A general 3-D nonlinear magnetostrictive constitutive model for soft ferromagnetic materials

In this paper, a new general nonlinear magnetostrictive constitutive model is proposed for soft ferromagnetic materials, and it can predict magnetostrictive strain and magnetization curves under various pre-stresses. From the viewpoint of magnetic domain, it is based on the important physical fact that a nonlinear part of the elastic strain produced by magnetic domain wall motion under a pre-stress is responsible for the change of the maximum magnetostrictive strain in accordance with the pre-stress. Then the reduction of magnetostrictive strain from the maximum is caused by the domain rotation. Meanwhile, the magnetization under various pre-stresses in this model is introduced by magnetostrictive effect under the same pre-stress. A simplified 3-D model is put forward by means of linearizing the nonlinear function, i.e. the nonlinear part of the elastic strain produced by domain wall motion, and by using the quartic of magnetization to describe domain rotation. Besides, for the convenience of engineering applications, two-dimensional (plate or film) and one-dimensional (rod) models are also given for isotropic materials and their application ranges are discussed too. In comparison with the experimental data of Kuruzar and Jiles, it is found that this model can predict magnetostrictive strain and magnetization curves under various pre-stresses. The numerical simulation further illustrates that the new model can effectively describe the effects of the pre-stress or residual stress on the magnetization and magnetostrictive strain curves. Additionally, this model can be degenerated to the existing magnetostrictive constitutive model for giant magnetostrictive materials (GMM), i.e. a special soft ferromagnetic material.     

A one-dimension coupled hysteresis model for giant magnetostrictive materials

This paper addresses the development of a one-dimension model for quantifying magnetic-elastic-thermal coupling and hysteresis inherent to giant magnetostrictive materials. Firstly, the anhysteretic law is modeled by considering the Gibbs free energy function G(σ, M, T), and thermodynamic relations are used to obtain the constitutive expressions. These expressions character the effects of coupling between stress, magnetization, and temperature in the giant magnetostrictive material but hysteresis, i.e. strain and magnetic intensity described by above the constitutive expressions are single-valued function of the magnetization. And then pinning is incorporated to describe hysteresis based on Jiles–Atherton model. The model considered in the paper is demonstrated valid by comparing the predicted results with experimental data. Moreover, the model proposed in the paper is convenient to be used in engineering applications since the parameters referred to the model have definite physical mean and can all be easily determined by experiments.     

Nonlinear constitutive law for ferroelectric/ferroelastic material and its finite element realization

The hysteresis phenomena of ferroelectric/ferroelastic material in polarization procedure are investigated. Some assumptions are presented based on the published experimental data. The electrical yielding criterion, mechanical yielding criterion and isotropic hardening model are established. The flow theory in incremental forms in polarization procedure is presented. The nonlinear constitutive law for electrical-mechanical coupling is proposed phenomenologically. Finally, the nonlinear constitutive law expressed in a form of matrices and vectors, which is immediately associated with finite element analysis, is formulated. In the example problem of a rectangular specimen subjected to a uniaxial electric field, the procedure from virgin state to fully polarized state is simulated. Afterward, a uniaxial compressive loading is applied to depolarizing the specimen. Results are in agreement with the experimental data.     

Tb0.3Dy0.7Fe2合金磁畴偏转的滞回特性研究

研究了不同载荷作用下Tb_0.3Dy_0.7Fe₂合金在压磁和磁弹性效应中磁畴偏转的滞回特性. 基于Stoner-Wolhfarth模型的能量极小原理, 采用绘制自由能-磁畴偏转角度关系曲线的求解方法, 研究了压磁和磁弹性效应中载荷作用下的磁畴角度偏转和磁化过程, 计算分析了不同载荷作用下磁畴偏转的滞回特性. 研究表明, 压磁和磁弹性效应中磁畴偏转均存在明显的滞回、跃迁效应, 其中磁化强度的滞回效应来源于磁畴偏转的角度跃迁; 压磁效应中预加磁场的施加将增大磁化强度的滞回, 同时使滞回曲线向大压应力方向偏移; 磁弹性效应中磁畴偏转的滞回存在两个临界磁场强度, 不同磁场强度下合金具有不同的磁畴偏转路径和磁化滞回曲线, 临界磁场强度的大小取决于预压应力的施加. 理论分析对类磁致伸缩材料磁畴偏转模型的完善和材料器件的设计应用非常有意义.     

