Finite element simulation of the magneto-mechanical response of a magnetic shape memory alloy sample

Abstract

In this paper, the stress- and magnetic field-induced variant reorientation in a magnetic shape memory alloy (MSMA) sample is simulated by using the finite element method. This model is set up based on a three-dimensional setting with the whole sample and the surrounding space taken into account. A typical loading pattern is proposed on the sample. The unknowns of the model governing system include the spatial displacement vector, the scalar magnetic potential and some internal variables related to the effective magnetization vector. By considering the different properties of the unknowns, an iterative computational scheme is proposed to derive the numerical solutions. With the obtained solutions, the magneto-mechanical response of the MSMA sample under different field and stress levels can be predicted. The distributions of the variant state and the effective magnetization in the sample can also be determined. By comparing with the experimental results, it is found that the numerical solutions obtained in this model can predict the response of the MSMA sample at a quantitative level.     

On the accuracy of FFT based magnetostatic field evaluation schemes in micromagnetic hysteresis modeling

Micromagnetic hysteresis models for large, bulk like samples are useful for the identification of relations between microscopic material properties and macroscopic magnetic behavior. To bridge the gap between the nanometer space scale of the micromagnetic theory and the large sample dimensions, time and memory efficient numerical schemes are needed. In micromagnetic computations, fast Fourier transforms (FFTs) have been widely adopted to speed up magnetostatic field computations. In this paper, two FFT schemes are compared. The first scheme evaluates the magnetostatic field directly starting from the magnetization and has a large accuracy, while in the second scheme the magnetostatic field is derived from the scalar magnetic potential resulting in a reduced accuracy but also in a CPU time reduction for a magnetostatic field evaluation to 65% and a reduction of memory requirements to 55%. The influence of the low accuracy evaluations on the simulated macroscopic hysteresis behavior is studied. Therefore, comparison is made with the influence of thermal effects in hysteresis simulations. It is found that the resulting changes in macroscopic hysteresis behavior are of the same order of magnitude as the ones obtained when thermal fluctuations are taken into account in the high accuracy computations.     

The ALICE experiment at the LHC

A free-energy function is constructed, which couples strain and magnetic moments in ferromagnetic shape memory alloys. The associated Gibbs function is used to calculate time-dependent transition probabilities between martensite variants in a magnetic field under applied stress. By keeping track of the variant fractions, the evolution of strain and magnetization is determined. The simulation model is built in a finite element program for structural analysis, in order to simulate magnetic field-dependent strain and magnetization characteristics of a test actuator. The influence of material parameters and sample geometry is discussed.     

磁记忆检测的力磁耦合型磁偶极子理论及解析解

磁偶极子理论在缺陷漏磁场解释中被成功广泛使用.由于磁荷密度等参数不易定量,磁偶极子理论在应用中常常进行归一化处理,被认为不适用于对应力相关的磁记忆信号做量化分析.本文通过建立力磁耦合型磁偶极子理论模型,以适用于分析磁记忆检测中应力对磁信号的影响.基于铁磁学理论确定应力和磁场联合作用下的等效场强度,基于弱磁化状态的一阶近似,获得了各向同性铁磁材料微弱环境磁场下的应力磁化解析解.结合磁信号二维问题中矩形和V形磁荷分布假定,建立了光滑与破坏试件表面磁信号、矩形和V形表面缺陷所诱导磁信号的力磁耦合型磁偶极子理论分析模型,并获得其解析解.基于力磁耦合型磁偶极子理论的解析解,对拉伸实验中试件破坏前后的信号差异、矩形和V形表面缺陷诱导磁信号,以及磁信号的影响因素和规律等进行了详细分析.理论研究表明,基于本文理论模型的解析解可实现对磁记忆检测中的一些基本实验现象和规律的解释.     

Disordered domain structures and domain boundaries in thin magnetic films

The behavior of a disordered domain structure and domain boundaries with a change in temperature and magnetic field has been studied. The concept of magnetostatic pressure is used to explain the experimental results. It is shown that “the memory effect” and stability interval of a domain structure with a change in temperature or magnetic field depends on the degree of domain structure disorder and the domain boundary energy.     

Diffusion of a pulsed field and electromagnetic forces in ferromagnets

Self-similar solutions of the magnetic field distribution in a conducting ferromagnet with a non-linear permeability are considered. The velocity of magnetic field penetration is calculated in various models of ferromagnetic properties of the conductor. Using the Maxwell tensor, equations are derived for bulk forces taking into account the possibility of saturation of the ferromagnet. A numerical solution for the distributions of the magnetic induction and of the density of the bulk force in a ferromagnetic conductor is obtained using the Preisach model taking hysteresis into account.     

