This work investigates the equivalence of thermodynamic potentials utilizing stress-induced anisotropy energy
and potentials using elastic, magnetoelastic, and mechanical work energies. The former is often used to model
changes in magnetization and strain due to magnetic field and stress in magnetostrictive materials. The enthalpy
of a ferromagnetic body with cubic symmetry is written with magnetization and strain as the internal
states and the equilibrium strains are calculated by minimizing the enthalpy. Evaluating the enthalpy using
the equilibrium strains, functions of the magnetization orientation, results in an enthalpy expression devoid
of strain. By inspecting this expression, the magnetoelastic, elastic, and mechanical work energies are identified to be equivalent to the stress-induced anisotropy plus magnetostriction-induced fourth order anisotropy.
It is shown that as long as the value of fourth order crystalline anisotropy constant K1 includes the value of
magnetostriction-induced fourth order anisotropy constant ΔK1, energy formulations involving magnetoelastic,
elastic, and mechanical work energies are equivalent to those involving stress-induced anisotropy energy. Further,
since the stress-induced anisotropy is only given for a uniaxial applied stress, an expression is developed for a
general 3D stress.