Three-dimensional fields in an infinite transversely isotropic magneto-electro-elastic space with multiple coplanar penny-shaped cracks

Abstract This paper investigates the Mode-I crack problem that a three-dimensional infinite space of transversely isotropic multi-ferroic composite medium is weakened by multiple coplanar penny-shaped cracks under uniform mechanical, electric and magnetic loadings. These cracks are arbitrarily distributed in an isotropic plane of the material. Four kinds of idealized electro-magnetic crack boundary conditions, which assume a crack to be electrically permeable (or impermeable) and magnetically permeable (or impermeable), are adopted, and all the possible combinations of these electro-magnetic crack boundary conditions are considered. An approximate three-dimensional solution of the field variables and expressions of some important fracture mechanics quantities are proposed, by virtue of Kachanov’s method and the generalized potential theory method. Numerical examples for some particular configurations of cracks are presented. Based on a two-crack system, the validity of the present solution is checked by comparing the results with their counterparts from a finite element simulation. Interaction of cracks is investigated as well, by taking the crack size and distance between two cracks as factors. From the phenomena shown in the numerical examples, a reduced solution and an empirical method for evaluating generalized stress intensity factors are proposed.