Phenomenological theory of magnetic-field-induced strains in ferromagnetic shape-memory materials

A phenomenological theory for the deformation of microstructures in ferromagnetic martensitic materials (shape memory alloys) is developed. The calculation of the equilibrium states is reduced to an independent minimization of the elastic energy and a subsequent solution of the corresponding micromagnetic problem. For a multivariant microstructure consisting of two tetragonal martensitic twins, the components of the strain tensor are derived as functions of external stresses and the volume fractions of the twin variants. The equations describing the evolution of a twinned microstructure in an applied magnetic field have been derived. An application of the theory shows qualitative agreement with experimental observations of magnetic-field-induced strain transformations in Ni-Mn-Ga systems, in particular under external stresses.