Numerical testing of homogenization formulas efficiency for magnetic composite materials

Magnetic composite materials are used for multiple applications. The macroscopic behavior of the material is influenced by its microscopic properties. Sometimes it is difficult to model the complex structure of the composite because the properties differ at the microscopic scale. Some simplifying assumptions are often needed, one of them being the homogenization of the material. In this paper two different composite materials were analyzed using a finite element software (COMSOL Multiphysics (C)). Both materials have a non-magnetic matrix with inclusions made of paramagnetic material for one of them, and ferromagnetic material for the other. The 3D numerical simulations were made for different particle concentrations and for different applied fields. The homogenization was implemented using two different formulas: Maxwell Garnett and Bruggeman. Numerical comparison was made between the magnetic properties of non-homogeneous materials and homogeneous ones showing each formula's efficiency for different cases.