Magneto-elastic modeling of composites containing chain-structured magnetostrictive particles

Magneto-elastic behavior is investigated for two-phase composites containing chain-structured magnetostrictive particles under both magnetic and mechanical loading. To derive the local magnetic and elastic fields, three modified Green's functions are derived and explicitly integrated for the infinite domain containing a spherical inclusion with a prescribed magnetization, body force, and eigenstrain. A representative volume element containing a chain of infinite particles is introduced to solve averaged magnetic and elastic fields in the particles and the matrix. Effective magnetostriction of composites is derived by considering the particle's magnetostriction and the magnetic interaction force. It is shown that there exists an optimal choice of the Young's modulus of the matrix and the volume fraction of the particles to achieve the maximum effective magnetostriction. A transversely isotropic effective elasticity is derived at the infinitesimal deformation. Disregarding the interaction term, this model provides the same effective elasticity as Mori-Tanaka's model. Comparisons of model results with the experimental data and other models show the efficacy of the model and suggest that the particle interactions have a considerable effect on the effective magneto-elastic properties of composites even for a low particle volume fraction.     

Experimental investigation of the coupled magneto-mechanical response in magnetorheological elastomers

Magnetorheological elastomers (MREs) are materials made of a soft elastomer matrix filled with magnetizable particles. These flexible composites that deform in response to an externally applied magnetic field are of special interest in advanced engineering applications such as actuators, artificial muscles or shape control. However, no systematic characterization of their coupled response has been undertaken so far, thus limiting the efficient design of MRE-based devices. In this study, we propose a framework—relying on both specially designed samples and a dedicated experimental setup—to characterize experimentally the coupled magneto-mechanical response of MREs since magnetization within the sample is nearly uniform and structural-dependent effects are minimized. The influence of particle content and arrangement within the composite are particularly studied and the corresponding experimental results give some insight into the underlying microstructural mechanisms that are responsible for the macroscopic deformation of MREs under combined magnetic and mechanical loading conditions. Such data is crucial for the design of new MRE composite materials in which the microstructure is optimized (to have the largest coupling effect with minimal energy input).     

Microstructure and magnetorheology of graphite-based MR elastomers

This study focuses on the magnetorheology of graphite-based magnetorheological elastomers (Gr MREs). By introducing graphite to conventional MREs, the Gr MREs with various graphite weight fractions are fabricated. Both steady-state and dynamic tests were conducted to study rheological properties of the samples. For dynamic tests, the effects of magnetic field, strain amplitude and frequency on both storage modulus and loss modulus were measured. The influence of graphite weight fraction on mechanical performances of these samples was summarized. Also, the microstructures of isotropic and anisotropic Gr MREs were observed. In anisotropic MREs, the graphite powders disperse in matrix randomly. The graphite particles lead to an increment of initial mechanical properties and a decrement of the MR effect.     

Incremental elastic motions superimposed on a finite deformation in the presence of an electromagnetic field

The equations describing the interaction of an electromagnetic sensitive elastic solid with electric and magnetic fields under finite deformations are summarized, both for time-independent deformations and, in the non-relativistic approximation, time-dependent motions. The equations are given in both Eulerian and Lagrangian form, and the latter are then used to derive the equations governing incremental motions and electromagnetic fields superimposed on a configuration with a known static finite deformation and time-independent electromagnetic field. As a first application the equations are specialized to the quasimagnetostatic approximation and in this context the general equations governing time-harmonic plane-wave disturbances of an initial static configuration are derived. For a prototype model of an incompressible isotropic magnetoelastic solid a specific formula for the acoustic shear wave speed is obtained, which allows results for different relative orientations of the underlying magnetic field and the direction of wave propagation to be compared. The general equations are then used to examine two-dimensional motions, and further expressions for the wave speed are obtained for a general incompressible isotropic magnetoelastic solid.     