Insights into the regulation mechanism of ring-shaped magnetoelectric energy harvesters via mechanical and magnetic conditions

This paper presents a theoretical model for predicting and tuning magnetoelectric(ME) effect of ring-shaped composites, in which stress boundary conditions are empoyed and the multi-field coupling property of giant magnetostrictive materials are taken into account. A linear analytical solutions for the closed-and open-circuit ME voltages are derived simultaneously using mechanical differential equations, interface and boundary conditions, and electrical equations. For nonlinear ME coupling effect, the nonlinear multi-field coupling constitutive equation is reduced to an equivalent form by expanding the strains as a Taylor series in the vicinity of bias magnetic field. Sequentially, the linear model is generalized to a nonlinear one involving the field-dependent material parameters. The results show that setting a stress-free condition is beneficial for reducing resonance frequency while applying clamped conditions on the inner and outer boundaries may improve the maximum output power density. In addition, performing stress conditions on one of the boundaries may enhance ME coupling significantly, without changing the corresponding resonance frequency and optimal resistance. When external stimuli like bias magnetic field and pre-stress are applied to the ring-shaped composites, a novel dual peak phenomenon in the ME voltage curve around resonance frequencies is revealed theoretically, indicating that strong ME coupling may be achieved within a wider bias field region. Eventually, the mutual coordination of the bias field and pre-stress may enhance ME coupling as well as tuning the resonance frequency, and thus is pivotal for tunable control of ME energy harvesters. The proposed model can be applied to design high-performance energy harvesters by manipulating the mechanical conditions and external stimuli.     

偏置磁场对磁致伸缩/弹性/压电层合材料磁电效应的影响

根据磁致伸缩材料的非线性本构关系得到其动态杨氏弹性模量和动态压磁系数,结合等效电路法得到磁致伸缩/弹性/压电层合材料的磁电效应与磁致伸缩材料的动态杨氏弹性模量和动态压磁系数的关系,讨论了偏置磁场对这种层合材料的谐振频率和谐振磁电电压转换系数的影响.理论推导和实验结果均表明,存在最佳偏置磁场使磁致伸缩/弹性/压电层合材料的谐振磁电电压转换系数最大. 关键词： 磁致伸缩/弹性/压电层合材料 磁电效应 偏置磁场 非线性本构关系     

Numerical simulation of nonlinear magnetic-mechanical-electric coupling effect in laminated magnetoelectric composites

Considering the significant nonlinear magnetoelectric (ME) characteristics in laminated ME composites, we build a numerical model of magnetic-mechanical-electric coupling effect based on the nonlinear magnetostrictive constitutive relation. The change of the ME field coefficients with bias magnetic field predicted by this model shows good agreement with the experimental result, both qualitatively and quantitatively. Furthermore, this paper considers and predicts the magnetoelectric conversion charateristics of laminated ME composites, calculates and analyzes the influence of the thickness ratio of magnetostrictive layer, the geometrical size of laminated composites, the saturation magnetization, and the types of piezoelectric materials on the ME conversion coefficient of ME laminated composites. We believe that this research provides a theoretical basis for the production of magnetoelectric devices with good magnetoelectric conversion characteristics.     

Capsule motion in flow: Deformation and membrane buckling

The objective of this review is to present the salient features of capsule mechanical behaviour under the influence of viscous deforming forces due to a flowing fluid. We focus on artificial capsules that are initially spherical with an internal liquid core and that are enclosed by a very thin hyperelastic membrane. Different constitutive laws, commonly used to describe the rheological behaviour of thin membranes, are presented. The motion and deformation of a single capsule freely suspended in a simple shear flow is presented as a function of membrane constitutive law and of initial pre-stress. The limitations of classical membrane models that neglect bending effects are discussed. To cite this article: D. Barthès-Biesel, C. R. Physique 10 (2009).     

Tb0.3Dy0.7Fe2合金的本构参数辨识方法研究

建立了一种简便的、适用于磁畴模型应用的Tb_0.3Dy_0.7Fe₂ 合金本构参数辨识方法. 针对Tb_0.3Dy_0.7Fe₂合金磁畴模型中本构参数不明确且直接实验测试困难的问题, 提出了一种数值计算与实验测试相结合的参数辨识方法. 采用坐标变换与绘制自由能等势曲线相结合的方法, 简化了载荷作用下Tb_0.3Dy_0.7Fe₂ 合金内磁畴角度偏转的数值计算, 研究了合金磁畴角度偏转模型的参数依赖性. 在此基础上, 结合简单的实验测试, 建立了Tb_0.3Dy_0.7Fe₂合金各向异性常数K₁ 和K₂、能量分布因子ω、晶轴取向分布的辨识及修正方法. 该方法能够简单、快速地完成Tb_0.3Dy_0.7Fe₂ 合金磁畴模型中本构参数的辨识, 对完善磁致伸缩材料磁畴偏转的数值计算模型非常有意义. 理论分析可为类磁致伸缩材料磁机耦合模型的建立、完善, 以及材料本构参数的辨识、获取提供参考.     

