Electrically and magnetically induced Maxwell stresses in a magneto-electro-elastic medium with periodic limited permeable cracks

In this work, the Maxwell stresses arising due to an electric and a magnetic field both at the crack faces and infinity are taken into account to determine and analyse some main fracture parameters for a periodic system of cracks in a magneto-electro-elastic material. A plane strain problem is formulated and analysed. At the crack faces, the limited permeable electromagnetic boundary conditions are assumed. The material is subjected to a relatively weak mechanical and a strong electric and magnetic loading applied at infinity. The solution of the problem is obtained in a closed form using a complex function theory. Formulas for stresses, magnetic induction and electric displacement vector, elastic displacements, magnetic and electric potential jumps at the interface as well as the intensity factors at the crack tips are presented as relatively simple analytical expressions. The system of two cubic equations is obtained for the electric displacement and magnetic induction in the crack regions. A case of a single limited permeable crack in a magneto-electro-elastic medium is studied as well, and the results related to this case and to the periodic crack set are compared.