Periodic limited permeable cracks in magneto-electro-elastic media

Abstract

A plane strain problem for a periodic set of the limited electrically and magnetically permeable cracks is considered in this work. The tensile mechanical stress, magnetic induction and electrical displacement are applied at infinity. Using the presentations of electro-magneto-mechanical components via sectionally analytic functions, the formulated problem is reduced to a matrix problem of linear relationships with the associated conditions at infinity. The exact analytical solution of this problem is found. A system of two transcendental equations for the determination of the electric displacement and magnetic induction in the crack regions is found. The solution of this system can be easily found by standard procedures. Formulae for the stresses, magnetic induction and electric displacement vectors, elastic displacements, magnetic and electric potential jumps at the interface as well as the intensity factors at the crack tips are presented in the form of simple analytical formulas. As a limiting case, a single limited permeable crack in magneto-electro-elastic media is studied as well. A comparison with the associated results for a periodic set of limited electrically and magnetically permeable cracks is performed.