  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.
