Magnetoelectroelastic Materials Research Articles

On Discovery of the Twelfth and Thirteenth New Nondispersive SH-SAWs in 6 mm Magnetoelectroelastics

This report acquaints the reader with an extra two new shear-horizontal surface acoustic waves (SH-SAWs). These new SH-SAWs can propagate along the free surface of the transversely isotropic (6 mm) magnetoelectroelastic materials. These (composite) materials can simultaneously possess the piezoelectric, piezomagnetic, and magnetoelectric effects. Some competition among these effects can lead to suitable solutions found for the following three possible coupling mechanisms: eα – hε, eµ – hα, εµ – α2. Here, the mechanically free interface between the solid and a vacuum was considered. This report discovers the twelfth (thirteenth) new SH-SAW for the magnetically closed (electrically open) case and continuity of both the normal component of the electrical (magnetic) displacement and the electrical (magnetic) potential when the coupling mechanism eα – hε (eµ – hα) works. The propagation velocities were obtained in explicit forms that take into account the contribution of the vacuum material parameters. The discovered waves were then graphically studied for the purpose of disclosing the dissipation phenomenon (the propagation velocity becomes imaginary) caused by the coupling with the vacuum properties. The obtained results can be useful for further investigations of interfacial and plate SH-waves, constitution of technical devices, nondestructive testing and evaluation, and application of some gravitational phenomena.

Surface effect on a nano‐elliptical hole or nano‐crack in magnetoelectroelastic materials under antiplane shear

AbstractBased on the Gurtin‐Murdoch surface/interface model, an antiplane shear problem of a magnetically and electrically impermeable nano‐elliptical hole in magnetoelectroelastic (MEE) materials with surface effect is presented subjected to far‐field anti‐plane mechanical and in‐plane electrical and magnetic loadings. By using the complex function method and conformal mapping technique, exact closed‐form solutions of the stress, electric displacement and magnetic induction intensity factors near the crack tip are obtained when the nano‐elliptical hole is reduced to a nano‐crack. Numerical examples are provided to show the effects of size of nano‐crack on the field intensity factors near the crack tip induced by mechanical, electrical and magnetic loadings for the piezoelectric (PE), piezomagnetic (PM) and MEE materials with surface effect. The interaction between the stress field, electric field and magnetic field around the nano‐hole is analyzed. The results show that the obtained solution is close to the classical elasticity solution with increasing size of the nano‐crack.

A multi-physics node-based smoothed radial point interpolation method for transient responses of magneto-electro-elastic structures

A multi-physics node-based smoothed radial point interpolation method (MNS-RPIM) for the transient responses of two-dimensional magneto-electro-elastic (MEE) structures is presented, the displacement, electrical potential and magnetic potential are obtained by combining the coupling MEE Newmark method. Based on constitutive equation of MEE material and introducing the weakened weak (W2) formulation and the G space theory, the discretized system equations are produced. The method developed here is suitable for arbitrary boundary conditions, which could be the complement to the analytical solution. For two-dimensional structures, triangular element is adopted to discrete models because it could be automatically generated for complex geometries. The generalized displacement is computed for a cantilever beam, a layered MEE sensor and a typical MEE energy harvester. Results shows the following important properties of MNS-RPIM: (1) insensitive to mesh distortion; (2) accurate and convergent; (3) volumetric locking free; (4) high efficiency over FEM at the same accuracy.

Fracture analysis of magnetoelectroelastic solid weakened by periodic cracks and line inclusions

This paper aims to a more fundamental understanding of multiple defects (cracks and rigid-line inclusions) on the fracture behavior of magnetoelectroelastic (MEE) materials. A theoretical study is conducted on a MEE solid weakened by a doubly periodic array of cracks and rigid-line inclusions under anti-plane mechanical and in-plane electric and magnetic loadings. By using the elliptic function theory, the conformal mapping technique and the analytic function boundary value theory, a rigorous analytical solution to the MEE heterogeneous material are obtained. The closed form formulae for the MEE field intensity factors and the energy release rates at crack tips and rigid-line tips are presented. Numerical examples of electrically and magnetically impermeable cracks and rigid-line inclusions are studied to reveal the relationship of the energy release rates with the period ratio of the microstructure, the length of the cracks, the length of the rigid-line inclusions and the applied mechanical loading, electrical loading and magnetic loading. The analytical solution obtained is general and many other results can be regarded as degenerated cases. The present analytical solution can provide theoretical benchmark results for the multiphysics fracture problem of MEE solid with a large number of defects.

