Three-dimensional coupling field for an electromagnetically semi-permeable elliptical crack in multiferroic composite media

Abstract This article is concerned with an electromagnetically semi-permeable elliptical crack embedded in a multiferroic composite medium. The multiferroic composite medium is infinite and subjected to combined magneto-electro-elastic loads applied symmetrically at infinity. The boundary integro-differential equations associated with this nonlinear problem are solved analytically, with the aid of the generalized method of potential theory. The complete and closed-form coupling field is obtained and expressed with two elliptic functions. In addition, the crucial quantities on the crack plane, including the generalized crack surface displacements, the behavior of normal stresses in the crack-tip field and the generalized stress intensity factors, are derived explicitly. Numerical calculation and the finite element analyses for a BaTiO 3 -CoFe 2 O 4 composite medium are performed to verify the present analytical results and to illustrate the important parameters on the crack plane graphically.