Framework for a Unified Macroscale Model of Magnetostriction

Abstract

This dissertation presents the development of a framework for a unified mutliscale model of magnetostriction. The lack of accurate models of macroscale hysteretic magnetostriction has inhibited the development of novel devices and savings. This thesis presents a framework for such a model. After motivating and providing the necessary background knowledge regarding these models, an analytic model of anhysteretic magnetostriction will be derived using equilibrium statistical mechanics. It will be shown 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. Additionally, a useful form of the analytic equations that ensures numerical accuracy will be provided. Furthermore, a comparison to experimental data performed for several magnetostrictive materials will show that the model accurately predicts the behavior of Terfenol-D while two different iron gallium alloys are modeled with varying accuracy. Next, this dissertation attempts to expand the 1D model to two dimensions. This requires numerical approximation techniques which take the form of quadrature methods in the existing magnetostrictive literature. Examining the inherent assumptions of models in the literature highlights that they often produce artificial spurious responses due to numerical inaccuracy. An analysis of several quadrature methods is presented and it is shown how the numerical accuracy of the approximation techniques impacts the validity of the resulting magnetostrictive constitutive models. The numerical accuracy for each method is presented, and the influence of this accuracy on the model's predictions is analyzed. The ability of the most accurate method to simulate experimental data from the literature is tested. Results show that when inaccurate numerical approximations are used the resulting constitutive mdoels have degenerate / non-physical behaviors that limit their utility. Finally, the preliminary research necessary to construct a thermodynamically consistent model for magnetostrictive hysteresis will be presented. This model will be inspired by existing continuum hysteresis models including the Jiles-Atherton model and plasticity-based models. The potential next steps of realizing this model are then proposed.