New exact solutions of the Einstein-Maxwell equations for magnetostatic fields

The symmetry reduction method based on the Fr′echet derivative of differential operators is applied to investigate symmetries of the Einstein-Maxwell field equations for magnetostatic fields, which is a coupled system of nonlinear partial differential equations of the second order. The technique yields invariant transformations that reduce the given system of partial differential equations to a system of nonlinear ordinary differential equations. Some of the reduced systems are further studied to obtain the exact solutions.     

Magnetostatic Green's functions for the description of spin waves in finite rectangular magnetic dots and stripes

We present derivation of the magnetostatic Green's functions used in calculations of spin-wave spectra of finite-size non-ellipsoidal (rectangular) magnetic elements. The elements (dots) are assumed to be single domain particles having uniform static magnetization. We consider the case of flat dots, when the in-plane dot size is much larger than the dot height (film thickness), and assume the uniform distribution of the variable magnetization along the dot height. The limiting cases of magnetic waveguides with rectangular cross-section and thin magnetic stripes are also considered. The developed method of tensorial Green's functions is used to solve the Maxwell equations in the magnetostatic limit, and to represent the Landau–Lifshitz equation of motion for the magnetization of a magnetic element in a closed integro-differential form.     

Magnetostatic mechanism for control of chirality of magnetization distributions

It has been shown that the magnetostatic interaction in an inhomogeneous medium leads to the removal of the chiral degeneracy of magnetic distributions. Noncollinear states of two magnetic dipoles and a helical cycloid placed over a superconducting half-space have been considered as examples. The influence of a finite penetration depth of the magnetic field on the efficiency of removal of the chiral degeneracy has been studied in the framework of the London approximation.     

非线性静磁表面波的传播特性

将文献[4]的理论结果加以推广,用微扰理论导出了微波场作用下铁磁材料的动态非线性磁化强度的各阶近似表达式。严格分析了在波矢k与外偏置磁场H₀成任意角度时非线性静磁表面波的传播特性。证明了静磁表面波在任何传播方向上都不能演化为静磁孤子。 关键词：     

Theoretical modelling,analysis and validation of the shaft motion and dynamic forces during rotor–stator contact

This paper deals with the theoretical study of a horizontal shaft, partially levitated by a passive magnetic bearing, impacting its stator. Rigid body dynamics are utilised in order to describe the governing nonlinear equations of motion of the shaft interacting with a passive magnetic bearing and stator. Expressions for the restoring magnetic forces are derived using Biot Savart law for uniformed magnetised bar magnets and the contact forces are derived by use of a compliant contact force model. The theoretical mathematical model is verified with experimental results, and shows good agreements. However, the simulated contact forces are higher in magnitude compared to the experimental results. The cause of this disagreement is addressed and shows that the formulation of the theoretical contact force model slightly overestimates the forces acting during a full annular backward whirl motion.     

Nonlinear surface magnetostatic waves in a ferrite semiconductor structure

A theoretical analysis is made of the propagation of a nonlinear surface magnetostatic wave in a planar ferrite semiconductor structure as a function of the carrier concentration in the semiconductor layer. It is shown that for certain concentrations the surface magnetostatic wave is unstable with respect to longitudinal perturbations and may propagate perpendicular to the magnetic field in the form of solitons. Zh. Tekh. Fiz. 69, 119–121 (June 1999)     

磁声参量振荡的理论

在本文中,我们从磁-弹性耦合的宏观表达式,通过经典场论的方法,求得弹性振动和磁振璗的耦合方程,用来分析了伴随波长约等于铁氧体样品的线度的声振动而存在的磁振璗(磁声模)。文中指出,Spencer和LeCraw所发现的磁声效应是磁声模和静磁模在注入场的激发下产生的参量振璗现象(也可以说是热声子的电磁讯号的放大)。我们引用Berk等人在讨论一种半静磁操作放大器的文章中给出的公式,算出Spencer-LeCraw实验所需要的功率,其结果与记录的数据相接近。我们提出了使任一静磁模配合磁声模产生振璗的调谐条件以及降低激发功率和观测几十到几百兆赫的声频的办法。通过磁声模和静磁模的交变场向量的空间对称性的分析,我们推导出磁声参量振璗的选择定则:对于球体三个主要弹性振动模(旋转模、向径模和椭球模),(1)静磁模(n,m,r)的Walker指标n是偶数者不产生磁声效应;(2)指标m是奇数者不与旋转模产生磁声效应,m是偶数者不与向径模或椭球模产生磁声效应。我们也举出第一类本征振动中有只可能和n是偶数、m是奇数的静磁模产生参量振璗的例子。Spencer-LeCraw局限于使静磁场调谐在(110)模上,所观察到的现象仅仅是本文所给出理论预见的一个特殊情况。他们发现了椭球模和向径模的频率显著地出现,但并无旋转模的频率,这是上述的选择定则的具体验证。最后,我们指出,热声子的参量放大可形成铁氧体微波放大器的噪声的来源。     