Dugdale plastic zone model of a penny-shaped crack in a magnetoelectroelastic cylinder under magnetoelectroelastic loads

This paper extends the Dugdale plastic zone to the penny-shaped crack problem for a magnetoelectroelastic (MEE) cylinder, where the crack surfaces are assumed to be magnetoelectrically permeable. Using potential function theory and Hankel transform method, the present boundary value problem is translated into solving a sectionalized Fredholm integral equation of the second kind. The non-singular field solutions are analyzed, and the effects of the applied MEE loads and geometric dimension on the width of plastic zone and crack opening displacements are evaluated. Numerical results show that for the considered model, each of the far-field MEE combination load $$\lambda $$ , the far-field magnetoelectric combination load $$\lambda _{\mathrm{EH}}$$ and the purely mechanical load $$\sigma _0$$ applied in the far field, respectively, plays an important role in the present fracture analysis. For a given mechanical load and a fixed crack configuration, the negative magnetoelectric loads are prone to promote the crack growth and propagation than the positive ones. These should be helpful for the design and manufacture of MEE materials and devices.

Interaction between many parallel screw dislocations and a semi-infinite crack in a magnetoelectroelastic solid**Project supported by the National Natural Science Foundation of China (Grant Nos. 11262017, 11262012, and 11462020), the Natural Science Foundation of Inner Mongolia Autonomous Region, China (Grant No. 2015MS0129), the Key Project of Inner Mongolia Normal University, China (Grant No. 2014ZD03), and the Graduate Research Innovation Project

Based on the fundamental equations of magnetoelectroelastic material and the analytic theory, and using the Muskhelishvili-introduced well-known elastic techniques combined with the superposition principle, the closed form solution of the generalized stress field of the interaction between many parallel screw dislocations and a semi-infinite crack in an infinite magnetoelectroelastic solid is obtained, on the assumption that the surface of the crack is impermeable electrically and magnetically. Besides, the Peach–Koehler formula of n parallel screw dislocations is given. Numerical examples show that the generalized stress varies with the position of point z and is related to the material constants. The results indicate that the stress concentration occurs at the dislocation core and the tip of the crack. The result of interaction makes the system stay in a lower energy state.

Finite element evaluation of free vibration characteristics of magneto-electro-elastic rectangular plates in hygrothermal environment using higher-order shear deformation theory

In this article, the effect of hygrothermal environment on the free vibration characteristics of magneto-electro-elastic (MEE) plates has been studied using finite element method. To this end, higher order shear deformation theory (HSDT) has been employed to assess the displacement fields. Further, using Hamilton’s principle and linear coupled constitutive equations of MEE material, the final equilibrium equations for free vibration behaviour of MEE plate in hygrothermal environment has been derived. A special attention has been paid to evaluate the effect of temperature and moisture dependent elastic coefficients on the natural frequencies. The results reveal that the external temperature and moisture fields predominantly affect the stiffness of the plate and hence alter the free vibration characteristics drastically. It is believed that the results presented in this study are useful for the precise design of sensors and actuators in hygrothermal environment.

Interface crack between magnetoelectroelastic and orthotropic half-spaces under in-plane loading

In this paper, an interface crack between magnetoelectroelastic and orthotropic half-spaces has been studied in detail. By using integral transform techniques the present mixed boundary value problem was reduced to the solution of singular integral equations, which can be further reduced to solving a Riemann-Hilbert problem with closed form solution. The crack-tip singularities of the interface crack have been investigated for possible combinations of the magnetoelectroelastic and orthotropic materials, a criterion based on the coefficient of the Riemann-Hilbert problem is introduced to study the possible singularity behavior of the interface crack, and it is shown that there can be either oscillatory or non-oscillatory singularity for the interface crack depending on the particular combination of the bi-materials. A closed form solution for stresses, electric fields, magnetic fields, electric displacement and magnetic induction in the cracked biomaterials is given, and of particular interests, the analytical expression of the stresses, electric displacements and magnetic inductions along the interface has been obtained.

New soliton solution to the longitudinal wave equation in a magneto-electro-elastic circular rod

Abstract This paper examines the effectiveness of an integration scheme which called the extended trial equation method (ETEM) in exactly solving a well-known nonlinear equation of partial differential equations (PDEs). In this respect, the longitudinal wave equation (LWE) that arises in mathematical physics with dispersion caused by the transverse Poisson’s effect in a magneto-electro-elastic (MEE) circular rod, which a series of exact traveling wave solutions for the aforementioned equation is formally extracted. Explicit new exact solutions are derived in different form such as dark solitons, bright solitons, solitary wave, periodic solitary wave, rational function, and elliptic function solutions of the longitudinal wave equation. The movements of obtained solutions are shown graphically, which helps to understand the physical phenomena of this longitudinal wave equation. Many other such types of nonlinear equations arising in non-destructive evaluation of structures made of the advanced MEE material can also be solved by this method.