Multi-frequency excitation of magnetorheological elastomer-based sandwich beam with conductive skins

The present work deals with the dynamic stability of a symmetric sandwich beam with magnetorheological elastomer (MRE) embedded viscoelastic core and conductive skins subjected to time varying axial force and magnetic field. The conductive skins induce magnetic loads and moments under the application of magnetic field during vibration. The MRE part works in shear mode and hence the dynamic properties of the sandwich beam can be controlled by magnetic fields due to the field dependent shear modulus of MRE material. Considering the core to be incompressible in transverse direction, classical sandwich beam theory has been used along with extended Hamilton's principle and Galarkin's method to derive the governing equation of motion. The resulting equation reduces to that of a multi-frequency parametrically excited system. Second order method of multiple scales has been used to study the stability of the system for simply supported and clamped free sandwich beams. Here the experimentally obtained properties of magnetorheological elastomers based on natural rubber have been considered in the numerical simulation. The results suggest that the stability of the MRE embedded sandwich beam can be improved by using magnetic field.     

The effect of particle shape and distribution on the macroscopic behavior of magnetoelastic composites

The magnetoelastic homogenization framework and the partial decoupling approximation proposed by Ponte Castañeda and Galipeau (2011) are used to estimate material properties for a class of magnetically susceptible elastomers. Specifically, we consider composites consisting of aligned, ellipsoidal magnetic particles distributed randomly with “ellipsoidal” symmetry under combined magnetic and mechanical loading. The model captures the coupling between the magnetic and mechanical fields, including the effects of magnetic saturation. The results help elucidate the effects of particle shape, distribution, and concentration on properties such as the magnetostriction, actuation stress, magnetic modulus, and magnetization behavior of a magnetorheological composite.     

Magnetoelectroelastic media containing a row of moving shear cracks

The elastic, electric and magnetic fields created within transversely isotropic magnetoelectroelastic media around an infinite row of uniformly-moving, collinear, antiplane shear cracks are studied, using an extension of the powerful method of dislocation layers. This analysis additionally provides the solutions for a finite magnetoelectroelastic plate containing a single crack and a plate with an edge crack.     

Field-stiffening effect of magneto-rheological elastomers

Magneto-rheological elastomers (MREs) are a class of soft active materials known for their tunable stiffness. Dispersed with magnetic particles, these polymer-based composites tend to be stiffer under a magnetic field. Such a stiffening effect is often attributed to the magnetic interaction among filler particles, but the well-acknowledged dipole-interaction model fails to explain the stiffening effect in tension/compression, which was observed in experiments. Other mechanisms, such as the effect of non-affine deformation, have been proposed, but there is no conclusive evidence on the dominating mechanism for the field-stiffening effect. This paper investigates various filler-chain structures, and seeks to identify the ultimate origin of the field-stiffening effect in MREs. Two different methods are used for cross verification: a dipole-interaction model and a finite-element simulation based on continuum field theories. This paper studies both the shear and axial deformation of the material, with a magnetic field applied in the particle-chain direction. It is found that while the magnetic interaction between particles is indeed the major cause of the stiffening effect, the wavy chain structure is the key to the modulus increase. Besides, chain–chain interaction and non-affine deformation are shown to be insignificant. In addition, the dependence of the stiffening effect on filler concentration is calculated, and the results qualitatively agree with experimental observations. The models also predict some interesting results that could be easily verified by future experiments.     

The Stress State of a Transversely Isotropic Ferromagnetic with a Parabolic Crack in a Homogeneous Magnetic Field

The magnetoelastic problem for a transversely isotropic ferromagnetic body with a parabolic crack in the plane of isotropy is solved explicitly. The body is in an external magnetic field, which is perpendicular to the plane of isotropy. The field induces elastic strains and a magnetic field in the body. The characteristics of the stress–strain distribution and induced magnetic field are determined; and their singularities in the neighborhood of the crack are analyzed. Formulas for the stress intensity factors of the mechanical and magnetic fields near the crack tip are presented     

General solution for the coupled equations of transversely isotropic magnetoelectroelastic solids

IntroductionMechanicsandphysicsofmediapossessingsimultaneouslypiezoelectric ,piezomagneticandmagnetoelectriceffects ,namely ,magnetoelectroelasticsolids,haveattractedmoreandmoreattentionduetotheirgreatpotentialapplicationsinthetechnologiesofsmartandadaptivematerialsystem[1] .Sometheoreticalinvestigationsappearedintheliteratureinclude :1)Theexistenceproblemofsurfacewavesinsemi_infiniteanisotropicmagnetoelectroelasticmediawithvariousboundaryconditions[2 ,3 ] ;2 )Green’sfunctions[4～ 7] ;3)Inho…     

