Effective magnetic susceptibility in magnetoactive composites

Abstract

Describing macroscopic samples made of composite material requires the development of an effective macro-continuum model where properties and microscopic arrangement of distinct phases are adequately taken into account. Here, we derive the effective magnetization behavior for compounds of magnetizable inclusions embedded in non-magnetizable medium. The homogenization is based on the dipole approximation and allows for a general formulation of the effective magnetic behavior, spanning from linear to saturation regime, for isotropic and anisotropic arrangements. For isotropic distributions presuming linear magnetization we reproduce an expression known from previous works, which proves to be very accurate in comparison to refined full-field calculations. Additionally, compelling agreement to existing experimental data is found. Consequently, we believe that our approach is of high practical relevance also in case of anisotropic distributions and beyond the linear magnetization. With a given particle arrangement and magnetization model on microscale, the expressions formulated here are obtained with low computational effort compared to homogenization based on micro-continuum approaches. The formulation can be directly implemented in a macroscopic material model for the composite of specified sample shape and solved by applying a macro-continuum approach.