Estimation of effective permeability for magnetoactive composites containing multi-chain-structured particles based on the generalized Mori–Tanaka approach

We present an analytic approach to evaluate the effective permeability of multi-chain-structured magnetic particle-filled composites which is formulated by a microstructure-based double-inclusion magnetic model with the generalized Mori-Tanaka theorem. The local magnetic field in a representative volume element (RVE) containing multi-chain-structured particles is derived by using a modified Green's function. The average fields in the particles, in a matrix coated by particles, and in an effective medium far away from particles are rendered by homogenization of the local magnetic distributions. By means of the relation between the average magnetic field and induction, the effective magnetic permeability of magnetoactive composites is explicitly derived; it exhibits anisotropic and universal behavior. The proposed model has been compared with the available experimental data and other microstructure-based models in the literature; it shows good agreement and gives reliable predictions for magnetic particle-filled composites, especially in terms of capturing the magnetic anisotropic characteristics with respect to the multi-chain-structured particle distribution.