Unsteady MHD flow and heat transfer of fractional Maxwell viscoelastic nanofluid with Cattaneo heat flux and different particle shapes

The paper aims to investigate the unsteady natural convection flow and heat transfer of fractional Maxwell viscoelastic nanofluid in magnetic field over a vertical plate. The effect of nanoparticle shape is first introduced to the study of fractional Maxwell viscoelastic nanofluid. Fractional shear stress and Cattaneo heat flux model are applied to construct the governing boundary layer equations of momentum and energy, which are solved numerically. The quantities of physical interest are graphically presented and discussed in detail. It is found that particle shape and fractional derivative parameters have profound influence on the flow and heat transfer.     

Covariant hysteretic constitutive theory for Maxwell’s equations: application to axially rotating media

This paper explores a class of non-linear constitutive relations for materials with memory in the framework of covariant macroscopic Maxwell theory. Based on earlier models for the response of hysteretic ferromagnetic materials to prescribed slowly varying magnetic background fields, generalized models are explored that are applicable to accelerating hysteretic magneto-electric substances coupled self-consistently to Maxwell fields. Using a parameterized model consistent with experimental data for a particular material that exhibits purely ferroelectric hysteresis when at rest in a slowly varying electric field, a constitutive model is constructed that permits a numerical analysis of its response to a driven harmonic electromagnetic field in a rectangular cavity. This response is then contrasted with its predicted response when set in uniform rotary motion in the cavity.     

Magnetic excitations in solids

This article presents a review of low to moderate frequency magnetic excitations, termed magnons or spin waves, in magnetically ordered materials. The emphasis is on intuitive behavior rather than analytical theory. Topics include spin waves, magnetostatic modes, dipole-exchange modes, surface anisotropy, dispersion properties, nonlinear effects, and relaxation. These phenomena are illustrated with experimental examples based on magnon light scattering results as well as conventional microwave techniques.     

Magnetic guns with cylindrical permanent magnets

The motion of a cylindrical permanent magnet (projectile) inside a tubular permanent magnet, with both magnets magnetized axially, illustrates nicely the physical principles behind the operation of magnetic guns. The force acting upon the projectile is expressed semi-analytically as derivative of the magnetostatic interaction energy. For comparison, the forces involved are also calculated numerically using finite elements methods. Based on the conservation of the magnetostatic and kinetic energies, the exit and asymptotic velocities are determined. The derived formulas can be used to optimize the generated forces and motion of the inner cylindrical magnet.     

Parametric excitation of hybrid mode in magnetised piezoelectric semiconductors

Using the hydrodynamic model of homogeneous plasma, the parametric decay of a laser beam into an acoustic wave and another electromagnetic wave has been studied in heavily dopedn-type piezoelectric semiconductors in the presence of a transverse magnetostatic field. This decay process results in the parametric excitation of the hybrid mode. The threshold electric field necessary for the onset of instability equals to zero. The magnetostatic field couples the acoustic and the electromagnetic waves and in its absence the instability disappears. The growth rate increases with the square of the magnetic field.     

Generalized maxwell equations and quantum mechanics. I. Dirac equation for the free electron

Some preliminary results presented in two previous papers are expanded upon. In the first it was shown that the Maxwell equations are equivalent to a nonlinear Dirac-like spinor equation. In the present paper it is shown that, in that formalism, the Dirac equation for the free electron is susceptible to a puzzling reinterpretation. In fact, it is shown that the Dirac equation is equivalent to the Maxwell equations for an electromagnetic field generated by two currents: one electric in nature and one, magnetic-monopolar. The elaboration of this result brings a nonlinear generalization of Maxwell's equations, as well as a nonlinear Dirac-like equation fully equivalent to them, from which both the electron mass as well as the magnetic monopole mass appear to be fully electromagnetic in nature, and the magnetic monopole to be tachyonic. The corresponding nonlinear Dirac equation reduces, under suitable approximations, to the ordinary Dirac equation for the free electron.     

Slow electromagneticw waves in tangentially magnetized ferromagnetic films

Dispersion and energy characteristics of slow volume electromagnetic waves in tangentially magnetized ferromagnetic films are computed in a rigorous manner. For a wave that experiences anomalous dispersion and propagates with the external magnetostatic field, distinguishing features of the energy-flux velocity and the ratio of the electric to the magnetic energy density as functions of the wave number are noted. A marked contrast between these results and those obtained within the magnetostatic approximation is revealed for a wide range of wave numbers.