Magnetoelectroelastic Medium Research Articles

Thermal Contact Response of a Transversely Isotropic Magneto-Electro-Elastic Coating.

The magneto-electro-elastic (MEE) medium is a typical intelligent material with promising application prospects in sensors and transducers, whose thermal contact response is responsible for their sensitivity and stability. An effective thermal contact model between a moving sphere and a coated MEE medium with transverse isotropy is established via a semi-analytical method (SAM) to explore its thermal contact response. First, a group of frequency response functions for the magneto-electro-thermo-elastic field of a coated medium are derived, assuming that the coating is perfectly bonded to the substrate. Then, with the aid of the discrete convolution-fast Fourier transform algorithm and conjugate gradient method, the contact pressure and heat flux can be determined. Subsequently, the induced elastic, thermal, electric and magnetic fields in the coating and substrate can be obtained via influence coefficients relating the induced field and external loads. With the proposed method, parametric studies on the influence of the sliding velocity and coating property are conducted to investigate the thermal contact behavior and resulting field responses of the MEE material. The sliding velocity and thermal properties of the coating have a significant effect on the thermal contact response of the MEE material; the coupled multi-field response can be controlled by changing the coating thickness between ~0.1 a0 and a0.

Stack of non-uniformly loaded shear cracks in magnetoelectroelastic materials

Detailed expressions are derived in closed-form for the field components at a general point in the deformation of magnetoelectroelastic media by a stack of parallel, antiplane shear cracks to which non-uniform mechanical, electric, and magnetic loads are applied, by exploiting a generalized technique of continuous distributions of dislocations. Their angular variations around a crack tip are deduced; from which comprehensive, novel representations for the appropriate stress, electric displacement, and magnetic induction intensity factors follow. Representative numerical results are illustrated graphically. The phenomenon of the so-called crack shielding effect is exhibited. Limiting special cases are considered as validation of this analysis.

Non-uniformly loaded row of moving shear cracks in magnetoelectroelastic media

Derivations and discussions are obtained in detail of the closed-form representations of the components of the deformation fields at a general point created by a moving row of smart magnetoelectroelastic shear cracks that are subjected to non-uniform mechanical, electric, and magnetic loadings. The creative analysis exploits a generalization of the basic dislocation layer method. Near a crack tip, their angular variations and the corresponding stress, electric displacement and magnetic induction intensity factors are deduced. Graphical displays of some illustrative numerical data are presented. As a particular case, the results for an analogous stationary row of non-constantly loaded magnetoelectroelastic cracks are derived. The correctness and validity of the results of this novel analysis are examined by the verification of their agreement with those previously presented for various limiting particular cases.

Dynamic equations of a prestressed magnetoelectroelastic medium

The constitutive relations of nonlinear mechanics of a magnetoelectroelastic medium subjected to initial mechanical stresses are linearized in the framework of material (Lagrangian) coordinates. The final expressions are constructed independently of the choice of curvilinear coordinates and are represented in a form convenient for theoretical and applied studies. The constitutive relations for the motion of a prestressed magnetoelectroelastic medium are given in rectangular Cartesian coordinates. The influence of the initial mechanical stresses on piezomagnetoelectric materials of the class 6mm is studied.

Dynamic contact modeling of anisotropic magneto-electro-elastic materials with volume fraction changes

The present paper addresses a dynamic contact problem for anisotropic semi-finite magneto-electro-elastic (MEE) materials loaded by a symmetrical stamp. The stamp moves at a constant speed. To deal with the difficulty caused by initial terms, the Galilean transform and the Fourier sine and cosine transforms are employed. The stated problem is reduced to singular integral equations for stamp possessing different electrical and magnetic features. Exact expressions for various physical quantities are obtained in terms of elementary functions under a flat stamp. Numerical results show that the mechanical stamp has the smallest effect, the fully conducting stamp has the largest effect on physical quantities inside the anisotropic MEE medium, and the results for transversely isotropic case can be covered by the present anisotropic case. The effects of volume fraction on contact behaviors under various surface contact conditions are detailed.

An analytical method for predicting the anti-plane effective magnetoelectroelastic coefficients of composites containing doubly periodic multicoated fibers

The present paper deals with the magnetoelectroelastic composites containing a doubly periodic array of multicoated fibers under anti-plane shear loads and in-plane electromagnetic loads. By introducing the generalized eigenstrain, the heterogeneous magnetoelectroelastic medium is equivalent to a homogeneous magnetoelectroelastic medium with the periodically distributed generalized eigenstrains. Then the homogeneous magnetoelectroelastic medium with the generalized eigenstrain is solved analytically under the applied load conditions, the generalized stresses and strains in the fibers, coatings and matrix are derived. Based on the average-field theory, the solutions of the generalized stresses and strains are applied to determine the anti-plane effective magnetoelectroelastic properties of the composites. Two-phase (fiber/matrix) and three-phase (fiber/coating/matrix) magnetoelectroelastic composites are examined, and the comparison between the obtained results and the existing results shows the accuracy of the proposed method. Several four-phase magnetoelectroelastic composites with epoxy matrix are studied, and the influences of the composites microstructures on the effective magnetoelectric coefficient are discussed.

