Evaluation of the mechanical deformation in incompressible linear and nonlinear magnetic materials using various electromagnetic force density methods

Mechanical deformation in incompressible linear and nonlinear magnetic materials was evaluated using various conventional electromagnetic volume and surface force density methods. These conventional force density methods are the Maxwell stress tensor method, Korteweg-Helmholtz force density method (KH), magnetic charge method, magnetizing current method, and Kelvin force density method (KV). The total force values obtained using these different force density methods were found to be the same and equal to the total force using the principle of virtual work, but the distribution of force density values calculated using the given force density methods was found to be different from each other. Using the given five force density methods, the mechanical deformations were evaluated and compared to one another. The KH and KV in incompressible material were shown to give the same mechanical deformation by employing the finite element method (FEM), verifying the theoretical equivalence. To implement the KV, the derivative of magnetic field intensity with respect to the geometrical position was calculated using a linear shape function of FEM along with the nodal field values in each element. A magnetic systems was tested to compare the mechanical deformation in linear and nonlinear magnetic materials.