Mode I crack in a soft ferromagnetic material

In the existing magnetoelastic theories, stress is proportional to the square of magnetic intensity and the linear model developed is usually used to analyse magnetoelastic problems. For a crack problem, the perturbation of the magnetic field caused by deformation is not much less than the applied field. In this paper, complex potentials for a mode I crack with a nonlinear relation for magnetic intensity are developed. The boundary conditions on crack faces are represented in terms of the continuity of the magnetic field. A solution of the crack problem is obtained by solving the Riemann-Hilbert problem. Making use of the solution, the effects of the boundary conditions on the crack faces on the magnetoelastic coupling are discussed.