Analytical solutions of the magnetic and stress fields on a soft ferromagnetic material containing a smooth rigid inclusion in two-dimensional space

Abstract

The analytical investigations on a rigid inclusion embedded in a soft ferromagnetic material in two-dimensional space subjected to uniform magnetic load at infinity have been carried out, with the magnetic insulation boundary of the rigid inclusion. In our study, explicit solutions of the magnetic and stress fields are obtained based on linear magnetoelastic theory and complex variable theory. The relative rigid-body displacement of the rigid inclusion is considered to ensure the boundary condition and constraint satisfied accurately. It is found that the analytic solutions of Kolosov-Muskhelishvili (K-M) potentials have a compact form when the shape of rigid inclusion is characterized by Laurent polynomial with finite terms. As examples, the rigid-body displacement, magnetic flux and stress on the boundary of elliptic and polygonal rigid inclusions are analyzed, respectively. Our results show that the rigid-body displacement caused by a non-strong magnetic load is small, while the orientation and contour curvature of the rigid inclusions have significant effects on the distribution of the stress and magnetic flux fields. In addition, the maximum magnetic flux and maximum stress do not always occur at the maximum curvature point. For polygonal rigid inclusions, the orientations in which the extreme concentration is obtained are closely related to the number of tips of the inclusions.