The buckling of piezoelectric plates on pasternak elastic foundation using higher-order shear deformation plate theories

In this article, an exact analytical solution for mechanical buckling analysis of magnetoelectroelastic plate resting on pasternak foundation is investigated based on the third-order shear deformation plate theory. The in-plane electric and magnetic fields can be ignored for plates. According to Maxwell equation and magnetoelectric boundary condition, the variation of electric and magnetic potentials along the thickness direction of the plate is determined. The von Karman model is exploited to capture the effect of nonlinearity. Navier\'s approach has been used to solve the governing equations for all edges simply supported boundary conditions. Numerical results reveal the effects of (i) lateral load, (ii) electric load, (iii) magnetic load and (iv) higher order shear deformation theory on the critical buckling load have been investigated. These results must be the analysis of intelligent structures constructed from magnetoelectroelastic materials.

Effective properties of magnetoelectroelastic interfaces weakened by micro‐cracks

AbstractThe effective properties of a microscopically damaged interface between two dissimilar magnetoelectroelastic materials are investigated using a micro‐statistical model. The interface is modeled as damaged by a periodic array of micro‐cracks. The micro‐cracks over a period interval of the interface are randomly generated and are either all (i) magnetically and electrically impermeable, or (ii) magnetically permeable and electrically impermeable, or (iii) electrically permeable and magnetically impermeable, or (iv) magnetically and electrically permeable. The conditions on the micro‐cracks are formulated in terms of hypersingular integro‐differential equations with the jumps in the elastic displacements, the electric potential and the magnetic potential across opposite micro‐crack faces being unknown functions to be determined. Once the unknown functions are determined, the effective properties of the microscopically damaged interface can be readily computed. The effects of the crack density and the material constants on the effective properties are investigated in detail.

Investigation of non-local theory solution to a three-dimensional rectangular permeable crack in magneto-electro-elastic materials

This paper presents the non-local theory solution to a three-dimensional rectangular permeable crack in magneto-electro-elastic materials (MEEMs) using the generalized Almansi's theorem and the Schmidt method. The problems are formulated through Fourier transform as three pairs of dual integral equations, in which the unknown variables are the jumps of elastic displacement, electric potential and magnetic potential jumps across the crack surfaces. The displacement jumps across the crack surfaces are directly expanded as a series of Jacobi polynomials to solve the dual integral equations and the resulting equations are solved using the Schmidt method. Numerical examples are provided to show the effects of the geometric shape of rectangular crack and the lattice parameter on the stress, the electric displacement and the magnetic flux fields near the crack edges in magneto-electro-elastic materials. Unlike the classical solution, the present solutions exhibit no stress, electric displacement and magnetic flux singularities near the crack edges in magneto-electro-elastic materials.

Multiphysics response of magneto-electro-elastic beams in thermo-mechanical environment

In this article, the multiphysics response of magneto-electro-elastic (MEE) cantilever beam subjected to thermo-mechanical loading is analysed. The equilibrium equations of the system are obtained with the aid of the principle of total potential energy. The constitutive equations of a MEE material accounting the thermal fields are used for analysis. The corresponding finite element (FE) formulation is derived and model of the beam is generated using an eight noded 3D brick element. The 3D FE formulation developed enables the representation of governing equations in all three axes, achieving accurate results. Also, geometric, constitutive and loading assumptions required to dimensionality reduction can be avoided. Numerical evaluation is performed on the basis of the derived formulation and the influence of various mechanical loading profiles and volume fractions on the direct quantities and stresses is evaluated. In addition, an attempt has been made to compare the individual effect of thermal and mechanical loading with the combined effect. It is believed that the numerical results obtained helps in accurate design and development of sensors and actuators.

Hygrothermal analysis of magneto-electro-elastic plate using 3D finite element analysis

In this article, the static response of magneto-electro-elastic (MEE) plate subjected to hygrothermal loads is investigated using the finite element (FE) method. A FE formulation is derived using the principle of total potential energy and linear coupled constitutive equations of MEE materials by taking into account the thermal and hygroscopic field effects. A uniform temperature rise and moisture concentration rise has been considered. The variations of static parameters are estimated along the MEE plate length by considering the temperature and moisture dependant elastic stiffness coefficients. The coupled FE equilibrium equations in terms of displacements, electric and magnetic potentials are solved directly using condensation procedure. Numerical examples of the FE results are presented and discussed in detail to understand the significant effects of hygrothermal loading, temperature and moisture dependent material properties, boundary conditions and aspect ratio on the direct (displacements, electric potential and magnetic potential) and derived quantities (stresses, electric displacement and magnetic flux density) of MEE plate.

