Equivalence of magnetoelastic, elastic, and mechanical work energies with stress-induced anisotropy

摘要

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 K_1 includes the value of magnetostriction-induced fourth order anisotropy constant △K_1, 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.