The development of a new generation of energy efficient, high torque and power density electrical machines is part of a solution toward the global energy problem. An important step in improving electrical machine performance involves optimization of the machine geometry, winding configuration, and overcoming limitations within traditional magnetic materials. In electrical machine, the magnetic iron core accounts for a significant portion of its weight and size. Under a rotating magnetic field, conventional iron cores are subjected to a nonuniform magnetic field distribution. This leads to uneven saturation distribution, extra core loss, and sub-optimal utilization of the permeability at certain regions within the iron cores. Deploying materials with non-homogeneous magnetic permeability can lead to a more uniform magnetic flux density distribution and potentially better power density. Additionally, a multi-permeability iron core, where the permeability is tuned as a function of both position and electrical machine performance, can lead to a more efficient use of the core and an additional degree of freedom for core design. This work evaluates the use of iron cores with non-homogeneous magnetic permeability for electrical machines. It is numerically demonstrated that an iron core with spatially tuned permeability can be used to manipulate the airgap flux density waveform, torque, and iron loss in electrical machines.