Asymptotic homogenization of magnetic composite for controllable permanent magnet.

Abstract A periodic composite microstructure consisting of permanent magnet and ferromagnetic material can be utilized to realize a controllable permanent magnet. For the microstructure design of the permanent magnet composite, its effective material properties should be estimated accurately and efficiently. For this, an asymptotic homogenization method is developed in this work. Specifically, the formulations for homogenized magnetic permeability and residual flux density are mathematically derived for both scalar and vector potential magnetostatic analysis approaches. Using the asymptotic expansion, cell problem equations are first derived, which will be solved by finite element method in microscopic coordinate. Then, the integral form formulations are derived for the calculation of homogenized effective properties. To show the design possibility of the composite, four numerical examples are investigated in this work. In each example, the accuracy of the obtained properties is numerically validated by comparing the magnetic field and energy produced by a homogeneous composite with the obtained effective properties and those produced by a heterogeneous model with actual periodic composite structures. In addition, the computation time of the homogeneous and heterogeneous models are compared to confirm the computational benefit of the developed homogenization method. [ABSTRACT FROM AUTHOR]