Estimation of the Effective Magnetic Permeability of Polycrystals Using a Self-consistent Scheme

In this work, we propose to determine the effective magnetic permeability of a heterogeneous medium by the self-consistent method. To do this, we are looking for an equation system based only on the magnetic field by a micro-mechanical approach based on the Green function techniques. The 1-site self-consistent scheme consists in replacing the interactions between a particular heterogeneity and the surrounding real environment by those existing between an inclusion and a homogeneous medium having the effective properties of the polycrystal. Finally, to solve the integral equation; we have to evaluate the interaction tensor. Once the interaction tensor is calculated, the system of equations can be solved and the effective magnetic permeability is determined by framing the self-consistence conditions. Another approach consists in considering the interaction of each grain with its close neighbors and replacing the rest with the Homogeneous Equivalent Medium whose behavior is identical to the macroscopic behavior of the polycrystal: this is the self-consistent N-Site scheme which takes into account the topological effects and therefore allows to take into account anisotropy.