Magnetoelectroelastic Composites Research Articles

Influences of magneto-electro-elastic layer properties of piezoelectric/piezomagnetic composites on dynamic intensity factors

Magneto-electro-elastic (MEE) materials are composed of piezoelectric (PE) and piezomagnetic (PM) phases, leading to the existence of a large number of interfaces between phases. Complex interface distributions bring a challenge for the dynamic fracture analysis of MEE composites, as the available fracture mechanics approaches usually need to avoid material interfaces. This work establishes a dynamic domain-independent interaction integral (DII-integral) to extract the dynamic intensity factors (IFs) for MEE materials. The DII-integral exhibits apparent superiority over available I-integral methods in the dynamic fracture studies of MEE composites with complicated interfaces due to its domain-independence for interfaces and avoidance of material property derivatives. After verifying the accuracy, the DII-integral method is applied to investigate the dynamic fracture of PE-MEE-PM layered composites. It is found that as the crack tip approaches the MEE middle layer, the dynamic IFs decrease for a crack in PE phase (BaTiO3) but increase for a crack in PM phase (CoFe2O4). The elastic stiffness, PE coefficient, PM coefficient and dielectric permittivity of MEE middle layer have a significant effect on the dynamic IFs, and the other material parameters have slightly effect.

Acoustic insulation characteristics improvement of a thick CNT-reinforced doubly-curved shell by using GPLRC and MEE composite layers

Noise reduction in structures and human living environments is one of the most important issues in engineering that is always given special attention. Sound insulation has always been improved using different methods, one of which is to use the properties of materials. Herewith, the aim of this paper is to take advantage of graphene-platelet reinforced composites and magneto-electro-elastic (MEE) material properties for sound attenuation. The present paper deals with the analysis of sound transmission loss (STL) through a three-layer sandwich doubly-curved shell where an MEE sheet is integrated with two nanocomposite sheets. In addition, these two nanocomposite sheets are reinforced by functionally graded (FG) distributions of CNT and graphene platelet (GPL)-reinforced composites, respectively. Firstly, the three-dimensional elasticity theory is employed to derive the governing equations of motion. Then, the vibroacoustic analysis for the resultant equations is completed according to the state space and transfer matrix method. Comparing the obtained results with the available literature discloses that the offered procedure has a high precision for structural acoustic problems. In the next step, in addition to inspecting two kinds of MEE composites, the effective parameters, such as layup configuration, FG distribution, volume fraction, weight fraction, radii of curvature, electromagnetic boundary conditions, and interphase thickness, are assessed on the STL. This assessment shows that the parameters involved in this paper are highly interdependent. Accordingly, the analysis of these parameters is done simultaneously with the aid of three- and four-dimensional plots in order that the optimal value for each parameter can be realized. As seen clearly in the outcomes, the electromagnetic boundary conditions parameters, compared to the other parameters, can much more alter the STL trend, so that a slight change in electric potential results in great change in the STL.

Field concentration and distribution in three-dimensional magneto-electro-elastic plates with open holes

In this work, the field concentration and distribution along the wall of elliptic holes in three-dimensional thick plates of anisotropic magneto-electro-elastic (MEE) materials are systematically analyzed using a three-dimensional weak finite-element formulation implemented in the COMSOL software. The proposed model is validated against existing solutions, and then applied to the analysis and design of multiferroic composites with an open hole, including multicoated circular fibrous MEE composites and MEE sandwich made of piezoelectric (BaTiO3) and magnetostrictive (CoFe2O4) materials. The distribution of field concentration factor, hoop stress, radial stress, and out-of-plane stress along the wall of elliptic holes for MEE plates under typical far-field uniform loads are analyzed, as well as the influence of hole shape, plate thickness and stacking sequence. Under far-field electric or magnetic fields, various unique features are observed which should be very helpful for strength and fatigue designs of MEE materials with notches and holes. An empirical formula is derived to predict accurately the maximum stress concentration factor along the thickness direction of the elliptical hole.

