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• W1973279931 abstract "In this paper, by systematically treating the integrals involved in the piezoelectric inclusion problem, we have obtained explicit results for the piezoelectric Eshelby tensor for cylindrical inclusions aligned along the axes either parallel or perpendicular to the axis of the anisotropy in a transversely isotropic piezoelectric material. First, based on Deeg's result (W.F. Deeg, The analysis of dislocation, crack and inclusion problems in piezoelectric solids, Ph.D. Dissertation, Stanford University, 1980) the integral representation for the piezoelectric Eshelby tensor for a general ellipsoid in an anisotropic piezoelectric material is derived in a simple and straightforward manner. In this derivation, a key transformation for the area element has been used, and the complete proof of this transformation is provided in Appendix A. Next, by carefully examining the integrals involved in the problem, we have obtained a representation of the components of the piezoelectric Eshelby tensor in terms of certain integrals for a general ellipsoid in a transversely isotropic piezoelectric material. Explicit results for the piezoelectric Eshelby tensor are obtained for the transeversely isotropic piezoelectric materials when the elliptic cylindrical inclusion is aligned along the axis of the anisotropy. These results coincide with the results obtained by M.L. Dunn (Electroelastic Green's functions for transversely isotropic piezoelectric media and their applications to the solutions of inclusion and inhomogeneity problems, Int. J. Engineering Science 32 (1994) 119–131) as well as J.H. Huang, J.S. Yu (Electroelastic Eshelby tensors for an ellipsoidal piezoelectric inclusion, Composites Engineering 4(11) (1994) 1182). Similarly, explicit results for the piezoelectric Eshelby tensor are also obtained for the transeversely isotropic piezoelectric materials when the elliptic cylindrical inclusion is aligned along the axis perpendicular to the axis of the anisotropy. This latter configuration becomes important when we consider piezoelectric composites where the piezoelectric fibers are placed perpendicular to the polling direction. To the best of the author's knowledge, this is a totally new result. It is also found in this paper that all of the elliptic crack-like inclusions either normal or parallel to the axis of the anisotropy have the same piezoelectric Eshelby tensor regardless of their aspect ratios in their respective configurations. Finally, by examining the integrals involved in the expressions for the piezoelectric Eshelby tensor, a new type of constraints on the piezoelectric material properties are found." @default.
• W1973279931 created "2016-06-24" @default.
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• W1973279931 date "2000-04-01" @default.
• W1973279931 modified "2023-09-24" @default.
• W1973279931 title "Determination of piezoelectric Eshelby tensor in transversely isotropic piezoelectric solids" @default.
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• W1973279931 doi "https://doi.org/10.1016/s0020-7225(99)00050-6" @default.
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