Magnetoelastic Model Research Articles

A 3D shell model for static and free vibration analysis of multilayered magneto-elastic structures

In this paper, an exact 3D coupled magneto-elastic shell model for static and free vibration analysis of multilayered piezomagnetic smart structures is presented. The introduction of the mixed curvilinear orthogonal reference system (α,β,z) allows investigations of plates, cylindrical shells, cylinders and spherical shells as actuators or sensors and also in free vibration conditions. The present exact 3D coupled shell model is composed of four second-order differential equations whose primary variables are the three displacements u, v and w and the magnetic potential ψ. Displacements, stresses, strains, magnetic potential, magnetic induction and circular frequency values are computed to understand the behaviour of piezomagnetic smart structures. The resolution method adopted for the present 3D magneto-elastic problem is based on harmonic forms in α and β in-plane directions and the exponential matrix method in the z direction. Simply supported one-layered/multilayered structures with 0° or 90° orthotropic angles have been analysed. The results section is divided into a first part related to the validation of the proposed 3D model and a second part where new benchmark cases are presented and discussed. Different lamination schemes, load boundary conditions, geometries and materials are studied. Magneto-elastic coupling, thickness and material layer effects are discussed for thin and thick structures. The main novelty of the present exact 3D coupled magneto-elastic shell model stands in the ability to analyse several geometries and multilayered configurations embedding piezomagnetic materials under the action of different boundary loads via a general mathematical formulation.

Wrinkling of compressible magnetic soft plates

This paper establishes an analytical method for the wrinkling of compressible magnetic soft (MS) plates subject to an in-plane biaxial stretching and an out-of-plane magnetic induction field. The bifurcation analysis is performed with external Maxwell stress considered by combining the surface impedance matrix method and the Stroh formulation in terms of true magnetic field variables. We decouple the resulting bifurcation equations into antisymmetric and symmetric modes and provide the explicit expressions within a neo-Hookean ideal magnetoelastic model. Numerical examples show that the antisymmetric wrinkling usually occurs prior to the symmetric one, unless the permeability of the plates μ is much smaller than that of the surroundings μ′, i.e., the normalized permeability μ/μ′→0. This observation is consistent with the previous studies on incompressible case. However, for nearly incompressible plates with μ/μ′>1, the compressible constitutive relation may impose an additional deformation constraint that noticeably limits the occurrence and extent of wrinkling in the plates. One intriguing observation in particular is that the critical stretches for the thin-plate instability exhibit a nonmonotonic character as the compressibility of plate varies. Release of compressibility plays a positive role on stabilizing the MS plates when 0<μ/μ′<1, yet a negative role when μ/μ′>1. This phenomenon may be attributed to the coupling effect between the compressibility and the normalized permeability μ/μ′, suggesting a potential way to regulate wrinkling behaviors of MS materials by tuning the surrounding permeability. The present work may serve as benchmark solutions for understanding structural failures in various related functional MS-based devices.

A magneto-elastic vector-play model including piezomagnetic behavior

The mechanical state strongly influences the magnetic response of ferromagnetic materials. In this paper, the effect of time-varying mechanical stresses on magnetic behavior is modeled by combining a vector-play model and a multiscale approach. The approach incorporates the influence of the crystallographic texture. The model is applied to a polycrystalline low-carbon steel (DC04). Uniaxial measurements are used to identify the dissipation parameters. The model is further validated under complex uniaxial magneto-elastic loading conditions, different from those used for parameter identification, including simultaneous variations of magnetic field and stress. To the best of our knowledge, the proposed approach is the first multiaxial magneto-elastic hysteresis model able to describe the response of a magnetic material to simultaneously varying magnetic field and stress and validated under such loading conditions.

Multiphysics modeling of magnetoelectric composite disks by a 2D axisymmetric finite element approach

A 2D axisymmetric finite element multiphysics model is proposed to study magnetoelectric composite disks. This modeling approach includes a nonlinear magneto-elastic model to replicate the behavior of magnetostrictive materials under static conditions. Additionally, it offers a harmonic regime resolution that considers frequency dependence, including the implicit inclusion of eddy currents in the formulation, as well as electrical load. To validate the model, simulation results regarding the dependence of the static magnetic field and frequency are presented and compared with experimental measurements from literature.

