Nonlinear One-Dimensional Constitutive Model for Magnetostrictive Materials

TL;DR

This paper develops an exact one-dimensional analytic model for magnetostriction in materials, simplifying complex three-dimensional micromagnetic energies, and demonstrates its accuracy across various materials and conditions.

Contribution

It introduces a novel exact one-dimensional model for magnetostriction derived from three-dimensional micromagnetic energies, improving predictive accuracy and numerical stability.

Findings

Accurately predicts Terfenol-D behavior

Models Galfenol with varying accuracy

Maintains accuracy over wide magnetic and stress ranges

Abstract

This paper presents an analytic model of one dimensional magnetostriction. We show how specific assumptions regarding the symmetry of key micromagnetic energies (magnetocrystalline, magnetoelastic, and Zeeman) reduce a general three-dimensional statistical mechanics model to a one-dimensional form with an exact solution. We additionally provide a useful form of the analytic equations to help ensure numerical accuracy. Numerical results show that the model maintains accuracy over a large range of applied magnetic fields and stress conditions extending well outside those produced in standard laboratory conditions. A comparison to experimental data is performed for several magnetostrictive materials. The model is shown to accurately predict the behavior of Terfenol-D, while two compositions of Galfenol are modeled with varying accuracy. To conclude we discuss what conditions facilitate the description of materials with cubic crystalline anisotropy as transversely isotropic, to achieve peak model performance.