Three-dimensional fundamental solution of a penny-shaped crack in an infinite thermo-magneto-electro-elastic medium with transverse isotropy

This paper investigates the problem of an infinite multiferroic composite medium weakened by a penny-shaped crack, which is symmetrically subjected to four pairs of generalized loads on the upper and lower surfaces. These loads could be mechanical pressures, electric displacements, magnetic inductions and temperature increments. In view of the magneto-electric properties of the crack surfaces, four mixed boundary problems are formulated. Based on the general solution, the three-dimensional thermo-magneto-electro-elastic coupling field variables in the three-dimensional full space for various boundary cases are explicitly obtained by means of the generalized potential theory method. Some important physical quantities in fracture mechanics, such as the generalized stress intensity factors and the generalized crack surface displacements, are presented as well. Numerical calculations are performed to validate the present solutions and to show the distributions of the 3D coupled fields. The influences of the magneto-electric properties of the crack surfaces on the generalized stresses and stress intensity factors are revealed. (C) 2017 Elsevier Ltd. All rights reserved.