Filled with iron particles, polymers can be made responsive to magnetic fields. Specifically, the elastomers that change
stiffness in response to a magnetic field are usually called magneto-rheological elastomers (MREs). Anisotropic MREs,
in which the particles are aligned during curing and form chain-like structures, exhibit a more significant magneto-rheological
(MR) effect, i.e. the field-induced stiffening. In this paper, we first develop a constitutive model for the
nonlinear behavior of deformable solids under magnetic field. Based on the filler-substrate microstructure of MREs, we
further implement the theory into a finite element method. The magneto-mechanical response of a representative unit
cell of MRE is studied using the finite element method. The MR effect in both the shear modulus and the tensile
modulus of an MRE is studied. In addition, we consider the viscoelasticity of the polymer matrix and study its effect on
the properties of an MRE. Using the viscoelastic model for MRE, we also investigate the frequency dependence of the
MR effect.
Magneto-active polymers (MAPs), composed of polymer matrices and magnetic filler particles, are smart materials that
deform quickly in an external magnetic field. The ability to produce large deformation of MAPs makes these materials
promising for actuators and sensors. Due to the viscoelasticity of the polymer matrices, MAPs usually demonstrate ratedependent
dynamic properties. However, very few models of coupled magnetic field and viscoelasticity in MAPs exist
in the literature, and even fewer are capable of reliable predictions. Starting from nonequilibrium thermodynamics, a
field theory is developed to fully couple the finite-deformation viscoelasticity and magnetostatics of MAPs. The theory
provides a guideline for experimental characterization of MAPs, and most material laws are readily applicable in this
framework. A specific material model is prescribed for an idealized MAP. As demonstrations, numerical examples are
implemented on the responses of the MAP in response to both uniform and nonuniform magnetic fields. In the nonviscous
limit, our theory recovers a model for elastic MAPs, and is capable of capturing instability phenomena observed
in the experiments.
Microforming requires high-precision motion due to scaling issues. A Terfenol-D transducer was considered to provide
bulk motion for micro-extrusion. Because Terfenol-D cannot practically produce the necessary 2.5 mm displacement for
this micro-extrusion experiment, a lever system was designed to amplify the output displacement. Compliant joints
(flexures) were used to replace conventional bearings, resulting in a flexible, solid-state lever mechanism. By
eliminating the backlash and static friction associated with conventional bearings, it should be possible to improve
displacement precision as required to meet the geometric tolerance demands of microforming. A chief concern when
designing flexure joints that see large amounts of axial loading is compliance, which leads to not only loss of motion but
also loss of accuracy as the lever system responds differently under different loads. However, because Terfenol-D
already has load-dependent response, this loss of accuracy is moot when coupled with a Terfenol-D prime mover, as it
already requires load-dependent control. Preliminary FEM analysis has shown this design to have lever ratio losses of
approximately 4% from half load to full load, with lower than predicted stress.
Ferrogels are compliant composite materials formed of a soft polymer matrix with a filler of magnetic powder. The
interaction of the magnetic filler with an applied magnetic field causes the deformation of the ferrogel. Strains of up to
40% have been measured with load capabilities of up to four times the sample's weight. As these materials move toward
application it is important to capture the actuator behavior in mathematical models so that materials can be designed and
the behavior predicted. In this work experimental testing captures the strain and strain rate behavior of these materials at
fields up to 0.5 T. A lumped parameter model is then developed that is much less computationally intensive than
existing modeling approaches. The ability of this model to capture the behavior of interest will be assessed.
Ferrogels are soft polymer materials containing a filler of magnetic particles that allow the material to be activated by
magnetic fields. These materials have shown capabilities for large strains, fast response, ease of synthesis and
biocompatibility and have potential applications including artificial muscles, controlled drug release systems, and
hyperthermia cancer treatment. In this work the actuator behavior for a selection of ferrogel compositions and synthesis
methods are characterized including their free strain and loading behavior. Samples were synthesized using either
chemical or physical methods for samples containing PVA of 4, 8, and 12 wt% and magnetic particles of 1, 5, and 10
wt%. This samples were then tested for free strain and strain under loads of up to 4 times their weight by exposing them
of fields from between 0.2 and 0.25T. Results show that softer samples with the largest amount of iron achieve the
largest strains. Thus, chemically crosslinked sample with 4 wt% PVA and 10 wt% iron achieved the largest strain of
almost 40%. Soft samples however exhibit low loaded capabilities with a blocked load of 1.7g identified. The
physically crosslinked samples which were stiffer achieved very good loading capabilities with only a 20% strain
decrease when loaded up to 400% of their weight. This translated in to a energy density of 320 J/m3 making these
materials very promising for actuator applications.
Ferromagnetic Shape Memory Alloys (FSMAs) in the nickel manganese gallium system have been shown to exhibit large magnetically induced strains of up to 9.5% due to magnetically driven twin variant reorientation. In order for this strain to be reversible, however, an external restoring stress or magnetic field needs to be applied orthogonal to the field and hence the implementation of Ni-Mn-Ga in applications involves the use of electromagnets, which tend to be heavy, bulky and narrowband. In previous work at The Ohio State University a sample of Ni50Mn28.7Ga21.3 has been shown to exhibit reversible compressive strains of -4200 microstrain along its [001] direction when a magnetic field is applied along this same direction and no externally applied restoring force is present. This reversible strain is possible because of an internal stress field associated with pinning sites induced during manufacture of the crystal. This paper analyzes the switching between two variant orientations in the presence of magnetic fields (Zeeman energy) and pinning sites (pinning energy) through the formulation of a Gibbs energy functional for the crystal lattice. Minimization of the Gibbs free energy yields a strain kernel which represents the predicted behavior of an idealized 2-dimensional homogeneous single crystal with a single twin boundary and pinning site. While adequate, the kernel has limitations because it does not account for the following: (a) Ni-Mn-Ga consists of a large number of twin variants and boundaries, (b) the strength of the pinning sites may vary, and (c) the local and applied magnetic field will differ due to neighbor-to-neighbor interactions. These limiting factors are addressed in this paper by considering stochastic homogenization. Stochastic distributions are used on the interaction field and on the pinning site strength, yielding a phenomenological model for the bulk strain behavior of Ni50Mn28.7Ga21.3. The model quantifies both the hysteresis and saturation of the strain. Constrained optimization is used to determine the necessary parameters and an error analysis is performed to assess the accuracy of the model for various loading conditions.
