Elliptical crack problem in magneto-electro-thermo-elasticity of transversely isotropic materials: 3D analytical and numerical solutions

Abstract Crack problems are of high research value for multi-ferroic composite media, which have great potential in developing multi-functional devices. In account of the magneto-electro-thermo-elastic coupling effect, this paper investigates an elliptical crack contained in an infinite body of transversely isotropic multi-ferroic composite medium. The two crack surfaces are symmetrically loaded by the combinations of uniform mechanical, electric, magnetic and temperature loadings. The electric and magnetic permeabilities of the crack are idealized to be completely permeable (or impermeable), and thus four combinations of boundary conditions are considered. The field variables in the 3D space, as well as some parameters with great significance in fracture mechanics, are derived analytically, with the generalized method of potential theory. A unified solution of the field variables appropriate for all the four cases is proposed. By the principle of virtual displacement, the finite element formulation is also presented. Numerical results obtained from analytical method and simulations are presented for validating the present analytical solutions, and discussing the effect of magneto-electro-thermo-elastic properties.