Exact Electromagnetothermoelastic Solution for a Transversely Isotropic Piezoelectric Hollow Sphere Subjected to Arbitrary Thermal Shock

This paper presents analytical study for electromagnetothermoelastic transient behavior of a transversely isotropic hollow sphere, placed in a uniform magnetic field, subjected to arbitrary thermal shock. Exact solutions for the transient responses of stresses, perturbation of magnetic field vector, electric displacement and electric potential in the transversely isotropic piezoelectric hollow sphere are obtained by means of the Hankel transform, the Laplace transform and their inverse transforms. An interpolation method is used to solve the Volterra integral equation of the second kind caused by interactions among electric, magnetic, thermal and elastic fields. From the sample numerical calculations, it is seen that the present method is suitable for the transversely isotropic hollow sphere, placed in a uniform magnetic field, subjected to arbitrary thermal shock. Finally, the result can be used as a reference to solve other transient coupling problems of electromagnetothermoelasticity.     

Stress State of a Transversely Isotropic Ferromagnetic with an Elliptic Crack in a Homogeneous Magnetic Field

The magnetoelastic stress-strain problem for a transversely isotropic ferromagnetic body with an elliptical crack in the isotropy plane is solved explicitly. The body is in an external magnetic field perpendicular to the isotropy plane. The magnetic field induces elastic strains and an internal magnetic field in the body. The main characteristics of stress-strain state and induced magnetic field are determined and their features in the neighborhood of the crack are analyzed. Formulas for the stress intensity factors of the mechanical and magnetic fields near the crack tip are presented__________Translated from Prikladnaya Mekhanika, Vol. 41, No. 1, pp. 48–59, January 2005.     

THE NONLINEAR MAGNETOELASTIC PROPERTIES OF 〈 110 〉 ORIENTED TBo.27DYo.73FE1.95 POLYCRYSTALLINE ALLOYS UNDER COUPLED MAGNETOMECHANICAL LOADING

In the paper, the nonlinear magnetoelastic properties of composition Tb0.27Dy0.73 Fel.95 〈 110 〉 oriented polycrystalline alloys are investigated under coupled loads of high mag- netic field and compressive stress. The magnetization and magnetostriction are measured simul- taneously under applied magnetic field from -800 to 800 kA/m and compressive stress from 0 to 25 MPa at room temperature. The strain coefficient and relative permeability are obtained by differential calculation from the experimental curves. The results show that the values of satura- tion magnetization （M~） under different compressive stresses remain invariably constant in the region of the high magnetic field. The saturation magnetostriction （As） increases with increasing compressive stress and reaches 1680 ~ 10-6 under 25 MPa. According to the increase of the com- pressive stress, the hysteretic loop area of magnetization and magnetostriction increases, while the maximum relative permeability and strain coefficient decrease. Additionally, the influence of the bias magnetic field on the mechanical property is taken into account. The stress-strain relation- ship is nonlinear and sensitive to the applied external magnetic fields along the axis of rod. The results obtained are a useful complement to the existing experiments for theoretical approaches and engineering applications.     

Three-dimensional elasticity solution for bending of transversely isotropic functionally graded plates

This paper presents a three-dimensional elasticity solution for a simply supported, transversely isotropic functionally graded plate subjected to transverse loading, with Young’s moduli and the shear modulus varying exponentially through the thickness and Poisson’s ratios being constant. The approach makes use of the recently developed displacement functions for inhomogeneous transversely isotropic media. Dependence of stress and displacement fields in the plate on the inhomogeneity ratio, geometry and degree of anisotropy is examined and discussed. The developed three-dimensional solution for transversely isotropic functionally graded plate is validated through comparison with the available three-dimensional solutions for isotropic functionally graded plates, as well as the classical and higher-order plate theories.     