On New Dispersive SH-Waves Propagating in Piezoelectromagnetic Plate

This theoretical work discovers four new dispersive shear-horizontal (SH) waves propagating in the transversely isotropic piezoelectromagnetic plate of class 6 mm. In this work, the following mechanical, electrical, and magnetic boundary conditions at both the upper and lower free surfaces of the piezoelectromagnetic plate are utilized: the mechanically free surface, continuity of both the electrical and magnetic potentials, and continuity of both the electrical and magnetic inductions. The solutions for the new SH-wave velocities (dispersion relations) are found in explicit forms and then graphically studied. The graphical investigation has soundly illuminated several interesting peculiarities that were also discussed. The piezoelectromagnetic materials, also known as the magnetoelectroelastic media, are famous as smart materials because the electrical subsystem of the materials can interact with the magnetic subsystem via the mechanical subsystem, and vice versa. Therefore, it is very important to know the wave characteristics of such (composite) materials because of possible constitution of new technical devices with a high level of integration. It is obvious that the plate waves can be preferable for further miniaturization of the technical devices and used for the nondestructive testing and evaluation of thin piezoelectromagnetic films.

Dramatic Influence of the Magnetoelectric Effect on the Existence of the New SH-SAWs Propagating in Magnetoelectroelastic Composites

This comparative study acquaints the reader with some properties of the eighth and tenth new shear-horizontal surface acoustic waves (SH-SAWs) propagating along the free surface of the magnetoelectroelastic (6 mm) medium. These new nondispersive SH-SAWs cannot exist when the electromagnetic constant α is equal to zero. The piezoelectromagnetic SH bulk acoustic wave and the surface Bleustein-Gulyaev-Melkumyan (BGM) wave are also chosen for comparison. The main problem of this report is the demonstration of the fact that the new waves can propagate slower than the BGM wave. This problem can be very important due to the fact that among the other known SH-SAWs the BGM wave can propagate significantly slower than the corresponding SH bulk acoustic wave. Two new SH-SAWs are analytically and graphically studied in dependence on the electromagnetic constant α. For the graphical study, two (6 mm) composites are used: BaTiO3– CoFe2O4 and PZT-5H–Terfenol-D. For the second composite it is solidly demonstrated that for small values of α, the eighth new SH-SAW cannot exist and its velocity starts with zero at some small threshold value of α rapidly reaching the BGM-wave velocity. This means that a weak magnetoelectric effect can dramatically slow down the speed of either new SH-SAW. As a result, the studied new SH-SAWs can be suitable for creation of new technical devices to sense the magnetoelectric effect. For the analytical study, extreme and inflexion points were evaluated in the velocities’ dependencies on the value of the electromagnetic constant α.

A Study of New Nondispersive SH-SAWs in Magnetoelectroelastic Medium of Symmetry Class 6 mm

Two additional solutions of new shear-horizontal surface acoustic waves (SH-SAWs) are found in this theoretical report. The SH-SAW propagation is managed by the free surface of a solid when it has a direct contact with a vacuum. The studied smart solid represents the transversely isotropic piezoelectromagnetic (magnetoelectroelastic or MEE) medium that pertains to crystal symmetry class 6 mm. In the developed theoretical treatment, the solid surface must be mechanically free. Also, the magnetic and electrical boundary conditions at the common interface between a vacuum and the solid surface read: the magnetic and electrical displacements must continue and the same for the magnetic and electrical potentials. To obtain these two new SH-SAW solutions, the natural coupling mechanisms such as eμ-hα and εμ-α2 present in the coefficient of the magnetoelectromechanical coupling (CMEMC) can be exploited. Based on the obtained theoretical results, it is possible that a set of technical devices (filters, sensors, delay lines, lab-on-a-chip, etc.) based on smart MEE media can be developed. It is also blatant that the obtained theoretical results can be helpful for the further theoretical and experimental studies on the propagation of the plate SH-waves and the interfacial SH-waves in the MEE (composite) media. The most important issue can be the influence of the magnetoelectric effect on the SH-wave propagation. One must also be familiar with the fact that the surface, interfacial, and plate SH-waves can frequently represent a common tool for nondestructive testing and evaluation of surfaces, interfaces, and plates, respectively.

