An accurate and computationally efficient non-linear magnetostrictive constitutive model is required to properly develop novel magnetostrictive technologies. While the authors have recently shown exact analytical solutions are available for one-dimensional constitutive models built with statistical mechanics, there are currently no known closed form three-dimensional solution. Instead, this presentation will evaluate the use of several different approximation techniques in a three-dimensional model including: Laplace’s method, series expansions, and multivariate spline interpolation. We will show the conditions under which each approximation is numerically accurate and present a model that maintains numerical accuracy over a wide range of applied fields and stresses.
By providing a fast and accurate constitutive model suitable for use in finite element analysis, a key barrier inhibiting the development of magnetostrictive technologies will be lowered. A magnetostrictive constitutive model must calculate the nonlinear magnetization and magnetostriction of a material in response to magnetic and mechanical loads. This presentation will analyze the accuracy and computational complexity of three different integration methods performing these calculations: Riemann sums, Clenshaw-Curtis (CCQ) quadrature, and Laplace’s Method. We will show how using Laplace’s method provides an accurate and computationally efficient calculation of nonlinear magnetization, magnetostriction, and material properties for use in a FEA program.
Work on magnetoelastic particulate composites and magnetorheological (MR) fluids has traditionally focused on frequencies that are small compared to the ferromagnetic resonance (FMR) frequency. Under these conditions the structural or fluid dynamics may be of importance, but the magnetic response is essentially quasi-static. This is in contrast to the response of magnetic materials in microwave devices where the nonlinear spin dynamics present a variety of novel phenomena. Notably, shifting the FMR frequency controls the transmission, absorption, and reflection of electromagnetic waves, with potential non-reciprocal propagation. The present work provides an analysis of a magnetoelastic inclusion in solid and fluid dielectrics, and shows how mechanical loads can control the resonant and relaxation characteristics of these composites at microwave frequencies.
Both analytical and numerical analysis of the coupled spin and mechanical dynamics will be provided. In the magnetic inclusion the equations of elastodynamics are coupled to the Landau-Lifshitz-Gilbert (LLG) equation. The considered magnetic anisotropy energies include Zeeman, magnetocrystalline, and magnetoelastic interactions. Altering the magnetocrystalline and magnetoelastic energies allows the magnetic moment to either rotate independent of the lattice or strongly couple to it (i.e., modeling superparamagnetic or permanent magnetics). Non-symmetric stress tensors arise in the strongly coupled case via the Maxwell stress. It will be shown under what loading conditions the effective magnetoelastic field shifts the FMR frequency and characteristic relaxation times. The effects are found to depend strongly on the crystallinity of the magnetic inclusion and nature of the applied load (i.e., hydrostatic pressure or general 3D stress state).
Traditional electric motors rapidly lose power density as their size decreases. Motors on the order of 1 cubic micron , roughly the size of a red blood cell, have nearly six orders of magnitude smaller power densities than cubic millimeter sized motors. Strain-mediated multiferroic motors have recently been predicted to be energy efficient and power dense at the micron scale. These motors leverage magnetoelastic anisotropy to control the magnetic moments of small nanodiscs or domain walls, and use dipolar forces to couple rotors or beads to the stray magnetic field. While deterministic control methods have already been proposed, a variety of device designs and motor concepts abound. This presentation will explore the relative merits of two key linear motor designs; one using individual magnetic nano-islands, and another focusing on propagating Bloch-type domain wall motion in structures analogous to magnetic ‘racetrack’ memory. A combination of Stoner-Wohlfarth magnetic macrospin modeling and numerical FEA simulations fully coupling micromagnetics and elastodynamics will be presented and analyzed. Results demonstrate the racetrack design is capable of applying larger forces to dipole coupled magnetic beads, but that the use of nano-islands may be capable of achieving higher linear velocities due to domain wall speed limits in the racetrack design.
