Abstract
For piezoelectric composites with nano-inclusions, the interface energy around the nano-inclusions will play important roles in predicting the electromechanical response under different loadings. In this paper, the interface energy effect on the electromechanical response of piezoelectric composites with a coated nano-inclusion of arbitrary shape under anti-plane mechanical and in-plane electric loadings is studied, and the analytical solutions of the stress and electric displacement are presented. Combining the Laurent series expansion technique and conformal mapping method, the general solutions of complex potentials are expressed. The unknown coefficients are determined by satisfying the boundary conditions with consideration of surface/interface effect. Some examples such as triangle and quasi-square shapes of nano-inclusions are given to show the distribution of internal stress and electric field. It is found that the interface energy effect shows significant variation with the shapes of nano-inclusions, and the effect in the case of circular shape is the smallest. The interface effect on the stress and electric field at the inner and outer boundaries is also examined.
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Wu L.Z., Chen J., Meng Q.G.: Two piezoelectric circular cylindrical inclusions in the infinite piezoelectric medium. Int. J. Eng. Sci. 38, 879–892 (2000)
Fang X.Q., Liu J.X., Dou L.H., Chen M.Z.: Dynamic strength around two interacting piezoelectric nano-fibers with surfaces/interfaces in solid under electro-elastic waves. Thin Solid Films 520, 3587–3592 (2012)
Wang X., Shen Y.P.: A solution of the elliptic piezoelectric inclusion problem under uniform heat flux. Int. J. Solids Struct. 38, 2503–2516 (2001)
Wang J.Z., Thomas M.M., Gao H.J.: Dynamic fiber inclusions with elliptical and arbitrary cross-sections and related retarded potentials in a quasi-plane piezoelectric medium. Int. J. Solids Struct. 40, 6307–6333 (2003)
Huang Z.Y., Kuang Z.B.: Dislocation inside a piezoelectric media with an elliptic inhomogeneity. Int. J. Solids Struct. 38, 8459–8479 (2001)
Yozo M.: Explicit determination of piezoelectric Eshelby tensors for a spheroidal inclusion. Int. J. Solids Struct. 38, 7045–7063 (2001)
Jiang B., Fang D.N., Keh-Chih H.: A unified model for piezocomposites with non-piezoelectric matrix and piezoelectric ellipsoidal inclusions. Int. J. Solids Struct. 36, 2707–2733 (1999)
Chen T.Y.: The translation of a rigid ellipsoidal inclusion embedded in an anisotropic piezoelectric medium. Int. J. Solids Struct. 31, 891–902 (1994)
Dinzart F., Sabar H.: Electroelastic behavior of piezoelectric composites with coated reinforcements: micromechanical approach and applications. Int. J. Solids Struct. 46, 3556–3564 (2009)
Malakooti M.H., Sodano H.A.: Multi-inclusion modeling of multiphase piezoelectric composites. Compos. Part B-Eng. 47, 181–189 (2013)
Rodriguez-Ramos R., Guinovart-Diaz R., Lopez-Realpozo J.C., Bravo-Castillero J., Sabina F.J.: Influence of imperfect elastic contact condition on the antiplane effective properties of piezoelectric fibrous composites. Arch. Appl. Mech. 80, 377–388 (2010)
Fang X.Q., Liu X.L., Huang M.J., Liu J.X.: Dynamic effective shear modulus of nanocomposites containing randomly distributed elliptical nano-fibers with interface effect. Compos. Sci. Technol. 87, 64–68 (2013)
Van den Ende D.A., Kempen S.E., Wu X.: Dielectrophoretically structured piezoelectric composites with high aspect ratio piezoelectric particles inclusions. J. Appl. Phys. 111, 124107 (2012)
Matteo B., Mark B., Alessandro G., Alessandro M., Marco S.: Memory characteristics of hysteresis and creep in multi-layer piezoelectric actuators: an experimental analysis. Physica B 435, 40–43 (2014)
Sudak L.J.: Effect of an interphase layer on the electroelastic stresses within a three-phase elliptic inclusion. Int. J. Eng. Sci. 41, 1019–1039 (2003)
Gao C.F., Noda N.: Faber series method for two-dimensional problems of an arbitrarily shaped inclusion in piezoelectric materials. Acta Mech. 171, 1–13 (2004)
Dai M., Gao C.F.: Perturbation solution of two arbitrarily-shaped holes in a piezoelectric solid. Int. J. Mech. Sci. 88, 37–45 (2014)
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Fang, X.Q., Liu, H.W., Liu, J.X. et al. Interface energy effect on electromechanical response of piezoelectric composites with an arbitrary nano-inclusion under anti-plane shear. Acta Mech 226, 2323–2333 (2015). https://doi.org/10.1007/s00707-015-1317-3
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DOI: https://doi.org/10.1007/s00707-015-1317-3