Mechanical response of neo-Hookean fiber reinforced incompressible nonlinearly elastic solids

The mechanical behavior of an incompressible neo-Hookean material, directionally reinforced by neo-Hookean fibers, is examined under homogeneous deformations. A composite model for this transversely isotropic material is developed based on a multiplicative decomposition of the deformation gradient which considers interaction between the fiber and the matrix. The so-called standard reinforcing model exhibits non-monotonic behavior in compression. The present composites-based approach leads to a modification of the standard reinforcing model in which monotonic behavior in compression is observed. This stems from the micromechanical basis of the model in which the fiber is treated as a neo-Hookean material. The conditions for loss of monotonicity and positivity in the stress-shear behavior in off-axis simple 2D shear are also obtained.     

Static analysis of simply supported functionally graded and layered magneto-electro-elastic plates

In this article, static analysis of functionally graded, anisotropic and linear magneto-electro-elastic plates have been carried out by semi-analytical finite element method. A series solution is assumed in the plane of the plate and finite element procedure is adopted across the thickness of the plate such a way that the three-dimensional character of the solution is preserved. The finite element model is derived based on constitutive equation of piezomagnetic material accounting for coupling between elasticity, electric and magnetic effect. The present finite element is modeled with displacement components, electric potential and magnetic potential as nodal degree of freedom. The other fields are calculated by post-computation through constitutive equation. The functionally graded material is assumed to be exponential in the thickness direction. The numerical results obtained by the present model are in good agreement with available functionally graded three-dimensional exact benchmark solutions given by Pan and Han [Pan, E., Han, F., in press. Green’s function for transversely isotropic piezoelectric functionally graded multilayered half spaces. Int. J. Solids Struct.]. Numerical study includes the influence of the different exponential factor, magneto-electro-elastic properties and effect of mechanical and electric type of loading on induced magneto-electro-elastic fields. In addition further study has been carried out on non-homogeneous transversely isotropic FGM magneto-electro-elastic plate available in the literature [Chen, W.Q., Lee, K.Y., Ding, H.J., 2005. On free vibration of non-homogeneous transversely isotropic magneto-electro-elastic plates].     

SCATTERING OF ANTI-PLANE SHEAR WAVES BY A SINGLE CRACK IN AN UNBOUNDED TRANSVERSELY ISOTROPIC ELECTRO-MAGNETO-ELASTIC MEDIUM

A theoretical treatment of the scattering of anti-plane shear (SH) waves is provided by a single crack in an unbounded transversely isotropic electro-magneto-elastic medium. Based on the differential equations of equilibrium, electric displacement and magnetic induction intensity differential equations, the governing equations for SH waves were obtained. By means of a linear transform, the governing equations were reduced to one Helmholtz and two Laplace equations. The Cauchy singular integral equations were gained by making use of Fourier transform and adopting electro-magneto imperme ableboundary conditions. The closed form expression for the resulting stress intensity factor at the crack was achieved by solving the appropriate singular integral equations using Chebyshev polynomial. Typical examples are provided to show the loading frequency upon the local stress fields around the crack tips. The study reveals the importance of the electro-magneto-mechanical coupling terms upon the resulting dynamic stress intensity factor.     

电磁功能材料的多场耦合实验研究进展

将对电磁功能材料多物理场耦合性能检测技术和设备做一综述介绍,介绍如何在多物理场耦合条件下测试电磁滞回线、蝶形曲线、电磁致伸缩、应力应变曲线和磁电效应等物理力学性能,并介绍电磁功能材料在多物理耦合场作用下的新的实验现象,包括铁电材料在多轴电场和双轴力载荷作用下的电滞回线、裂纹尖端的畴变规律、磁致伪弹性、磁致伸缩的"回落"等现象.这对于理解电磁功能材料和结构在耦合场下的变形与断裂机制有重要的意义.     

基于唯象相变理论的磁致伸缩材料耦合滞回动力学模拟

本文基于改进的Landau唯象相变理论,构造一个耦合的非线性常微分方程模型来模拟一维磁致伸缩材料的磁滞动态特性。模型的构造通过引入一个非凸的自由能函数来模拟磁致伸缩磁材料中不可逆的磁极化翻转与磁致应变,该自由能函数的每一个局部极小值都对应材料的一个磁化方向。通过热力学平衡条件建立能刻画磁致伸缩效应的非线性本构关系。所构造的模型成功地模拟出了磁场与弹性场之间的磁滞曲线和蝶形曲线,并采用实验结果对模型进行了验证。