Our previous work on ferromagnetic shape memory Ni50Mn28.7Ga21.3 demonstrates reversible compressive strains of -4100 microstrain along the [001] direction under the application of a magnetic field also along the [001] direction with no external orthogonal restoring force. The reversibility of the strains is due to internal bias stresses oriented orthogonal to the field. These results show promise for the use of Ni-Mn-Ga as the core material in solenoid transducers. In this paper, the reversible strains are explained by considering pinning sites as the source of the internal bias stresses in the material. Following prior work by Kiefer and Lagoudas, a phenomenological model is constructed for the motion of twin variants in the presence of an orthogonal pair formed by a magnetic field and an internal bias stress. The model is formulated by considering the Zeeman, elastic, and pinning energies, from which an appropriate Gibbs energy function is constructed. Minimization of the Gibbs function then yields a constitutive model for the strain. The accuracy of this model is studied and its implementation as a hysteresis kernel in homogenization theories is discussed.
Ferromagnetic shape memory nickel-manganese-gallium (Ni-Mn-Ga) has shown tremendous promise as an actuator material due to its large strain and high bandwidth. However, current Ni-Mn-Ga devices are electromagnet based as this configuration allows for an externally applied force perpendicular to the applied field, and are therefore bulky, energy inefficient, and narrowband. We investigate the dynamic response of Ni-Mn-Ga driven by a solenoid transducer in which the magnetic field is aligned collinearly with the loading stress. The work focusses on the quasistatic and dynamic testing of a Ni50Mn28.7Ga21.3 sample which is believed to have an internal stress field which plays the role of the restoring force necessary for reversible strains. This sample is shown to exhibit reversible compressive strains of -0.41% with no external forces applied. Several experimental apparatus are used in order to verify these results. The measurements demonstrate a 231% change in stiffness with applied dc magnetic fields.
Ferromagnetic shape memory martensites in the Ni-Mn-Ga system have been demonstrated to achieve a number of the criteria required for next generation actuators including the production of large theoretical strains up to 6%. The large strain originates in the rotation of twin variants and associated twin boundary motion which occurs in response to magnetic fields. The magnetic activation holds promise in actuator design because it can lead to higher bandwidths than those achieved through pure martensite-austenite phase transformation, as is the case with thermally-activated shape memory alloys. In this paper, we report on experimental measurements collected from a cylindrical Ni49.0Mn30.0Ga21.0sample alloy, driven as cast by a collinear magnetic field-stress pair. Despite the lack of a known restoring force and the fact that no "training" procedures are applied, quasi-static strains as large as 4300 micro-strain are shown. Furthermore, dynamic results in the DC-20kHz range are presented which would suggest the presence of a Delta-E effect similar to that seen in Terfenol-D but exhibiting an opposite dependence of stiffness with DC field. The potential implications of the results for the design and control of dynamic structures based on Ni-Mn-Ga are very significant.
In numerous applications, smart material transducers are employed to actuate upon virtually immovable structures, that is, structures whose stiffness approaches infinity in comparison with that of the transducer itself. Such mechanically blocked transducer configurations can be found in applications ranging from seismic testing and isolation of civil structures, to clamping mechanisms in linear or rotational inchworm motors. In addition to providing high blocking forces, smart materials for this type of applications must often be small in size and lightweight in order for design constraints to be met. This paper provides a characterization of the force produced by a 0.9 cm (0.35 in) diameter, 2.0 cm (0.79i in) long Terfenol-D operated under mechanically blocked conditions. Experimental results are shown for several mechanical preloads as well as various magnetic field intensities, waveforms, and frequencies. Optimal levels are deduced and discussed and the results are compared to published data for a PZT transducer of similar size operated in mechanically blocked configuration. The comparison reveals that the Terfenol-D rod provides higher blocking forces than its PZT counterpart. It is thus feasible to employ small magnetostrictive drivers in applications involving zero or near-zero displacement, particularly those based on hybrid magnetostrictive/piezoelectric designs in which high efficiencies are achieved by driving the two electrically complementary transducer materials at electrical resonance.
This paper presents an experimental study of the effects of varied magnetic bias, AC magnetic field amplitude and frequency on the characteristics of hysteresis loops produced in a magnetostrictive transducer. The study uses a magnetostrictive transducer designed at Iowa State University that utilizes an 11.5 cm (4.54 in) long by 1.27 cm (0.5 in) diameter cylindrical Terfenol-D rod. This transducer allows controlled variation of the following operating conditions: mechanical prestress, magnitude and frequency of AC magnetic field, and magnetic bias. By performing extensive experimental tests, material property trends can be developed for use in the optimization of transducer design parameters for different applications. For the results presented, the magnetic bias, the AC magnetic field amplitude, and the frequency of excitation were independently varied while temperature, mass load and prestress were kept constant. The minor hysteresis loops of the strain versus applied magnetic field, flux density versus applied magnetic field, and magnetization versus applied magnetic field are presented and compared. Material property trends identified from the minor loops are presented for the axial strain coefficient, permeability, susceptibility, and energy losses.
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