Nonlinear electromechanical analysis: a constitutive theory for perovskite type ferroelectrics

A constitutive theory is established in this paper to describe the nonlinear electromechanical behavior of perovskite type ferroelectrics subjected to external stress and external electric field. In the proposed theory, each domain is considered as an inclusion. The Helmholtz free energy and Gibbs free energy of a constituent element, that are derived by using micromechanics approaches, are functionals of the orientation distribution function (ODF) that depicts the domain distribution patterns. By applying the internal variable theory and expanding ODF in Fourier series, the yielding condition, the evolution of ODF, and the constitutive relation are obtained. In terms of the simplification of the constitutive relation, theoretical predictions are compared with experimental results. There is an agreement between the theoretical and the experimental results, indicating that the theory is reasonable and applicable. It should be pointed out that the constitutive model proposed in this paper is restricted to ferroelectric materials exhibiting transformation from cubic to tetragonal only.     

Nonlinear pulsed ultrasound beams radiated by rectangular focused diagnostic transducers

A numerical model for simulating nonlinear pulsed beams radiated by rectangular focused transducers, which are typical of diagnostic ultrasound systems, is presented. The model is based on a KZK-type nonlinear evolution equation generalized to an arbitrary frequency-dependent absorption. The method of fractional steps with an operator-splitting procedure is employed in the combined frequency-time domain algorithm. The diffraction is described using the implicit backward finite-difference scheme and the alternate direction implicit method. An analytic solution in the time domain is employed for the nonlinearity operator. The absorption and dispersion of the sound speed are also described using an analytic solution but in the frequency domain. Numerical solutions are obtained for the nonlinear acoustic field in a homogeneous tissue-like medium obeying a linear frequency law of absorption and in a thermoviscous fluid with a quadratic frequency law of absorption. The model is applied to study the spatial distributions of the fundamental and second harmonics for a typical diagnostic ultrasound source. The nonlinear distortion of pulses and their spectra due to the propagation in tissues are presented. A better understanding of nonlinear propagation in tissue may lead to improvements in nonlinear imaging and in specific tissue harmonic imaging. Published in Russian in Akusticheskiĭ Zhurnal, 2006, Vol. 52, No. 4, pp. 560–570. This article was translated by the authors.     

Magnetization and magnetostriction studies of TbFeCo/YFeCo multilayers

Exchange-spring TbFeCo/YFeCo multilayers exhibit interesting magnetic and magnetostrictive properties that are rather promising for application in microsystems. In this paper, we present a study of the effect of the exchange coupling on the magnetic properties of these magnetostrictive multilayers. An exchange bias phenomenon, revealed by a shift of the minor hysteresis loop along the applied field axis, is found as the result of the creation of interfacial domain walls. This effect strongly depends on the magnetic properties of the soft YFeCo layer, and becomes more pronounced at low temperatures due to the enhancement of the magnitude of the exchange coupling between the layers.     

离轴磁场退火后Tb0.3Dy0.7Fe1.95〈110〉取向晶体的磁致伸缩"跳跃"效应

将〈110〉取向Tb_0.3Dy_0.7Fe_1.95合金棒放在与轴向成35°夹角的外磁场中退火处理,研究其在0—30 MPa预压应力σpre作用下的磁致伸缩效应.结果表明,σpre=0条件下的饱和磁致伸缩值λs由退火前的1023×10^-6提高到1650×10^-6;σpre 关键词： 磁致伸缩 磁场退火 磁致伸缩"跳跃"效应     

Dynamic hysteresis for Potts spin system: a Monte Carlo simulation

A Monte Carlo approach based on the Q-state Potts model is developed to describe and simulate the dynamic hysteresis of Potts spin lattice against periodic time-varying external field E. The dynamic responses of the hysteresis loops against frequency P of applied field and domain size R are studied. It is revealed that the hysteresis loops for the system energy W, polarization P, and domain wall fraction @ depend considerably on the frequency and domain size. The remnant polarization P_r shows a single-peak pattern as a function of P. The P-E loop exhibits thin rhomb and fat rhomb patterns at low P, whereas a tip-smoothed rhomb and roughly elliptical pattern is observed at high P. The loop area can be scaled with Q,P^1/3 at low P. The frequency dependency of the dynamic hysteresis is explained in terms of a simplified phenomenological model. At very small domain size, the dynamic hysteresis is significantly compressed, predicting the polarization weakening effect at small domain size.     