Interaction integral method for thermal fracture of nonhomogeneous magneto-electro-elastic materials

This paper focuses on the thermal fracture performance of magneto-electro-elastic (MEE) materials and proposes a new interaction integral (I-integral) method for extracting the key fracture parameters, including stress intensity factors (SIFs), electric displacement intensity factor (EDIF) and magnetic induction intensity factor (MIIF). After introducing the integrals along the interfaces with mismatched thermal properties, the I-integral is strictly proved to be independent of the integration domain size. This domain-independence is numerically validated for nonhomogeneous and discontinuous MEE materials (relative deviation <1%). Through the combination with the extended finite element method (XFEM), the developed I-integral method is employed to study thermal crack problems of MEE materials. The results show that the I-integral can achieve high numerical accuracy in determining the intensity factors. The thermal boundary condition of crack surface affects the intensity factors significantly. Finally, this paper focuses on the thermal fracture of laminated and fiber reinforced MEE composites. As for MEE composites (BaTiO3/CoFe2O4), the SIFs increase as the volume fraction of PM (CoFe2O4). Reducing the percentage of piezomagnetic phase can enhance the fracture resistance of MEE multiphase composites. At the identical volume fraction of components, the fracture resistance of fiber-reinforced MEE composites is generally better than that of laminated MEE composites and the PE-fiber composite exhibits greater fracture resistance than the PM-fiber composite.

Wave motion of magneto-electro-elastic laminated plates with membrane-type interfacial imperfections

A theoretical analysis for the free vibration of magneto-electro-elastic (MEE) laminated plates with generalized membrane-type interfacial imperfections is proposed. The wave motion characteristics, such as the dispersion curves and mode shapes, are investigated. The pseudo-Stroh formalism and the propagator matrix method are employed to derive the analytical solutions for an orthotropic and multilayered MEE plate with imperfect interfaces. The effect of generalized membrane-type interfacial imperfections on the dispersion curve, mode shape, and magnetoelectric coupling factor for piezoelectric BaTiO 3 and piezomagnetic CoFe 2O4 sandwich plates are studied in detail. Numerical calculations show that the membrane-type interfacial imperfection has a significant effect on the dispersion curve, mode shape, and magnetoelectric coupling factor in layered MEE composites. This exact solution provides important insight to assess the wave characteristics of the MEE laminated composites with membrane-type interfacial imperfections.

The generalized self-consistent micromechanics prediction of the magnetoelectroelastic properties of multi-coated nanocomposites with surface effect

A theoretical study on the effective magnetoelectroelastic (MEE) properties of the multi-coated nanocomposites is reported based on a generalized self-consistent model with surface MEE effect under far-field antiplane shear load, inplane electric load and inplane magnetic load. A rigorous analytical solution of overall generalized MEE stress and strain fields in each component is presented via the complex potential function theory. The closed-form solution of the effective MEE coefficients is obtained by using the average-field theory. Several existing and new results can be regarded as the special cases of the present solution. A comparison with other theoretical results shows good agreement, which illustrates the accuracy of the proposed method. Numerical examples reveal the size dependence of the effective MEE coefficients when the size of the coated fiber is at nanoscale. Several typical MEE composites with the epoxy matrix are investigated, and the influences of the microstructure parameters on the magnetoelectric coupling effect are discussed.

Semi-permeable Yoffe-type interfacial crack analysis in MEE composites based on the strip electro-magnetic polarization saturation model

Fracture analysis of a semi-permeable Yoffe-type interfacial crack propagating subsonically in magneto-electro-elastic (MEE) composites is presented based on the strip electro-magnetic polarization saturation (SEMPS) model. The electro-magnetic fields inside the crack are considered under the semi-permeable boundary condition. Nonlinear effects near the interfacial crack tip are represented by different electro-magnetic saturation zones. Utilizing the extended Stroh's method, we derive the moving dislocation densities as well as intensity factor and energy release rate for Yoffe-type MEE interfacial crack. Numerical results through an iterative approach are presented to show the characteristics of fracture-dominant parameters with respect to propagation velocity and boundary condition category. The fracture-dominant parameters under the semi-permeable boundary condition are lower than those under the impermeable one, which implies that the electro-magnetic fields in the crack gap can retard the propagation of MEE interfacial crack.

Coupled magneto-electro-mechanical lumped parameter model for a novel vibration-based magneto-electro-elastic energy harvesting systems

The objective of this paper is to present a coupled magneto-electro-mechanical (MEM) lumped parameter model for the response of the proposed magneto-electro-elastic (MEE) energy harvesting systems under base excitation. The proposed model can be used to create self-powering systems, which are not limited to a finite battery energy. As a novel approach, the MEE composites are used instead of the conventional piezoelectric materials in order to enhance the harvested electrical power. The considered structure consists of a MEE layer deposited on a layer of non-MEE material, in the framework of unimorph cantilever bars (longitudinal displacement) and beams (transverse displacement). To use the generated electrical potential, two electrodes are connected to the top and bottom surfaces of the MEE layer. Additionally, a stationary external coil is wrapped around the vibrating structure to induce a voltage in the coil by the magnetic field generated in the MEE layer. In order to simplify the design procedure of the proposed energy harvester and obtain closed form solutions, a lumped parameter model is prepared. As a first step in modeling process, the governing constitutive equations, Gauss's and Faraday's laws, are used to derive the coupled MEM differential equations. The derived equations are then solved analytically to obtain the dynamic behavior and the harvested voltages and powers of the proposed energy harvesting systems. Finally, the influences of the parameters that affect the performance of the MEE energy harvesters such as excitation frequency, external resistive loads and number of coil turns are discussed in detail. The results clearly show the benefit of the coil circuit implementation, whereby significant increases in the total useful harvested power as much as 38% and 36% are obtained for the beam and bar systems, respectively.

