Efficient magnetic hysteresis model for field and stress application in magnetostrictive Galfenol

Abstract

We present a discrete energy-averaged model for the nonlinear and hysteretic relation of magnetization and strain to magnetic field and stress. Analytic expressions from energy minimization describe three-dimensional rotations of domains about easy crystal directions in regions where domain rotation is the dominant process and provide a means for direct calculation of magnetic anisotropy constants. The anhysteretic material behavior due to the combined effect of domain rotation and domain wall motion is described with an energy weighted average while the hysteretic material behavior is described with an evolution equation for the domain volume fractions. As a result of using a finite set of locally defined energy expressions rather than a single globally defined expression, the model is 100 times faster than previous energy weighting models and is accurate for materials with any magnetocrystalline anisotropy. The model is used to interpret magnetization and strain measurements of ⟨100⟩ oriented Fe79.1Ga20.9 and Fe81.5Ga18.5 as well as ⟨110⟩ oriented Fe81.6Ga18.4.

A general one-dimension nonlinear magneto-elastic coupled constitutive model for magnetostrictive materials

“…Just the magnetization and magnetostrictive strain of Metglas could reach the saturations in a small magnetic field. What's more, Mahadevan et al 13 and Evans et al 14 measured the magnetostrictive and magnetization curves of magnetostrictive material Galfenol under different pre-stresses, and found the effects of pre-stresses on magnetostrictive strain and magnetization of Galfenol were similar to Terfenol-D. While for the negative magnetostrictive material Ni6, it also can be found from Feng's experimental magnetostrictive and magnetization loops under different per-stresses 15 that the effects of pre-stress on magnetostrictive and magnetization loops of Ni6 were contrary to the effect on positive magnetostrictive material Terfenol-D. That is to say, the effect of compressive stress on negative magnetostrictive material was similar to the effect of tensile stress on positive magnetostrictive material for magnetostrictive strain curve.…”

Coupled axisymmetric finite element model of a hydraulically amplified magnetostrictive actuator for active powertrain mounts

“…Atulasimha et al [26] improved the accuracy of these models at the cost of increased computational load by tracking the volume fractions of domains aligned along 98 crystallographic orientations for Galfenol. Evans and Dapino [18] developed a constitutive model for Galfenol by choosing orientations which minimize an energy functional locally defined about each easy axis direction. This eliminated the loss in accuracy in the Armstrong model caused by the restricted choice of moment orientations without adding significant computational burden.…”

“…Evans and Dapino [17] presented a fully coupled dynamic model for 3D magnetostrictive transducers simultaneously incorporating the effects of eddy currents, structural dynamics, and flux leakage on transducer performance. This paper couples the weak form equations presented by Evans and Dapino [18] with a nonlinear energy-averaged constitutive model for Terfenol-D to describe the response of the magneto-hydraulic mount actuator developed by Chakrabarti and Dapino [7]. In order to exploit the axisymmetric geometry of the device, the equations are reduced to a 2D axisymmetric form.…”

Robust solution procedure for the discrete energy-averaged model on the calculation of 3D hysteretic magnetization and magnetostriction of iron–gallium alloys

“…Atulasimha et al [10] improved efficiency by only considering 98 fixed orientations. Evans and Dapino [11] proposed a discrete energyaveraged (DEA) model, which greatly improved efficiency while maintaining accuracy by solving for the local energy minimum about each of Galfenol's six easy crystallographic directions. The speed of this model is further increased by Chakrabarti [13], whose model is the starting point of our development.…”