External circular crack problem in magneto–electro-elasticity: Shear mode

Crack problems of multiferroic composites are of engineering significance and academic value. External circular crack is one of the basic configurations in the theoretical analyses. This paper examines an external circular crack on the shear mode embedded in an infinite space of multiferroic composite materials. By the potential theory method, the governing equation for arbitrarily shaped planar cracks under arbitrarily distributed shear loads, are established. The fundamental solution expressed by elementary functions is derived, from which the complex stress intensity factor at the crack tip is further deduced. It is interesting that the crack neck has a “shielding effect” on the physical quantities on the crack plane. The fundamental solution obtained in this work can provide foundations for numerical study and theoretical analysis of many complex boundary value problems.