KEYWORDS: Magnetism, Anisotropy, Control systems, Composites, Heterojunctions, Ferromagnetics, Mechanics, Multifunctional materials, Current controlled current source
As traditional electric motors scale down, the available power density rapidly decreases. For a motor occupying a volume of 1 micron cubed, the available power density is roughly six orders of magnitude lower than a 1 millimeter cubed motor. Strain-mediated multiferroic heterostructures have recently been proposed to create high power density, micron scale, magnetic motors. These motors leverage magnetoelastic anisotropy to rotate the magnetic moment of a small disk, and use dipolar forces to couple rotors or beads to the stray magnetic field. A key challenge to the creation of these motors is to deterministically control magnetization rotations without the need for complex fabrication or control schemes. This presentation demonstrates how controlling the relative orientation of magnetic exchange bias and magnetoelastic anisotropies can be used to deterministically control motor rotations over a broad frequency range.
A Stoner-Wohlfarth magnetic macrospin model is created that couples a single domain magnetic disc to a [011] cut PMN-PT substrate. This model accounts for magnetoelastic, shape, and exchange anisotropy energies. The exchange anisotropy is rotated relative to the biaxial strain created by the PMN-PT substrate. Results demonstrate precessional magnetization dynamics deterministically controlled with an oscillating voltage on the PMN-PT substrate. This approach enables 360 degree rotations over a broad frequency range. The frequency response is provided up through ferromagnetic resonance, and power density calculations are made with comparison to existing micromechanical motors.
Electric antennas are still large structures (approximately 1m for 300 MHz operation), and have so far eluded the miniaturization trend common in the electronics industry. This is due in large part to an impedance mismatch with free space, and an increase in system losses from ohmic heating as antenna dimensions shrink. Recent work has proposed using multiferroic heterostructures to create small energy efficient antennas. This idea was first explored by Rowen’s 1961 paper on electromagnetic (EM) radiation from YIG, and Mindlin’s 1973 paper on radiation from quartz. Since then limited work has looked at EM radiation from adaptive materials, and there are currently no analytical models describing such a device. This presentation provides an analytical model to examine small mechanically powered energy efficient antennas.
An analytical framework is provided that couples elastodynamics and electrodynamics using piezoelectric and piezomagnetic constitutive behavior. This approach uses an eigenmode expansion of the undamped longitudinal vibrations in a prismatic rod to describe EM radiation from each harmonic mode. The problem is reduced to examination of damped harmonic oscillators, and EM radiation is shown equivalent to an effective volumetric strain-rate dependent damping. This approach provides the frequency response of a mechanical antenna, and demonstrates important scaling behavior relative to conventional antennas. Resonant analysis leads to simple closed form expressions for antenna efficiency, and leads to a metric directly comparing mechanical and conventional antennas, facilitating both material selection and device design. To summarize, this presentation provides a first look at the strain-mediated control of wireless communications.
Hypervelocity impacts generate shockwaves causing catastrophic damage and failure of surrounding material and structures. Adaptive materials have been previously studied to mitigate shockwaves by providing diagnostics tools, wave steering, and dissipating mechanical energy. Numerous ferroelectric studies have been conducted, with less focus on ferromagnets, or magnetoelasticity. This presentation explores the response of magnetoelastic Galfenol (Fe81.6Ga18.4) to high strain-rate, high stress amplitude loading.
Experimentally, 2 GPa rarefacted shockwaves are generated in Galfenol using a Nd:YAG laser. Magnetization changes are recorded using inductive coils along the sample length and interferometry is used to infer the stress amplitude at the specimen’s back surface. The experimental results highlight how the shockwave evolves as it travels, including the onset of lateral release waves. Magnetic field control of the mechanical wave speed by 20% is observed, accompanied by large control of the measured magnetization changes. These changes highlight the coupled magnetoelastic nature of the effect. Furthermore, it is observed that the magnetization more strongly couples to lateral release waves than the incident compressive pulse. Last, magnetization changes are seen to precede the propagating mechanical wave, indicating dipolar coupling can transfer energy ahead of the mechanical wave front.
A numerical model has been developed to provide further insight into the experimental study. This model fully couples elastodynamics with magnetostatics using a nonlinear magnetoelastic constitutive behavior. The nonlinear model captures the main findings of the experimental study, including wave evolution, and strong magnetoelastic coupling to the release waves.
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