Piezomagnetic Research Articles

Surface effects on wave propagation in piezoelectric–piezomagnetic loosely bonded bilayer system using nonlocal theory of elasticity

This study investigates nonlocal and surface effects on the dispersion behaviors of Shear horizontal (SH) waves in piezoelectric(PE)-piezomagnetic(PM) bilayer systems. The interface between these two layers is imperfectly bonded. The general governing equations are derived from the nonlocal magnetoelectroelastic (MEE) theory by adding an inherent length. The G-M model and generalized Young-Laplace equations have been used to incorporate surface effects into the boundary conditions of the bilayer systems. The closed-form dispersion equation is obtained analytically for electrically open and magnetically short conditions. Numerical solutions are utilized to investigate the effects of nonlocal scale parameters and surface parameters on SH surface wave propagation. Contrary to the results of classical theory, the coupling effects of nonlocal small-scale and surface piezoelectricity are more significant than individual effects. Also, it has been observed that the imperfectness parameter across the interface and the thickness ratio of the bilayer significantly affect the phase velocity. Moreover, 2D and 3D plots of the mode shapes of field variables for the propagation of SH waves are presented graphically. These results are validated by conducting analyses excluding nonlocal effects. This allows us to isolate the specific impact of surface effects in the piezoelectric–piezomagnetic bilayer system, drawing connections to existing results and enhancing the robustness of our findings. This study provides valuable insights into complex wave dynamics, helping to optimize the performance and functionality of such smart composites in various engineering applications.

Generalized dynamic domain-independent interaction integral in the transient fracture investigation of magneto-electro-elastic composites

The domain-independent interaction integral (DII-integral) is a powerful tool for dealing with crack issues of nonhomogeneous materials, due to its feature of being independent of the scale of integration domain, regardless of the nonhomogeneous properties and complex material interfaces. As an important part of the interaction integral (I-integral), the auxiliary field conditions required to establish the dynamic DII-integral have not been clearly clarified so far. For the first time, this work rigorously proves and gives the requirements of the auxiliary fields for building the dynamic DII-integral in anisotropic linear elastic, piezoelectric (PE), piezomagnetic (PM) and MEE materials, respectively, and a theoretical framework is derived for designing the dynamic DII-integral for new functional materials in the future. This proof guarantees the successful utilization of DII-integral to investigate the transient response in cracked composites without employing homogenized material parameters, while considering internal microstructure and complex interfaces. Using the extended finite element method (XFEM) as a pre-processing technique, the accuracy of the DII-integral is verified by comparing available references. Then, the domain-independence is confirmed with multiple integration domains, especially for those containing interfaces. Finally, the arrangements of PE/PM layers, locations and distributions of PE/PM particles affecting dynamic IFs are systematically investigated. Simultaneously, illustrations of elastic wave in cracked MEE composites are depicted to better understand the dynamic fracture response.

Circumferential SH wave in piezo-reinforced composite structure with imperfect interface bonding

The present study fundamentally focuses on analyzing the limitations and transference of circumferential shear horizontal (CSH) waves in a four-layered compounded cylinder. The geometrical structure consists of cylinders of infinite length composed of self-reinforced (SR), fibre-reinforced (FR), piezo-magnetic (PM), and piezo-electric(PE) materials. In order to make the structure sensitive to the application pertaining to sensors and actuators, the PM and PE cylinders have been categorically placed in the outer part of the geometry. Whereas in order to provide stiffness and stability to the structure, the inner part consists of SR and FR materials. The common boundary between each of the cylinders has been essentially considered as imperfectly bounded. At the interface of PE and PM media, mechanical, electrical, magnetic, and inter-coupled types of imperfections have been exhibited. The closed-form of dispersion relation has been deduced for two contrast cases i.e. electrically open magnetically short (EOMS) and electrically short and magnetically open (ESMO) circuit conditions. Dispersion curves have been plotted to illustrate the salient features of parameters like normalized imperfect interface parameters, initial stresses, and radii of the concentric cylinders. The comparative effect of each one of these parameters on the phase velocity of the wave has been enlisted and marked individually. Every graph has been presented with two successive modes for a comprehensive understanding. This theoretical study may be implemented to improvise the performance of surface acoustic wave (SAW) sensors, actuators, and Piezo-cables in the form of Piezo-polymer sensors consisting of piezo-electric quartz, piezo-composite concentric cylinders, and coaxial piezo-cables.

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.