Magneto–electro interaction of two offset indenters in frictionless contact with magnetoelectroelastic materials

• Interaction of two perfectly conducting indenters is examined. • Various intensity factors are defined to measure singular behavior at the edges. • Degradation from two perfectly conducting indenters to one indenter is done. • Interaction between two semi-cylindrical indenters is revealed. • Singularities at the edges can be suppressed because of multi-field coupling. Within the theory of linear full-field magneto–electro–elasticity, magneto–electro interaction of two electrically-conducting and magnetically-conducting indenters acting over the surface of magnetoelectroelastic materials widely used in practical industries is examined. The operation theory, Fourier transform technique and integral equation technique are employed to address the two-dimensional, mixed boundary-value problem explicitly. The surface stresses, electric displacement and magnetic induction and their respective intensity factors are obtained in closed forms for two perfectly conducting semi-cylindrical indenters. Degradation from two perfectly conducting semi-cylindrical indenters to one single perfectly conducting cylindrical indenter is discussed. Numerical analyses are detailed to reveal the effects of the interactions between two semi-cylindrical indenters on contact behaviors subjected to multi-field loadings.

Moving crack with a contact zone at interface of magnetoelectroelastic bimaterial

The plane-strain problem of a moving crack at the interface of two dissimilar magnetoelectroelastic (MEE) materials is investigated. Assuming that the crack moves at a constant speed in the subsonic regime, a fracture analysis of a finite crack under concentrated loading imposed onto the crack face is first carried out. By applying magnetoelectric (ME) permeable boundary conditions at the crack face, a combined Dirichlet-Riemann problem is formulated and solved analytically. The expressions for the fracture parameters, including the relative length of the contact zone and field intensity factors (FIFs), are obtained in the analytical form. A crack of a semi-infinite length with a contact zone under concentrated loading is further presented as a specific case examined with the obtained solution. Then a moving crack of finite length at the interface under remote mix-mode loading is also analyzed and the corresponding fracture parameters are presented in an analytical form. Finally, numerical examples are provided for the material combination of barium titanate-cobalt ferrite composites to examine the influence of the speed of the moving crack, poling direction, material volume fraction, load position and load ratio on the fracture parameters, from which some new and interesting conclusions related to the crack model in this study are drawn.

A finite element based assessment of static behavior of multiphase magneto-electro-elastic beams under different thermal loading

In this article, static analysis of a magneto-electro-elastic (MEE) beam subjected to various thermal loading and boundary conditions has been investigated. Influence of pyroeffects (pyroelectric and pyromagnetic) on the direct quantities (displacements and the potentials) of the MEE beam under different boundary conditions is studied. The finite element (FE) formulation of the MEE beam is developed using the total potential energy principle and the constitutive equations of the MEE material taking into account the coupling between elastic, electric, magnetic and thermal properties. Using the Maxwell electrostatic and electromagnetic relations, variation of stresses, displacements, electric and magnetic potentials along the length of the MEE beam are investigated. Effect of volume fractions, aspect ratio and boundary conditions on the direct quantities in thermal environment has been determined. The present investigation may be useful in design and analysis of magnetoelectroelastic smart structures and sensor applications.

Modeling and analysis of loaded multilayered magnetoelectroelastic structures composite materials: Applications

This paper presents the detailed analysis of fiber- reinforced magnetoelectroelastic composite plates. The work is divided into two major sections. The first one deals with the homogenization of the properties of each layer based on the Mori-Tanaka mean field approach where all the needed effective coefficients of each layer are determined. Then, in order to perform analysis of the considered, the Stroh formalism is used to provide solutions for multifunctional multilayered magnetoelectroelastic composites, to predict exactly the mechanical and electrical behaviors near or across the interface of material layers.

Multiphase Differential Scheme for Effective Properties of Magnetoelectroelastic Composite Materials

The differential scheme is extended to predict the effective properties of multiphase magnetoelectroelastic composite materials. The prediction of effective properties is done gradually by adding a series of incremental additions of a small volume of particulate phase materials to an initial material (matrix phase). The construction process is compatible with high volume concentration of inclusion. A system of coupled differential equations is formulated and its numerical solution leads to effective properties of reinforced magnetoelectroelastic composites. For the numerical results, two-phase and three-phase magnetoelectroelastic composites are considered. The effective properties are presented as function of volume fractions and shapes of inclusions and compared with predictions based on the Mori–Tanaka and incremental self-consistent models.

Exact solution for an elliptical cavity or crack in a reinforced magnetoelectroelastic material under anti-plane shear

An exact solution for an elliptical cavity embedded in a reinforced, magnetoelectroelastic material under anti-plane shear and in-plane electric and magnetic loading is provided in this paper. Explicit forms of the mechanical, electric and magnetic fields in the matrix, the reinforcement layer and the elliptical cavity are obtained by means of the method of complex potentials. The electromagnetic fields inside the elliptical cavity have been taken into consideration, and explicit solutions for a mode III crack, either impermeable or permeable, are obtained when the elliptical cavity is reduced to a crack. The change of energy due to the presence of the cavity and reinforcement layer has been derived. Some special cases, such as the elliptical cavity problem and crack problem are discussed in detail to illustrate the validity and versatility of the current formulation.