Analytic solutions of multiple Mode III cracks in a circular bar reinforced by a magneto-electro-elastic layer under torsional loading

In this paper, the Saint-Venant torsion of a circular bar reinforced by a magneto-electro-elastic coating containing multiple cracks is analyzed. Pure Mode III stress intensity factors are studied in this paper. An electric displacement and a magnetic induction are applied to the outer edge of the magneto-electro-elastic coating. The stress field of the circular bar coated by the magneto-electro-elastic layer containing a screw dislocation is first found in terms of the dislocation density using finite Fourier transform. Then, the stress field is reduced to a set of Cauchy-type integral equations in the circular cross-section with the magneto-electro-elastic layer using the distributed dislocation method. The torsional rigidity of the cracked domain and the stress intensity factors (SIFs) are found by a numerical procedure of this type of integral equation. Several numerical examples are presented to check the effect of the magneto-electro-elastic layer and critical parameters on the stress intensity factors and torsional rigidity. In addition, the stress intensity factors can be eliminated using appropriate values of the electric displacement and magnetic induction.