Measurements are performed to characterize the nonlinear and hysteretic magnetomechanical coupling of iron-gallium
(Galfenol) alloys. Magnetization of production and research grade Galfenol is measured under applied
stress at constant field, applied field at constant stress, and alternately applied field and stress. A high degree
of reversibility in the magnetomechanical coupling is observed by comparing a series of applied field at constant
stress experiments with a single applied stress at constant field experiment. Accommodation is not evident
and magnetic hysteresis for both applied field and stress is shown to be coupled. A stress, field, and orientation
dependent hysteron is developed from continuum thermodynamics which employs a unified hysteresis mechanism
for both applied stress and field. The hysteron has an instantaneous loss mechanism similar to Coulomb-friction
or Preisach-type models and is shown to satisfy the second law of thermodynamics. Stochastic homogenization
is employed to account for the smoothing effect that material inhomogeneities have on the magnetization.
A general framework is developed to model the nonlinear magnetization and strain response of cubic magnetostrictive
materials to 3-D dynamic magnetic fields and 3-D stresses. Dynamic eddy current losses and inertial stresses are modeled by coupling Maxwell's equations to Newton's second law through a nonlinear constitutive model. The constitutive model is derived from continuum thermodynamics and incorporates rate-dependent
thermal effects. The framework is implemented in 1-D to describe a Tonpilz transducer in both dynamic actuation
and sensing modes. The model is shown to qualitatively describe the effect of increase in magnetic hysteresis with increasing frequency, the shearing of the magnetization loops with increasing stress, and the decrease in the magnetostriction with increasing load stiffness.
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 <i>K</i><sub>1</sub> includes the value of
magnetostriction-induced fourth order anisotropy constant Δ<i>K</i><sub>1</sub>, 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.
A fully-coupled, nonlinear model is presented that characterizes the 3-D strain and magnetization response of
magnetostrictive materials to magnetic fields and mechanical stresses. The model provides an efficient framework
for characterization, design, and control of Galfenol (Fe<sub>1-<i>x</i></sub>Ga<sub><i>x</i></sub>) devices with 3-D functionality subjected
to combined magnetic field and stress loading. A thermodynamic approach is taken to determine possible domain
orientations considering the magnetocrystalline anisotropy, magnetomechanical, and Zeeman energies. The
domain configuration is determined through minimization of the total Gibbs energy of a collection of domains.
To incorporate material texture, the orientation of the applied field and stress with respect to the local crystal
orientation is included as a statistically distributed parameter. Hysteresis due to irreversible domain wall motion
is modeled by accounting for the energy loss due to domain wall pinning sites.
A homogenized energy model was implemented in a model-based nonlinear control design to accurately track
a reference displacement signal for high frequency magnetostrictive actuator applications. Rate dependent nonlinear
and hysteretic magnetostrictive constitutive behavior is incorporated into the finite-dimensional optimal
control design to improve control at high frequency. The integration of the rate-dependent nonlinear and hysteretic
magnetostrictive constitutive model in the control design minimized the amount of feedback required
for precision control. The control design is validated experimentally and shown to accurately track a reference
signal at frequencies up to at least 1 kHz.
We present a thermodynamic framework to quantify the magnetization and magnetostriction of Galfenol alloys
in response to magnetic fields, mechanical stress, and/or stress-annealing. The framework utilizes only physical
parameters and thus provides useful information for material characterization. Furthermore, we formulate the
model in state-space form, thus facilitating the computational implementation for design and control of dynamic