Effective Material Properties in Multiferroic Composite Materials by a Galerkin BEM

In this paper, the effective material parameters of magnetoelectroelastic composites are computed on the base of homogenization techniques performed on the representative volume element (RVE). For this purpose, the resulting boundary value problem is formulated as boundary integral equations (BIEs). The Galerkin method is applied for spatial discretization. The required average stresses and strains are obtained directly from the primary values of the BIEs and therefore additional numerical differentiations as necessary in other methods are avoided. Numerical examples will be presented and discussed to show the efficiency of the present boundary element method (BEM) and the influences of the voids on the effective material properties.

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.

Viscomagnetoelectroelastic effective properties’ modeling for multi-phase and multi-coated magnetoelectroelastic composites

In this article, the effective properties of new active–passive multifunctional viscomagnetoelectroelastic composite materials are modeled and numerically predicted. The correspondence principle, extended to linear viscomagnetoelectroelasticity, and the Carson transform are coupled to the Mori–Tanaka micromechanical mean field approach. Based on the viscomagnetoelectroelastic convolution integral equations and the interfacial operators, the concentration tensors are derived for multi-phase and multi-coated viscomagnetoelectroelastic composites. The effective properties are derived in the frequency domain and then inverted numerically to the time domain using the inverse transform. The effective properties are thus obtained in both frequency and time domains. The obtained hybrid multifunctional coefficients can be used for their active and passive properties. The resulting visco-magneto-electro-elastic effects can be enhanced by a proper choice of the shape and volume fraction of reinforcements as well as by coating thickness.

Homogenization and multiscale stability analysis in finite magneto-electro-elasticity. Application to soft matter EE, ME and MEE composites

Soft matter electro-elastic (EE), magneto-elastic (ME) and magneto-electro-elastic (MEE) composites exhibit coupled material behavior at large strains. Examples are electro-active polymers and magneto-rheological elastomers, which respond by a deformation to applied electric or magnetic fields, and are used in advanced industrial environments as sensors and actuators. Polymer-based magneto-electric-elastic composites are a new class of tailor-made materials with promising future applications. Here, a magneto-electric coupling effect is achieved as a homogenized macro-response of the composite with electro-active and magneto-active constituents. These soft composite materials show different types of instability phenomena, which even might be exploited for future enhancement of their performance. This covers micro-structural instabilities, such as buckling of micro-fibers or particles, as well as material instabilities in the form of limit-points in the local constitutive response. Here, the homogenization-based scale bridging links long wavelength micro-structural instabilities to material instabilities at the macro-scale. This work outlines a comprehensive framework of an energy-based computational homogenization in electro-magneto-mechanics, which allows a tracking of postcritical solution paths such as those related to pull-in instabilities. It provides variational-based definitions of multiscale structural and material stability phenomena. The starting point is a minimization principle of averaged electro-magneto-elastic energy, that is discretized by using electric and magnetic vector potentials. Next, computationally more effective representations based on scalar potentials are considered by a reformulation of the energy in terms of an averaged enthalpy functional. Structural stability is analyzed based on perturbations of the averaged energy, while local material stability is defined by a generalized quasi-convexity condition. It is shown that the incremental arrays which govern the stability criteria appear within the convenient enthalpy-based representation in a distinct diagonal form, containing mechanical and electro-magnetic partitions. Representative simulations demonstrate a tracking of inhomogeneous EE, ME and MEE composites, showing the development of postcritical zones in the microstructure and a possible unstable homogenized material response.

Variational asymptotic homogenization of magneto-electro-elastic materials with coated fibers

The effective properties as well as local fields of heterogenous magneto-electro-elastic (MEE) materials with coated fibers are investigated by using the variational asymptotic homogenization method. Starting from the total electromagnetic enthalpy of the heterogenous continuum, the multiphysics micromechanics model is formulated as a constrained minimization problem taking advantage of the face that the size of the microstructure is small compared to the macroscopic size of the material. To treat general microstructure of smart material in engineering applications, this new model is implemented using finite element technique. A comparison with the finite element analysis (FEA) results demonstrates the application and accuracy of the proposed model for prediction of multiphysical behavior. The effects of the coating with different thickness and stiffness on the stress concentration factor and effective MEE properties are discussed and a lot of interesting MEE interaction phenomena are revealed, which are useful to estimate and optimize the performance of such MEE composites.

