A continuum thermodynamics formulation for micro-magnetomechanics with applications to ferromagnetic shape memory alloys

Abstract

A continuum thermodynamics formulation for micromagnetics coupled with mechanics is devised to model the evolution of magnetic domain structures in magnetostrictive materials. The theory falls into the class of phase-field or diffuse-interface modeling approaches. In addition to the standard mechanical and magnetic balance laws, a set of micro-forces their associated balance laws are postulated. Thereafter, the second law of thermodynamics is analyzed to identify the appropriate material constitutive relationships. The general formulation does not constrain the magnitude of the magnetization to be constant, allowing for the possibilities of spontaneous magnetization changes associated with strain and temperature. The approach is shown to yield the commonly accepted Landau-Lifshitz-Gilbert equations for the evolution of the magnetization when the magnetization magnitude is constant. Within the theory a form for the free energy is postulated that can be applied to fit the general elastic and magnetic properties of a ferromagnetic shape memory material near its spontaneously magnetized state.