Highly sensitive surface acoustic wave magnetic field sensor based on the loss mechanism

Currently, the surface acoustic wave (SAW) magnetic field sensing technique utilises the SAW velocity/frequency mechanism of magnetoacoustic interaction as an indicator of the magnetic sensitivity mechanism. However, this method has low sensitivity and poor stability. To address this problem, a dynamic magnetoelastic coupling theoretical model is constructed to theoretically simulate the influence of the ΔE effect of magnetically sensitive thin films on SAW propagation attenuation. This study describes a high-sensitivity SAW magnetic field sensing mechanism based on magnetoacoustic attenuation. The simulation results show a clear relationship between the acoustic propagation loss and external magnetic field, indicating a structure-property relationship. An amorphous soft magnetic material (Fe90Co10)78Si12B10 was used as a magnetically sensitive thin film due to its high permeability, low coercivity (Hc), low hysteresis, ease of magnetisation and demagnetisation. SAW magnetosensitive device operating on a frequency of 200 MHz has been experimentally developed using a standard semiconductor photolithography process. A SiO2 layer was deposited on a 36° YX-LiTaO3 substrate as a waveguide, and a (Fe90Co10)78Si12B10 layer was on the top of the propagation area as a magnetosensitive film. The experimental results showed that the acoustic loss change due to the magnetic field variation was 4.63 dB within a magnetic field range of 0 Oe to ±10 Oe, which agreed with the theoretical results. The sensor had a sensitivity of 0.7546 dB Oe−1 within the range of 0–4 Oe and the lower detection limit of magnetic fields was 0.272 Oe, low hysteresis error of 0.54%, multiple repeatability error of 0.13%, excellent repeatability and stability were achieved in the experiments from the developed sensing device.

Research on magnetoelastic coupling model based on magnetic dipole theory

In this paper, a theoretical model of a magnetoelastic coupling magnetic dipole is established to analyse the influence of stress on the magnetic signal in magnetic memory testing. Based on the theory of ferromagnetism, the equivalent field strength under the combined action of stress and the magnetic field is determined and a numerical solution for the stress magnetisation of isotropic ferromagnetic materials under a weak environmental magnetic field is obtained. Based on the assumption of a double rectangular crack in a three-dimensional problem for the magnetic signal, a theoretical analysis model of a magnetoelastic coupling-type magnetic dipole is established. Based on the theory of the magnetoelastic coupling magnetic dipole, the influence factors and rules of the magnetic signal are analysed in detail. The theoretical research shows that the solution based on the theoretical model in this paper can explain some basic experimental phenomena and laws in magnetic memory inspection. The magnetic signal of a defect-free plate shows a 'horseshoe shape'. The length, width and height of the plate will affect Hx but have no effect on Hy . In addition, the lift-off value has a great influence on the magnetic signal of the plate. When the two cracks are a small distance apart, the magnetic signal of the plate is the superposition of the magnetic signals of the two cracks. For plates with cracks, the crack size, spacing, external magnetic field strength and stress will affect the magnetic signal of the plate.

A magneto-elastic vector-play model under rotating fields and multiaxial stress states

A magneto-elastic vector-play model under rotating fields and multiaxial stress states

Dual-mode coupling resonance and dynamic stability of axially moving ferromagnetic thin plate strips in alternating magnetic field

