Fields produced by three-dimensional dislocation loops in anisotropic magneto-electro-elastic materials

In this article, we analyze the coupled elastic, electric and magnetic fields produced by an arbitrary three-dimensional dislocation loop in general anisotropic magneto-electro-elastic materials. We first extend the anisotropic elastic formulae of dislocations to the corresponding magneto-electro-elastic material system, including a general line-integration solution and the solution of a straight-line segment of dislocation. We then develop a new line-integral solution for the extended displacement field as well as the extended stress field. Furthermore, we derive analytical expressions for some useful parametric dislocation curves, such as the elliptic arc and straight line. Our solutions contain the piezoelectric, piezomagnetic, and purely anisotropic elastic solutions as special cases. As numerical examples, the fields produced by elliptic, hexagonal and cardioid shape dislocation loops in both piezoelectric crystals and magneto-electro-elastic materials are calculated. The efficiency and accuracy of different integral solutions of dislocation loops are compared and discussed. More important, the coupling magneto-electro-elastic effect is illustrated. It is shown that, due to the coupling among the elastic, electric and magnetic fields, an elastic dislocation, an electric potential discontinuity, or a magnetic potential discontinuity can induce all the elastic, electric and magnetic fields and that the coupling effect could be very strong near the dislocation loop line.