Semi-permeable crack analysis in a 2D magnetoelectroelastic medium based on the EMPS model

For a crack in a magnetoelectroelastic plane under the electrically and magnetically semi-permeable boundary condition, we derive the non-linear analytical solution of the strip electric–magnetic polarization saturation (EMPS) model. Using the extended dislocation theory and integral equation method, we obtain the electric and magnetic yielding zones, as well as the field intensity factor and local J-integral. Adapting an iterative method, numerical examples were performed to analyze the effect of different boundary conditions and the electric–magnetic saturated properties on the electric displacement and magnetic induction in the crack cavity, electric and magnetic yielding zones, stress intensity factor and local J-integral.

An axisymmetric problem of an embedded mixed-mode crack in a functionally graded magnetoelectroelastic infinite medium

This paper investigates the problem of an axisymmetric penny shaped crack embedded in an infinite functionally graded magneto electro elastic medium. The loading consists of magnetoelectromechanical loads applied on the crack surfaces assumed to be magneto electrically impermeable. The material’s gradient is parallel to the axisymmetric direction and is perpendicular to the crack plane. An anisotropic constitutive law is adopted to model the material behavior. The governing equations are converted analytically using Hankel transform into coupled singular integral equations, which are solved numerically to yield the crack tip stress, electric displacement and magnetic induction intensity factors. A similar problem but with a different crack morphology, that is a plane crack embedded in an infinite functionally graded magneto electro elastic medium, was considered by the authors in a previous work (Rekik et al., 2012) [25]. While the overall solution schemes look similar, the axisymmetric problem resulted in more mathematical complexities and let to different conclusions with respect to the influence of coupling between elastic, electric and magnetic effects. The main focus of this paper is to study the effect of material non-homogeneity on the fields’ intensity factors to understand further the behavior of graded magnetoelectroelastic materials containing penny shaped cracks and to inspect the effect of varying the crack geometry.

Numerical method for nonlinear models of penny-shaped cracks in three-dimensional magnetoelectroelastic media

Green functions corresponding to uniformly distributed extended displacement discontinuities on an annular crack element in the isotropic plane of a three-dimensional transversely isotropic magnetoelectroelastic medium are derived. Using the obtained Green functions, an extended displacement discontinuity method is presented to analyze a penny-shaped crack under axisymmetric loadings. Using the electric and magnetic polarization saturation model and the electric and magnetic breakdown model, the electric and magnetic yielding zones, the extended displacement discontinuities, the extended stress intensity factors and the J-integral are numerically calculated. The accuracy and efficiency of the proposed method are demonstrated by comparing the numerical results with those obtained from analytical solutions.

Coupled 2D electric, magnetic, and mechanical fields in dielectrics with cracks and thin inclusions

We apply methods of the theory of thermoelastic deformation of bodies with thin inclusions to study magnetoelectroelastic media with thin inhomogeneities. We construct the integral equations of the problem and propose an efficient numerical procedure of the boundary-element method for their solution. It is established that the fields of mechanical stresses, electric displacements, and magnetic induction near the tip (front) of a thin inclusion, the mathematical model of which can be based on the coupling principle for continua of different dimensions, have a square-root singularity. For the complete description of asymptotic relations for stresses, displacements, and other quantities near the front of an inhomogeneity, we introduce 10 generalized intensity factors for stresses, electric displacements, and magnetic induction. We obtain analytical solutions of the problem for the limiting cases of a permeable crack and a rigid electroconductive inclusion in a magnetoelectroelastic medium. Results of the numerical analysis of intensity factors for an elastic isotropic inclusion in an anisotropic magnetoelectroelastic medium are presented.

Three-dimensional vertical cracks in magnetoelectroelastic media via the extended displacement discontinuity boundary integral equation method

In this article, the extended displacement discontinuity method is extended to study the fracture problem in a three-dimensional transversely isotropic magnetoelectroelastic medium with a planar crack vertical to the plane of isotropy. Considering the electric and magnetic fields in the crack cavity, and using the Somigliana identity along with the displacement discontinuity Green’s functions, the hyper-singular boundary integral equations for the unknown displacement discontinuities across the crack face are derived. The singularity features along the crack fronts are analyzed, and the extended field intensity factors are expressed in terms of the extended displacement discontinuities on the crack face. Numerical examples on the field intensity factors are finally calculated for a vertical square crack using the exact closed-form Green’s functions due to constant displacement discontinuities over a rectangular crack element, and some interesting features are observed, which are different from the case where the crack is located in the plane of isotropy. The influence of the electric and magnetic boundary conditions along the crack face on the field intensity factors is further studied.