This paper investigates the dual-mode coupling resonance and dynamic stability of axially moving ferromagnetic thin plate strips in alternating magnetic field. According to the basic electromagnetic theory and the magnetoelastic mechanics model, Lorentz electromagnetic force and torque generated by eddy current effect and the magnetizing force generated by magnetization are determined for the ferromagnetic plate strip. Introducing Von Karman geometric nonlinearity, the nonlinear governing equation of axially moving ferromagnetic plate strips under the combined action of mechanical load and magnetizing force is established by Hamilton's principle. For the simply supported plate strip, Galerkin method and the multi-scale method are employed to solve the modal coupling resonance dominated by electromagnetic excitation, obtaining the amplitude-frequency response equations. The stability of resonance responses is analyzed by the Lyapunov stability theory. Through parametric research, the amplitude-frequency characteristic curves, bifurcation diagrams and Lyapunov exponent spectra of each mode are plotted; the effect of different parameters on vibration characteristics and dynamic stability under the modal coupling is analyzed for the system. The results show that as one of the modal amplitudes enters the resonance region, the other modal amplitude decays into the "collapse" region due to energy exchange between modes; each modal amplitudes has more complex multi-valued and jumping phenomena for the nonlinear coupling effect. The increase in velocity will affect the stability of system; the enhancement of magnetic field will make the system change into chaos at high velocity.

Direct-Current Electrical Detection of Surface-Acoustic-Wave-Driven Ferromagnetic Resonance.

Surface acoustic waves (SAW) provide a promising platform to study spin-phonon coupling, which can be achieved by SAW-driven ferromagnetic resonance (FMR) for efficient acoustic manipulation of spin. Although the magneto-elastic effective field model has achieved great success in describing SAW-driven FMR, the magnitude of the effective field acting on the magnetization induced by SAW still remains hard to access. Here, by integrating ferromagnetic stripes with SAW devices, direct-current detection for SAW-driven FMR based on electrical rectification is reported. By analyzing FMR rectified voltage, the effective fields are straightforwardly characterized and extracted, which exhibitsthe advantages of better integration compatibility and lower cost than traditional methods such as vector-network analyzer-based techniques. A large nonreciprocal rectified voltage is obtained, which is attributed to the coexistence of in-plane and out-of-plane effective fields. The effective fields can be modulated by controlling the longitudinal and shear strains within the films to achieve almost 100% nonreciprocity ratio, demonstrating the potential for electrical switches. Besides its fundamental significance, this finding provides a unique opportunity for a designable spin acousto-electronic device and its convenient signal readout.

Observation of enhanced dynamic ΔG effect near ferromagnetic resonance frequency

The field-dependence elastic modulus of magnetostrictive films, also called ΔE or ΔG effect, is crucial for ultrasensitive magnetic field sensors based on surface acoustic waves (SAWs). In spite of a lot of demonstrations, rare attention was paid to the frequency-dependence of ΔE or ΔG effect. In this work, shear horizontal-type SAW delay lines coated with a thin FeCoSiB layer have been studied at various frequencies upon applying magnetic fields. The change of shear modulus of FeCoSiB has been extracted by measuring the field dependent phase shift of SAWs. It is found that the ΔG effect is significantly enhanced at high-order harmonic frequencies close to the ferromagnetic resonance frequency, increasing by ∼82% compared to that at the first SAW mode (128 MHz). In addition, the smaller the effective damping factor of a magnetostrictive layer, the more pronounced ΔG effect can be obtained, which is explained by our proposed dynamic magnetoelastic coupling model.

Kirchhoff rod-based three-dimensional dynamical model and real-time simulation for medical-magnetic guidewires

Background and Objective: Magnetic guidewire, fabricated from hard-magnetic soft composites, has recently emerged as an appropriate candidate for magnetic actuation systems to perform intravascular surgical navigation, owing to its elastic, magnetically steerable properties and good interphase with biological tissues. A suitable and efficient mathematical model for the magnetic guidewire is essential in the system to execute remote manipulation and active control. Methods: This paper presents a real-time Kirchhoff rod-based dynamical modeling approach, the magneto-elastic rod model, to simulate magnetic guidewire, which provides accurate simulations for two- and three-dimensional dynamic deflections induced by external magnetic fields and obtains deformed guidewire shapes in quasi-static status. Results: The proposed model is capable of describing the intrinsic principles of elastic body actuation by torques generated from the hard-magnetic soft matrix. The effectiveness of the developed model is validated, and the real-time simulation application is conducted via the semi-implicit numerical integration method. Conclusions: It has been shown that the presented dynamical model captures large nonlinear deformations and transient responses of the magnetic guidewire in an imitated human blood environment, which could offer robust support for the construction of a simulated magnetically driven surgical system.

