Interaction body force density and mechanical deformation in soft magnetic materials with external field by freezing procedure of magnetization

The quantitative interaction body force density was calculated in soft magnetic materials by using a freezing procedure of magnetization and virtual air-gap scheme, which were implemented by using the Finite Element Method. Until now, the virtual air-gap concept has been successfully applied to evaluating contact force and body force density in soft magnetic materials. When the generalized methods, methodologies with virtual air-gap scheme, are introduced, one can have an irregular force field, which seems to be random distribution of body force density. Even though this irregular pattern generates a correct global force and reasonable trend of mechanical deformation, it is quite difficult to predict the resultant deformation by the irregular force field. This irregular force field pattern is originated from the field direction to the finite element edge where the virtual air gap is inserted and an additional strong force arises with the outward normal direction. To remove this irregular pattern and evaluate an interaction body force density, the self-force density by the frozen magnetization should be withdrawn from the total body force density. To verify the proposed method, first, a critical magnetic system, which cannot be solved by the equivalent magnetizing source methods, were tested for evaluating the interaction body force density corresponding to the resultant mechanical deformations. After confirming the interaction force, two additional specific models were tested with the resultant mechanical deformations due to the different local force densities.