Interfacial debonding of a circular inhomogeneity in piezoelectric–piezomagnetic composites under anti-plane mechanical and in-plane electromagnetic loading

This paper studies the problem of a partially debonded piezomagnetic circular inhomogeneity in an infinite piezoelectric matrix, or vice versa. The debonded parts are modeled by a set of circular-arc interfacial cracks. Crack surfaces are assumed to be electrically open and magnetically closed. The matrix is subjected to remote anti-plane mechanical and in-plane electromagnetic loadings. A general solution to the problem studied is obtained by employing the analytical continuation theory. Detailed analysis is made for a single circular-arc interfacial crack. The closed-form expressions of the complex potentials are obtained in both the inhomogeneity and the matrix. The intensity factors of stress, electric displacement and magnetic induction are also provided explicitly. For the case of piezoelectric matrix and piezomagnetic inclusion, the influence of crack geometry and the magnitudes of mechanical and electromagnetic loadings on the intensity factors are discussed in detail. In the case where anti-plane strain, in-plane electric and magnetic fields are applied simultaneously, the intensity factors only depend on the effective magneto-electro-elastic material constants, and whether the matrix is piezoelectric or piezomagnetic does not affect these intensity factors.