Numerical Homogenization for Nonlinear Multiscale Analysis of Electropermanent Magnet Composites

This study presents a numerical homogenization model to predict the effective nonlinear behavior of highly heterogeneous electropermanent magnet (EPM) composites. EPM composites consist of periodic microstructures composed of both soft and hard ferromagnetic materials (i.e., iron and permanent magnets). EPM composites possess unique ability to self-generate magnetic fields while adjusting them using external current, making them promising for use in electromechanical devices. However, direct numerical analysis of EPM composite structures requires huge computational costs, particularly in nonlinear ranges where electromechanical devices typically operate. This challenge can be alleviated through multiscale analysis using homogenization method. The developed homogenization model is constructed using the energy-based approach, assuming magnetic energy equivalence between heterogeneous and homogeneous media. Specifically, the effective B-H curve of EPM composite is computed by interpolating B-H pairs obtained by solving cell problems through finite element analysis. To validate the proposed homogenization model, three numerical examples including an actuator and a magnetic bearing, are investigated. In each example, the magnetic field distribution, magnetic energy, or magnetic force, along with computational time, of actual EPM heterogeneous structures are compared with those of equivalent structures having homogeneous effective B-H curve. These comparisons confirm the accuracy and computational efficiency of the developed numerical homogenization model.