Bending Analysis of Multiferroic Semiconductor Composite Beam towards Smart Cement-Based Materials

A beam-like structure of antisymmetric laminated multiferroic piezoelectric semiconductor (LMPS), which consists of two piezomagnetic (PM) and two piezoelectric semiconductor (PS) layers is proposed. The structure could be in pure flexure deformation under an applied magnetic field. Through this deformation mode and the induced polarization field through the magneto-electro-semiconductive (MES) coupling mechanism, the semiconducting properties of PS layers can be manipulated by the applied magnetic field. In order to better understand and quantitatively describe this deformation mode, the one-dimensional governing equations for the LMPS beam are developed based on the three-dimensional theory. The analytical solutions are then presented for the LMPS cantilever beam with open-circuit conditions. The multi-field coupling responses of the LMPS cantilever beam under the longitudinal magnetic field are investigated. Numerical results show that the amplitude of each physical quantity is proportional to the applied magnetic field, and the thickness ratio of the PS phase plays a significant role in the MES coupling behaviors of the LMPS beam. The proposed structure can be integrated into cement structures but also fabricated cement-based multiferroic PS composite materials and structures. It provides an important material and structure basis for developing structural health monitoring systems in the fields of civil and transportation infrastructures.

On dynamic modeling of piezomagnetic/flexomagnetic microstructures based on Lord–Shulman thermoelastic model

We study a time-dependent thermoelastic coupling within free vibrations of piezomagnetic (PM) microbeams considering the flexomagnetic (FM) phenomenon. The flexomagneticity relates to a magnetic field with a gradient of strains. Here, we use the generalized thermoelasticity theory of Lord–Shulman to analyze the interaction between elastic deformation and thermal conductivity. The uniform magnetic field is permeated in line with the transverse axis. Using the strain gradient approach, the beam yields microstructural properties. The analytical solving process has been gotten via applying sine Fourier technique on displacements. Graphical illustrations are assigned to shape numerical examples concerning variations in essential physical quantities. It was observed that the flexomagnetic effect could be extraordinary if the thermal conductivity of the material is higher or the thermal relaxation time of the heat source is lesser. This theoretical study will provide the way of starting studies on magneto-thermoelastic small-scale piezo-flexomagnetic structures based on the heat conduction models.

Modeling of the Liouville–Green method to approximate the mechanical waves in functionally graded and piezo material with a comparative study

The present research article studies and compares the surface waves transmission through the functionally graded piezoelectric material (FGPM) club between the piezomagnetic (PM) layer -and half-space, and for a comparative study, lower half-space is assumed to be piezoelectric material. The transmission of mechanical waves in a smart structure is analyzed by following the elastic wave theory of magneto-electro-elasticity. The Liouville-Green (LG) approximation technique is used to solve the differential equation in the FGPM stratum, where exponential variation is assumed in material gradients. It is noticed that the material gradients depend considerably on the angular frequency, which should be a crucial factor in regulating the dispersion characteristics of functionally graded materials (FGM) waveguides. In closed determinant form, the dispersion relation has been obtained for FGPM plate for electrically open and short cases. The profound effect of parameters, such as material gradient, a width of the layer on phase velocity, coupled electromechanical factor, and angular velocity, is observed and delineated graphically. Different parametric plots are sub-plotted into a single figure to increase the readability of the graphs.

Modeling of an energy harvester with porous piezoelectric/piezomagnetic nanocomposite structure

Micro-energy harvesters are attracting more and more attention due to the demand of the miniaturization and the self-power for the electrical devices. A three-layered porous piezoelectric (PE)/piezomagnetic (PM) energy harvester at the nanoscale is modeled in this paper. The layered PE/PM structure works in the magnetic field; the electrical power can be obtained from the PE layer due to the magnetostriction of the PM layers. Based on the surface elasticity and Boit’s porous theory, the governing equations and the analytical expressions of the harvester with the thickness-shear mode are derived. The numerical analysis indicates that the electrical energy capture capability of the porous PE/PM energy harvester is much superior to its nonporous alternative. Then, the influences of the porous properties, the surface effects, and the constitution of the PE/PM materials on the energy capture performance are discussed. The results indicate that the nano PE/PM energy harvester with pores can be controlled and optimized by improving the porous, surface, and geometrical parameters.

Propagation of conductive crack along interface of piezoelectric/piezomagnetic bimaterials

This paper investigates the fracture characteristics of a Yoffe conductive crack moving along the interface of piezoelectric (PE)/piezomagnetic (PM) bimaterials. By assuming that the tangential electric- and magnetic-fields along the crack surface are zero and that the speed of the moving crack is lower than the minimum shear wave speed of the bimaterial system, the considered problem can be transformed into a Riemann–Hilbert boundary value problem of vector form. Then, the singularity parameters are exactly solved for different speed regions. In contrast to the anti-plane moving crack model including impermeable and permeable crack-face assumptions along the interface of magnetoelectroelastic (MEE) bimaterials studied before, which shows inverse square-root singularity, three novel kinds of singularities are found as the speed of the moving crack is varied for the present PE/PM interface model, which can be defined as δ1,2 = − 1/2 ± ie (Case 1), δ1,2 = − 1 ± ie (Case 2) and δ1,2 = − 1/2 ± κ (Case 3), and the third parameter δ3 = − 1/2 always holds true for all three cases. Two bimaterial combinations, i.e., BaTiO3/CoFe2O4 and BaTiO3/Terfenol-D, are numerically examined. Different from the piezoelectric case, Case 3 does not appear for BaTiO3/CoFe2O4 bimaterial combination. Above all, the singularity parameters significantly depend on the speed of the moving crack and the material properties of bimaterial systems.

