# Modelling Stress-Dependent Magnetic Permeability Using Two-Domain Approach with an Effective Anisotropic Wall Energy in Grain-Oriented Electrical Steel

## TL;DR

This paper introduces a new model to predict how mechanical stress affects magnetic permeability in electrical steel using a two-domain approach.

## Contribution

The novelty lies in incorporating an effective anisotropic wall energy to accurately model stress-dependent magnetic permeability in grain-oriented steel.

## Key findings

- The model successfully reproduces stress-dependent 2D permeability tensors with R-squared exceeding 98%.
- The anisotropic domain wall energy concept is a genuine novelty in low-field magnetic permeability analysis.

## Abstract

The magnetoelastic effect in grain-oriented electrical steels arises from interactions between magnetocrystalline anisotropy, domain wall confinement, and applied mechanical stress. This presents a comprehensive model based on the minimization of total magnetic energy in a two-domain system separated by a 180° Bloch wall. The model uniquely permits independent variation in the magnetization angle and external field direction, allowing accurate representation of energy competition among magnetostatic coupling, inter-domain interactions, and multi-component anisotropic confinement. The effective anisotropic wall energy incorporates isotropic, uniaxial, and six-fold crystallographic anisotropies modified by stress-induced terms. The Bloch wall position and the actual direction of magnetization are the variables that minimize the energy. Transformation to dimensionless variables enables efficient parameter identification via tri-division search. Experimental validation on M120-27s grain-oriented steel demonstrates that the model quantitatively reproduces stress-dependent 2D permeability tensors across arbitrary cutting orientations with very good quality, confirmed by determination coefficient R-squared exceeding 98%, which verifies the physical validity of the proposed model. This satisfactory agreement, together with the concept of anisotropic domain wall effective energy, represents a genuine novelty in the analysis of low-field magnetic permeability in grain-oriented electrical steels.