Magnetization reversal in (0 0 1)Fe thin films studied by combining domain images and MOKE hysteresis loops

The magnetization reversal of epitaxial single-crystal Fe films has been studied by combining domain images and hysteresis loops. The reversal is quantitatively described by combining the coherent rotation model and the domain wall displacement model. The pinning energy exerted on the domain walls and the domain wall angle at the switching fields are obtained by fitting this model to experimental hysteresis loops. The field-dependent pinning energy and the domain wall angle in the reversal process, and the contributions of second-order magneto-optic effect to hysteresis loops, are revealed to be two important features of single-crystal Fe films.     

稀薄气体流动非线性耦合本构关系研究进展

临近空间高超声速飞行器流场蕴含着复杂的非线性流动机理与丰富的热化学非平衡流动现象, 基于Newton摩擦定律和Fourier热传导定律的Navier-Stokes(N-S)方程不足以描述高超声速飞行器从连续流到稀薄流的多尺度非平衡现象。非线性耦合本构关系(nonlinear coupled constitutive relations, NCCR)作为一种全新的本构方程体系, 在严格满足热力学熵条件的基础上, 巧妙地构建了应力与热流的非线性表达形式。然而, NCCR方程的强非线性耦合特性是求解过程的一大难题。为了克服这一技术瓶颈, 提出了混合迭代算法, 为实现NCCR方程的高效稳定求解提供了坚实的理论基础。在该理论研究的基础上, 考虑到原始NCCR方程对热通量演化方程的简化处理, 降低了方程的计算精度, 提出了改进的NCCR+方程。该方程在强激波压缩区域和膨胀区域表现出比传统NCCR方程更高的计算精度与更强的非平衡流动模拟能力。同时, 为了解决临近空间高超声速空气动力学的多尺度与多物理效应耦合难题, 提出了NCCR与转动非平衡的耦合计算模型, 拓展了NCCR方程在双原子气体中的模拟能力。为了揭示稀薄气体效应与真实气体效应的耦合作用机理, 进一步建立了NCCR与热化学反应的耦合计算方法。大量研究结果表明, 考虑多物理效应的NCCR方程在低Kn下能够恢复到与N-S方程一致的解。随着Kn的增加, 流场的非平衡程度逐渐增强, 其结果与N-S方程差异显著, 而与DSMC方法计算结果和实验数据具有更好的一致性。      

An analysis of interacting bistable magnetic microwires: from ordered to chaotic behaviours

Fe-based magnetostrictive amorphous wires are bistable exhibiting square-shaped longitudinal hysteresis loops. This is a consequence of their particular domain structure that allows them to be approached as magnetic dipoles. Arrays of such bistables wires are accordingly shown to be coupled by magnetostatic interactions. Furthermore, an analysis of these interactions allows us to conclude that depending on the relative strength of the magnetostatic and Zeeman interactions, ordered, complex or chaotic behaviours are found in the temporal variation of the array magnetisation.     

用于电流传感的声表面波磁致伸缩效应

利用声表面波(SAW)磁致伸缩效应可以实现一种快速、高灵敏度的电流检测方法,但磁致伸缩薄膜内部矫顽力导致了明显的磁滞误差。磁致伸缩薄膜的栅阵化设计可以减小磁致伸缩时薄膜内部矫顽力,抑制磁滞现象,从而实现高灵敏和低迟滞误差的SAW电流检测。结合有限元和耦合模理论对沉积铁钴(FeCo)薄膜栅阵的声表面波电流传感器中的磁致伸缩效应进行分析,对传感响应进行仿真,确定优化的传感结构参数。为验证理论分析,实验研制了频率为150 MHz的声表面波电流传感器件,并结合差分振荡电路及亥姆霍兹线圈,建立传感器测试系统.实验结果表明,磁致伸缩薄膜的栅阵设计大幅降低了迟滞误差,并显著提升了传感器灵敏度。      

基于能量转换原理的磁电层合材料低频磁电响应分析

提出了一种基于能量转换原理的磁致伸缩/压电层合材料低频磁电响应模型,并对不同层合结构的磁电响应特性进行了对比研究.该模型假定层合材料层间能量传递通过层间剪切力来实现,利用应力函数法分析了磁致伸缩层和压电层的应力与应变,求出了磁致伸缩层的应变能和存储磁场能以及压电层的应变能和电场能;利用Hamilton最小能量原理求出了层间剪切力的大小,获得了开路状态下层合材料的低频磁电响应模型.发现磁电电压系数与磁致伸缩材料的磁导率、泊松比、磁机耦合系数以及压电材料的泊松比、机电耦合系数等有关,并对这些参数的影响进行了分析.同时对两层和三层结构的层合材料磁电特性进行了对比研究,发现层合结构不同则获得的磁电系数公式不同,用相应的公式计算得到的误差才会最小.研究结果表明,本文的理论误差小于6.5%,与其他方法相比,本文的理论模型能更好地描述磁电层合材料的低频磁电响应特性.