Reection and refraction of plane waves at the interface between magnetoelectroelastic and liquid media

This paper analyzes the reflection and refraction of plane wave incidences at the interface between magnetoelectroelastic (MEE) and liquid media. The MEE medium is assumed to be transversely isotropic and the liquid medium to be nonviscous. Three cases, i.e., the coupled quasipressure wave incidence from the MEE medium, the coupled quasi-shear vertical wave incidence from the MEE medium, and the pressure wave incidence from the liquid medium, are discussed. The expressions of reflection and transmission coefficients varying with the incident angle are obtained. This investigation would be useful to the MEE acoustic device field.

Stroh formalism based boundary integral equations for 2D magnetoelectroelasticity

This paper presents a novel approach for obtaining boundary integral equations of 2D anisotropic magnetoelectroelasticity. This approach is based on the holomorphy theorems and the Stroh formalism and allows developing of the integral equations for the aperiodic, singly and doubly periodic problems of magnetoelectroelasticity. Obtained equations contain the unknown discontinuities of displacement, electric and magnetic potentials and also traction, electric displacement and magnetic induction that allow adopting the existing boundary element procedures for their solution. Analytical solutions for systems of collinear permeable or impermeable cracks are obtained. Numerical boundary element solutions are obtained for the singly and doubly periodic sets of permeable and impermeable cracks in the magnetoelectroelastic medium and a half-plane. Comparison with analytical solutions and other available results validate the present formulations and numerical computation.

Fracture and effective properties of finite magnetoelectroelastic media

Magnetoelectroelastic materials are inherently brittle and prone to cracking. It is important to understand how cracks influence the magnetoelectrical coupling properties of the magnetoelectroelastic materials. This article establishes an analytical model for a finite crack in a finite magnetoelectroelastic medium. The stress, electric displacement, and magnetic induction and their intensity factors are obtained by the integral equation technique. The temperature effect is also studied. The effect of cracking on the effective thermomagnetoelectromechanical properties is discussed. In addition, crack is modeled as a notch of finite height to study the effect of the crack-face electric and magnetic boundary condition assumptions on the predicted properties of the magnetoelectroelastic medium.

Screw dislocation and elliptic inhomogeneity of a confocal crack in magnetoelectroelastic medium: Comparison of energy release rate and strain energy density

This work is devoted to investigate the magnetoelectroelastic interaction between a generalized screw dislocation and an elliptic inhomogeneity containing a confocal crack in piezoelectric/piezomagnetic composite subjected to remote anti-plane shear stress field, in-plane electric and magnetic field. By using the complex variable method of elasticity, the closed-form expressions of complex potentials of matrix and inhomogeneity are obtained for the dislocation locating both in matrix and inhomogeneity. The expressions of the generalized stress/strain field, image force, the generalized stress intensity factor and energy release rate of crack tip, and strain energy density are derived explicitly. Then, the influence laws of material parameters, the shape of elliptic inhomogeneity and remote loading on these quantities are analyzed. The results show that the image force has different variation laws in magnetoelectroelastic materials with that in elastic materials; stress intensity factor has the same distributing law as electric displacement intensity factor, but is different from magnetic induction intensity factor; the energy release rate (ERR) can be positive and negative depending on the combined action of applied fields, the in-plane electric field and magnetic field. This makes the ERR interpretation unphysical. ERR is not permitted to change sign. The strain energy density function is shown to be positive definite under all conditions.

Doubly periodic arrays of cracks and thin inhomogeneities in an infinite magnetoelectroelastic medium

A two-dimensional boundary element method for the analysis of a magnetoelectroelastic medium containing doubly periodic sets of cracks or thin inclusions is developed in this paper. The integral equations and closed-form expressions for corresponding kernels are obtained. Based on the quasi-periodicity of extended displacement and stress function, the integral representations for average stress, strain, electric displacement, magnetic induction etc. are developed. The algorithm of effective properties determination is given. The numerical examples prove the efficiency and high accuracy of the proposed approach in determination of stress, electric displacement and magnetic induction intensity factors and effective properties of the material containing doubly periodic arrays of cracks or thin inclusions.

An embedded mixed-mode crack in a functionally graded magnetoelectroelastic infinite medium

This paper focuses on the study of the influence of a mixed-mode crack on the coupled response of a functionally graded magnetoelectroelastic material (FGMEEM). The crack is embedded at the center of a 2D infinite medium subjected to magnetoelectromechanical loads. The material is graded in the direction orthogonal to the crack plane and is modeled as a nonhomogeneous medium with anisotropic constitutive laws. Using Fourier transform, the resulting plane magnetoelectroelasticity equations are converted analytically into singular integral equations which are solved numerically to yield the crack-tip mode I and II stress intensity factors, the electric displacement intensity factors and the magnetic induction intensity factors. The main objective of this paper is to study the influence of material nonhomogeneity on the fields’ intensity factors for the purpose of gaining better understanding on the behavior of graded magnetoelectroelastic materials.