Plane Problem of Magnetoelasticity for a Piezomagnetic Medium with Cracks

We solve a boundary-value problem of magnetoelasticity for a piezomagnetic plane weakened by cracks. For this purpose, we generalize the method aimed at the solution of similar problems for anisotropic media. The boundary-value problem is reduced to a matrix singular integral equation and the solution of this equation is found in the class of vector functions unbounded at the ends of the notches. The numerical solution of this equation is obtained by the method of mechanical quadratures. The proposed numerical-analytic algorithm is used to investigate the influence of magnetoelastic fields on the stress intensity factors in the vicinity of the crack tips.