Analytical Mode III electromagnetic permeable cracks in magnetoelectroelastic materials

Fracture mechanism is pertinent to minimize the catastrophic failures and optimize the structural design. An exact treatment on the electromagnetic permeable crack problems in a magnetoelectroelastic medium is presented by establishing a Hamiltonian system in terms of the symplectic eigenfunctions. The coefficients of the series are determined from the lateral boundary conditions at the crack surfaces and the outer boundary conditions along the geometric domain. Analytical formulations of intensity factors and distributions of dual variables are obtained by the symplectic expansion method. The various intensity factors are directly related to the first few terms of the non-zero eigenvalue solutions.