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Closed form solutions for partially debonded circular inclusion in piezoelectric materials

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Summary

This paper deals with the problem of a partially debonded piezoelectric circular inclusion in a piezoelectric matrix. This boundary value problem is reduced to two Riemann-Hilbert problems through the use of the analytical continuation theory.Closed form solutions are obtained by considering the behavior of the complex field potentials at origin and infinity. The formulae for the electro-elastic field intensity factors of the interfacial crack are derivedexplicitly. Several particular cases are provided to show the effect of the crack angle, the mechanical and electrical properties and the loads on the electroelastic field singularities.

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References

  1. Wang, B.: Three-dimensional analysis of an ellipsoidal inclusion in piezoelectric material. Int. J. Solids Struct.29, 293–308 (1992).

    Google Scholar 

  2. Dunn, M. L., Taya, M.: An analysis of piezoelectric composite materials containing ellipsoidal inhomogeneity. Proc. R. Soc. London Ser.A443, 265–287 (1993).

    Google Scholar 

  3. Liang, J., Han, J.-C., Wang, B., Du, S.: Electro-elastic modelling of anisotropic piezoelectric materials with an elliptic inclusion. Int. J. Solids Struct.32, 2989–3000 (1995).

    Google Scholar 

  4. Chung, M. Y., Ting, T. C. T.: Piezoelectric solid with an elliptical inclusion or hole. Int. J. Solids Struct.33, 3343–3361 (1996).

    Google Scholar 

  5. Meguid, S. A., Deng, W.: Electro-elastic interaction between a screw dislocation and an elliptical inhomogeneity in piezoelectric materials. Int. J. Solids Struct.35, 1467–1482 (1998).

    Google Scholar 

  6. Pak, Y. E.: Crack extension force in a piezoelectric material. J. Appl. Mech.57, 647–653 (1990).

    Google Scholar 

  7. Pak, Y. E.: Circular inclusion problem in antiplane peizoelectricity. Int. J. Solids Struct.29, 2403–2419 (1992).

    Google Scholar 

  8. Honein, T., Honein, B. V., Honein, E., Herrmann, G.: On the interaction of two piezoelectric fi embedded in an intelligent material. ASME AD-35, 105–112 (1993).

    Google Scholar 

  9. Zhang, T.-Y., Tong, P.: Fracture mechanics for a mode II crack in a piezoelectric material. Int. J. Solids Struct.33, 343–359 (1996).

    Google Scholar 

  10. Dunn, M. L., Wienecke, H. A.: Inclusions and inhomogeneities in transversely isotropic piezoelectric solids. Int. J. Solids Struct.34, 3571–3582 (1997).

    Google Scholar 

  11. Meguid, S. A., Zhong, Z.: Analysis of a circular arc-crack in piezoelectric materials. Int. J. Fracture84, 143–158 (1997).

    Google Scholar 

  12. Deng, W., Meguid, S. A.: Analysis of a screw dislocation inside an elliptical inhomogeneity in piezoelectric solids. Int. J. Solids Struct.36, 1449–1469 (1999).

    Google Scholar 

  13. Kuo, C.-M., Barnett, D. M.: In: Modern theory of anisotropic elasticity and applications (Wu, J. J., Ting, T. C. T., Barnett, D. M., eds.), pp. 35–50. Philadelphia: SIAM Proceedings 1991.

    Google Scholar 

  14. Suo, Z., Kuo, C.-M., Barnett, D. M., Willis, J. R.: Fracture mechanics for piezoelectric ceramics. J. Mech. Phys. Solids40, 739–765 (1992).

    Google Scholar 

  15. Deng, W., Meguid, S. A.: Analysis of a conducting rigid inclusion at the interface of two dissimilar piezoelectric materials. ASME J. Appl. Mech.65, 76–84 (1998).

    Google Scholar 

  16. Zhong, Z., Meguid, S. A.: Interfacial debonding of a circular inhomogeneity in piezoelectric materials. Int. J. Solids Struct.34, 1965–1984 (1997).

    Google Scholar 

  17. Deeg, W. F.: The analysis of dislocation, crack, and inclusion problems in piezoelectric solids. Ph. D. Thesis, Stanford University 1980.

  18. Muskhelishvili, N. I.: Some basic problems of the mathematical theory of elasticity. Leyden: Noordhoff 1975.

    Google Scholar 

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Deng, W., Meguid, S.A. Closed form solutions for partially debonded circular inclusion in piezoelectric materials. Acta Mechanica 137, 167–181 (1999). https://doi.org/10.1007/BF01179207

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  • DOI: https://doi.org/10.1007/BF01179207

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