Magnetoelastic simultaneous resonance of axially moving plate strip under a line load in stationary magnetic field

This paper studies the primary-internal simultaneous resonance of the moving ferromagnetic thin plate with the action of an alternating line load in a transverse stationary magnetic field. Based on the theory of thin plates, expressions of strain energy and kinetic energy of the thin plate are given. According to the theoretical magnetoelastic model for ferromagnets, the calculation formula for electromagnetic force is derived. The magnetoelastic coupling nonlinear vibration equation is established by using Hamilton’s principle. Duffing-type nonlinear differential equations are obtained for the clamped-hinged plate strip by applying the Galerkin method. The steady-state response of the system with primary resonance and 1:3 internal resonance is given by using the method of multiple scales, and the stability of steady-state solutions are analyzed according to the theory of Lyapunov stability. The primary-internal simultaneous resonance characteristics of the plate strip are presented through numerical examples. Results show that: energy exchange between the first two modes is available and the first mode dominates; jump phenomena exist in amplitude–frequency curves; both the values of steady solutions and the multi-valued regions of amplitude change with varieties of physical parameters; and numerical results agree with analytical results, which verifies the reliability of analytical research method in this paper.

A discrete model for the geometrically nonlinear mechanics of hard-magnetic slender structures

Hard-magnetic soft (HMS) materials and structures, which can undergo rapid configurational transformation under non-contact magnetic stimuli, have attracted extensive attentions in a wide range of engineering applications, such as soft robotics, biomedical devices and stretchable electronics, etc. In order to realize the full potentials of HMS structures, it is crucial to be able to predict their mechanical (both static and dynamic) responses. In this work, we propose a discrete magneto-elastic rod model with the aim to analyse the mechanical behaviours of slender structures made of HMS materials under magnetic loading. The configuration of a slender object is described by multiply connected nodes and edges, from which the force vector and the associated Hessian matrix are derived by taking the variation of Kirchhoff-like magneto-elastic potentials. The nonlinear dynamical equations of motion are next evaluated through Newton-type optimization, and the static analysis can be obtained using dynamical relaxation method. For verification, we quantitatively compare our numerical results with either analytical solutions or experimental data for several representative cases. Good agreements in all these cases indicate the correctness and accuracy of our discrete model. We further extend the model to take the dipole–dipole interaction and viscous effect into consideration. Finally, as a demonstration, we perform simulations to reproduce the locomotion of a magnetic crawling robot. The developed discrete magneto-elastic model significantly improves the computational efficiency, enabling the practicability of simulating the mechanical, especially dynamic, behaviours of the hard-magnetic slender structures.

Influence of the bi-nonlinearity on the characterization of mode I fracture parameter [formula omitted] for a cracked giant magnetostrictive material in the coupled magneto-elastic field: An experimental and numerical study

Terfenol-D, a giant magnetostrictive material exhibits bi-nonlinear stress-strain relationship in coupled magneto-elastic field. A novel hyperbolic vector generalized magneto-elastic constitutive model is employed to describe this bi-nonlinear stress-strain behaviour. Some physics-based experiments for magnetization and magnetostriction hysteresis loops and mechanical compression tests under the applied magnetic field are conducted. The general HM and stress-strain relationships are programmed in C language to define the coupled field constitutive material model. Coupled magneto-elastic response from the performed finite element analyses are compared with experiments to optimize the material parameters. Fracture experiments employing single edge notch bend (SENB) specimens are conducted with and without external magnetic field as per ASTM E399. The digital image correlation technique is used to capture the load line and crack opening displacement variation with peak fracture load data. Two parameter Weibull statistical theory of strength has been utilised to forecast the mean peak fracture load. The Weibull modulus and goodness of fit are assessed using linear regression analysis (LIN2), biased and unbiased maximum likelihood estimation (MLE2-B & MLE2-U) approach. Finite element crack propagation model based on the optimized nonlinear constitutive relations is built concerning to magnetization and stress dependent elasticity problem of Terfenol-D fracture. Three-dimensional J-integral is formulated considering the effects of magneto-elastic fields, which is subsequently used to characterize the crack front singularity near the fracture process zone. Critical strain energy release rate JIc was calculated using the mean peak fracture load in both absence and presence of the external magnetic field. Finally, the influence of bi-nonlinear modularity and applied external magnetic field on the fracture behaviour of the Terfenol-D SENB fracture specimen were compared with the unimodular experimental results and substantial differences were reported. The stipulation and importance of considering the bi-nonlinear critical strain energy release rate JIc in the context of a coupled magneto-elastic field was discussed certifying the observations.