2D fracture analysis of magnetoelectroelastic composites by the SBFEM

This paper extends the scaled boundary finite element method (SBFEM) to 2D fracture analysis of magnetoelectroelastic composites. The generalized extended stress intensity factors, i.e., the stress intensity factors, the electric displacement intensity factor and the magnetic induction intensity factor, for different crack configurations and material combinations are evaluated. The governing equations of the SBFEM for magnetoelectroelastic materials are derived based on the virtual work principle. The generalized extended stress intensity factors are determined from the solution of the singular stress, electric displacement and magnetic induction fields by extending the definition of the generalized stress intensity factors. The electrically and magnetically impermeable and permeable crack face boundary conditions are implemented and discussed. Numerical examples including the cracks in magnetoelectroelastic materials, the interface cracks between magnetoelectroelastic bimaterials and magnetoelectroelastic bimaterial wedge are presented to validate the proposed technique. The accuracy of the proposed technique is verified by comparison with the reference results.

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.

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.

Determination of fracture parameters for interface cracks in transverse isotropic magnetoelectroelastic composites

Abstract To determine fracture parameters of interfacial cracks in transverse isotropic magnetoelectroelastic composites, a displacement extrapolation formula was derived. The matrix-form formula can be applicable for both material components with arbitrary poling directions. The corresponding explicit expression of this formula was obtained for each poling direction normal to the crack plane. This displacement extrapolation formula is only related to the boundary quantities of the extended crack opening displacements across crack faces, which is convenient for numerical applications, especially for BEM. Meantime, an alternative extrapolation formula based on the path-independent J-integral and displacement ratios was presented which may be more adaptable for any domain-based numerical techniques like FEM. A numerical example was presented to show the correctness of these formulae.

A domain-independent interaction integral for magneto-electro-elastic materials

Magneto-electro-elastic (MEE) materials usually consist of piezoelectric (PE) and piezomagnetic (PM) phases. Between different constituent phases, there exist lots of interfaces with discontinuous MEE properties. Complex interface distribution brings a great difficulty to the fracture analysis of MEE materials since the present fracture mechanics methods can hardly solve the fracture parameters efficiently of a crack surrounded by complex interfaces. This paper develops a new domain formulation of the interaction integral for the computation of the fracture parameters including stress intensity factors (SIFs), electric displacement intensity factor (EDIF) and magnetic induction intensity factor (MIIF) for linear MEE materials. The formulation derived here does not involve any derivatives of material properties and moreover, it can be proved that an arbitrary interface in the integral domain does not affect the validity and the value of the interaction integral. Namely, the interaction integral is domain-independent for material interfaces and thus, its application does not require material parameters to be continuous. Due to this advantage, the interaction integral becomes an effective approach for extracting the fracture parameters of MEE materials with complex interfaces. Combined with the extended finite element method (XFEM), the interaction integral is employed to solve several representative problems to verify its accuracy and domain-independence. Good results show the effectiveness of the present method in the fracture analysis of MEE materials with continuous and discontinuous properties. Finally, the particulate MEE composites composed of PE and PM phases are considered and four schemes of different property-homogenization level are proposed for comparing their effectiveness.

Effective property of multiferroic fibrous composites with imperfect interfaces

This paper studies the effective behavior of piezoelectric and piezomagnetic circular fibrous composites with imperfect interfaces under longitudinal shear with in-plane electromagnetic fields. Two kinds of imperfect contact are investigated: mechanically stiff and dielectrically/magnetically highly conducting interfaces, and mechanically compliant and dielectrically/magnetically weakly conducting interfaces. For the former case, the potential field is continuous, while the normal component of the flux undergoes a discontinuity across the interface. For the latter case, the normal component of the flux is continuous, while there is a jump of potential field at such a contact. The classic work of Rayleigh (1892 Phil. Mag. 34 481–502) in a periodic conductive perfect composite is generalized to the current coupled magnetoelectroelastic composites with imperfect interfaces. It is shown that the expression of the effective property has exactly the same form as that in the ideal coupling composite. Finally, this method is used to study BaTiO3–CoFe2O4 composites and provide insights into enhancing the effective magnetoelectric voltage coefficient by properly choosing the interface.