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Uniformity of electroelastic field within a three-phase anisotropic piezoelectric elliptical inhomogeneity in anti-plane shear

Wang X., Schiavone P.

Archives of Mechanics

2022

Vol. 74, nr 2-3

143--156

Using the Stroh quartic formalism, we prove that the internal electroelastic field is unconditionally uniform inside a three-phase anisotropic piezoelectric elliptical inhomogeneity with two confocal elliptical interfaces when the surrounding matrix is subjected to uniform remote anti-plane mechanical and in-plane electrical loading. The inhomogeneity and the matrix comprise monoclinic piezoelectric materials with symmetry plane at x3 = 0 and with poling in the x3-direction; the intermediate interphase layer is a transversely isotropic piezoelectric material with poling in the x3-direction. Moreover, we obtain the internal uniform electroelastic field inside the elliptical inhomogeneity and the non-uniform electroelastic field in the interphase layer in real-form in terms of the fundamental piezoelectricity matrices for both the inhomogeneity and the matrix and the generalized Barnett–Lothe tensors for both the interphase layer and the matrix.