Self-Biased Magnetic Field Sensors Based on Surface Acoustic Waves through Angle-Dependent Magnetoacoustic Coupling

Surface-acoustic-wave- (SAW) based devices emerge as promising technology in magnetic field sensing by integrating a magnetostrictive layer with the giant \ensuremath{\Delta}E/\ensuremath{\Delta}G effect. However, almost all SAW magnetic field sensors require a bias field to obtain high sensitivity. In addition, the true nature of magnetoacoustic coupling still presents a major challenge in understanding and designing this kind of device. Here, a dynamic magnetoelastic model for the \ensuremath{\Delta}E/\ensuremath{\Delta}G effect is established in consideration of the important role of the dipole-dipole interaction. The model is also implemented in finite-element-method software to calculate the resonance-frequency responses of multiple fabricated sensors with different \ensuremath{\psi} angles between the acoustic wave vector and the induced uniaxial magnetic anisotropy. The measured results are in excellent agreement with the simulated ones. A strong resonance-frequency sensitivity (${S}_{\mathrm{RF}}$) of 630.4 kHz/Oe is achieved at zero bias field for the device with an optimized \ensuremath{\psi} angle. Furthermore, the ${S}_{\mathrm{RF}}$ measurements along different directions verify its vector-sensing capability.

Modeling of stator sheets punching effect on EV motor performances—SMM25:374178

The effect of punching of electric motor sheets on electrical machine performances is addressed. The approach is using first measurement of mechanical stress effect on magnetic behavior. An evaluation of residual stress field in stator sheets after punching process is then carried out by FEM. A new coupled magneto-elastic Preisach model is proposed to model the B(H) curves and introduced in magnetic FEM software using residual stresses as an input. Modeling of EV motor highlights a weak torque reduction.

Microstructural model of the behavior of a ferroalloy with shape memory in a magnetic field

In the article, within the framework of the theory of micromagnetism, a magneto-elastic microstructural model of the behavior of a ferromagnetic material with the shape memory (Heusler alloy) in a magnetic field is constructed. The dynamics of the magnetic process is described by the Landau-Lifshitz-Gilbert equation. Using the Galerkin procedure, variational equations corresponding to the differential relations of the magnetic problem are written out. A martensitic structure of the type “herringbone” (a twinned variant of martensite) with magnetic domains located at an angle of 180 ° is considered. 90-degree magnetic domain walls are the boundaries of the twins. The finite element method models the formation of these walls and the distribution of the magnetization vector in them. The evolution of this magnetic structure is investigated, namely the movement and interaction of 180-degree magnetic domain walls when an external magnetic field is applied in various directions. The problems of the formation of twins from the martensite variants (the twinning problem) and their disappearance (the detwinning problem) in an external magnetic field are considered. On the plane separating the two variants of martensite, the Hadamard compatibility condition (or twinning equation) is written out. The solution of this equation is given and the processes, that this equation describes, are considered in detail. The detwinning condition for a ferroalloy with the shape memory in a magnetic field is proposed and the processes related to the reorientation (detwinning) of the martensitic variants forming a twin are discussed. The problems considered earlier without taking into account the detwinning process are supplemented by this process, the magnetization curves are constructed and the components of the strain tensor are determined. The results obtained are in good agreement with the known experimental data.

