connection between the present solution and the solution via the Green's function method is established and numerically verified. The singularity at the vertices of the arbitrary polygon is further analysed via the basic functions. The general solution and the numerical results for the constant, linear, quadratic and cubic eigenstrains presented in this paper enable us to investigate the features of the inclusion and inhomogeneity problem concerning polynomial eigenstrains in semiconductors and advanced composites, while the results can further serve as benchmarks for future analyses of Eshelby's inclusion problem.

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“…For plane piezoelectric material without considering thermal effect, Sosa and Khutoryansky [6] obtained an analytical solution of piezoelectricity with an elliptic hole based on Lekhnitskii's formulation and conformal mapping. Chung and Ting [ 7] developed a general solution for piezoelectric plate with an elliptic inclusion. Recently, Qin, Mai and Yu [s] derived an analytical solution for a 1998 piezoelectric solid with a hole of various shapes subjected to mixed mechanical, electric and thermal loads.…”

Section: Introductionmentioning

confidence: 99%

A new solution for thermopiezoelectric solid with an insulated elliptic hole

Qin

1998

Acta Mech Sinica

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A new solution is obtained for thermal analysis of insulated elliptic hole embedded in an infinite thermopiezoelectric plate. In contrast to our previous results, the present formulation is based on the use of exact electric boundary conditions at the rim of the hole, thus avoiding the common assumption of electric impermeability. Using Lekhnitskii's formulation and conformal mapping, the elastic and electric fields can be expressed in a closed form in terms of complex potentials. The solutions for the crack problem are obtained by setting the minor axis of the ellipse approach to zero. As a consequence, the stress and electric displacement (SED) intensity factors and strain energy release rate can be derived analytically. One numerical example is considered to illustrate the application of the proposed formulation and compare with those obtained from impermeable model.

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Piezoelectric solid with an elliptic inclusion or hole

Cited by 142 publications

References 13 publications

Generalized 2D problem of piezoelectric media containing collinear cracks

Generalized 2D problem of piezoelectric media containing collinear cracks

Eshelby's problem of polygonal inclusions with polynomial eigenstrains in an anisotropic magneto-electro-elastic full plane

A new solution for thermopiezoelectric solid with an insulated elliptic hole

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