Investigation of a mode III crack in functionally graded magnetoelectroelastic materials

In this study, an anti-plane crack in a functionally graded magnetoelectroelastic materials is investigated. It is assumed that the material properties such as elastic stiffness c44(y), piezoelectric coefficient e15(y), dielectric constant 11(y), piezomagnetic coefficient 15(y), magnetoelectric coupling coefficient μ11(y) and magnetic permeability ʋ11(y) vary one-dimensionally on the y-coordinate with a series of functions f(y). An asymptotic analysis is done and the problem is solved by means of singular integral equation technique. The influence of the material inhomogeneity on crack tip stress, electric displacement and magnetic induction intensity factors are studied. The results are considered to reveal the effect of material inhomogeneity and geometry of the crack on the field intensity factors.