Bio-Inspired Bianisotropic Magneto-Sensitive Elastomers with Excellent Multimodal Transformation.

Magneto-sensitive soft materials that can accomplish fast, remote, and reversible shape morphing are highly desirable for practical applications including biomedical devices, soft robotics, and flexible electronics. In conventional magneto-sensitive elastomers (MSEs), there is a tradeoff between employing hard magnetic particles with costly magnetic programming and utilizing soft magnetic particle chains causing tedious and small deformation. Here, inspired by the shape and movement of mimosa, a novel soft magnetic particle doped shape material bianisotropic magneto-sensitive elastomer (SM bianisotropic MSE) with multimodal transformation and superior deformability is developed. The high-aspect-ratio shape anisotropy and the material anisotropy in which the magnetic particles are arranged in a chainlike structure together impart magnetic anisotropy to the SM bianisotropic MSE. A magneto-elastic analysis model is proposed, and it is elucidated that magnetic anisotropy leads to peculiar field-direction-dependent multimodal transformation. More importantly, a quadrilateral assembly and a regular hexagon assembly based on this SM bianisotropic MSE are designed, and they exhibit 2.4 and 1.7 times the deformation capacity of shape anisotropic samples, respectively. By exploiting the multidegree of freedom and excellent deformability of the SM bianisotropic MSE, flexible logic switches and ultrasoft magnetic manipulators are further demonstrated, which prove its potential applications in future intelligent flexible electronics and autonomous soft robotics.

Magnon-phonon interaction and the underlying role of the Pauli exclusion principle

The magnon-phonon interaction is receiving growing attention due to its key role in spin caloritronics and the emerging field of acoustic spintronics. At resonance, this magnetoelastic interaction forms magnon polarons, which underpin exotic phenomena such as magnonic heat currents and phononic spin, but is mostly investigated using mesoscopic spin-lattice models. Motivated to integrate the magnon-phonon interaction into first-principles many-body electronic structure theory, we set out to derive the exchange contribution, which is subtler than the spin-orbit contribution, using Schwinger functional derivatives. To avoid having to solve the famous Hedin-Baym equations self-consistently, the phonons are treated as perturbations to the electronic structure. A formalism based on imposing a crossing-symmetric electron-electron interaction is developed in order to treat charge and spin on equal footing to respect the Pauli exclusion principle. Due to spin conservation, the magnon-phonon interaction first enters to second order through the magnon-magnon interaction, which renormalizes the magnons. We show by iteration that the magnon-magnon interaction contains a ``screened $T$ matrix'' term and an arguably more important term which, in the local-spin limit, enables first-principles phonon emission and absorption amplitudes, predicted by phenomenological magnetoelastic models. These terms are, respectively, of first and second order in the screened collective four-point interaction $\mathcal{W}$---a crossing-symmetric analog of Hedin's $W$. Proof-of-principle results are presented at varying temperatures for an isotropic magnon spectrum in three dimensions in the presence of a flat optical phonon branch.

Magnetoelastic coupling and effects of uniaxial strain in α−RuCl3 from first principles

We present first-principles results on the magnetoelastic coupling in $\alpha$-RuCl$_3$ and uncover a striking dependence of the magnetic coupling constants on strain effects. Different magnetic interactions are found to respond very unequally to variations in the lattice, with the Kitaev interaction being the most sensitive. Exact diagonalization results on our magnetoelastic model reproduce recent measurements of the structural Gr\"uneisen parameter and explain the origin of the negative magnetostriction of $\alpha$-RuCl$_3$, disentangling contributions related to different anisotropic interactions and g factors. Uniaxial strain perpendicular to the honeycomb planes is predicted to reorganize the relative coupling strengths, strongly enhancing the Kitaev interaction while simultaneously weakening the other anisotropic exchanges under compression. Uniaxial strain may therefore pose a fruitful route to experimentally tune $\alpha$-RuCl$_3$ nearer to the Kitaev limit.