Anti-plane analysis of multiple cracks originating from a circular hole in a magnetoelectroelastic solid

The anti-plane problem of multiple cracks originating from a circular hole in a magnetoelectroelastic solid is investigated under remotely uniform anti-plane mechanical loading and in-plane electromagnetic loadings. The boundary value problem is reduced to a Cauchy integral equation by a new mapping function and the complex variable method, which is further solved exactly. The analytic expressions of the complex potentials, the field intensity factors and the energy release rate are derived in closed-form under the assumption that the surfaces of the cracks and hole are both electrically and magnetically impermeable. The effects of crack configurations and combined loadings on the energy release rate are shown graphically. Several useful results which may have potential applications to the design and fracture analysis of magnetoelectroelastic structures are given.