Frequency characteristics of a multiferroic Piezoelectric/LEMV/CFRP/Piezomagnetic composite hollow cylinder under the influence of rotation and hydrostatic stress

An analytical model is consider to scrutinize axisymmetric wave propagation in multiferroic hollow cylinder with rotating and initial stressed forces, where a piezomagnetic (PM) material layer is bonded to a piezoelectric (PE) cylinder together by Linear elastic materials with voids. Both distinct material combos are taken into account. Three displacement potential functions are introduced to uncouple the equations of motion, electric and magnetic induction. The numerical calculations are carried out for the non-dimensional frequency by fixing wave number and thickness. The arrived outputs are plotted as the dispersion curves for different layers. The results obtained in this paper can offer significance to the application of PE/PM composite hollow cylinder via LEMV and CFRP layers for the acoustic wave and microwave technologies.

Analysis of SH wave in hollow piezo-composite cylinder with coupled imperfect interface condition

Present study primarily focuses on interpreting the propagation pattern of Shear horizontal (SH) wave in a piezo-composite layered cylinder. The structure consists of three concentric cylinders composed of hollow fiber-reinforced (FR) cylinder enclosed within piezomagnetic (PM) cylinder along the curved surface area which is similarly superimposed by a piezoelectric (PE) cylinder. The overall system is believed to be pre-stressed in a circumferential direction. The common boundary between each of the cylinder is demonstrated as imperfectly bonded. At the interface of PM and PE media, mechanical, electrical, magnetic and inter-coupled types of imperfections are assumed. Dispersion relations have been obtained for both the electrically open magnetically short (EOMS) and electrically short magnetically open (ESMO) circuit condition. Dispersion curves have been plotted to unravel the peculiarities of parameters like the radius of the hollow cylinder, thickness of FR and PM cylinder, thickness ratio of PM and PE cylinder, initial stress parameters, helical angle of the reinforcement. The influence of different interface parameters on the phase velocity of the wave has been studied and marked distinctly. For a detailed study, two successive modes have been plotted. Present study may help in improving the performance of piezo-composite cylindrical surface acoustic wave (SAW) sensors.

Effects of Magnetic Fields on PN Junctions in Piezomagnetic–Piezoelectric Semiconductor Composite Fibers

We study the electromechanical and electrical behaviors of a PN junction in a multiferroic composite fiber, consisting of a piezoelectric semiconductor (PS) layer between two piezomagnetic (PM) layers, under a transverse magnetic field. Based on the derived one-dimensional model for multiferroic composite semiconductor structures, we obtain the linear analytical solution for the built-in potential and electric field in the junction when there is no applied voltage between the two ends of the fiber. When a bias voltage is applied over the two ends of the fiber, a nonlinear numerical analysis is performed for the current–voltage relation. Both a homogeneous junction with a uniform PS layer and a heterogeneous junction with two different PSs on different sides of the junctions are studied. It is found that overall the homogeneous junction is essentially unaffected by the magnetic field, and the heterojunction is sensitive to the magnetic field with potential applications in piezotronics.

Dynamic manipulation of piezotronic behaviors of composite multiferroic semiconductors through time-dependent magnetic field

A dynamic non-contact approach to tuning the semiconducting (SM) properties of multiferroic composite semiconductor (MCS) fibers by applying a time-dependent magnetic field is proposed and theoretically demonstrated in this paper. The considered fiber is symmetric with respect to its geometrical middle plane and made from two outer piezomagnetic (PM) layers, two piezoelectric (PE) layers, and a SM core. Through the interface strain or deformation transfer, the MCS fiber exhibits not only the conventional magnetoelectric (ME) coupling effect but also the comprehensive magneto-electro-semiconductive (MES) coupling effect. Based on a one-dimensional model for the MCS fibers, we present the analytical solutions for the physical fields of the MCS fiber with a pure longitudinal deformation under a time-dependent magnetic field. The electrons redistribute themselves in the MCS fiber under the driving of the induced piezoelectric field due to the MES coupling effect. Near the natural frequencies, the magnetic field has a remarkable tuning effect. The ME and MES coefficients achieve their local peak values at the natural frequencies. There is an optimal range for the volume fraction of the PM or PE layer for the MES coupling effects. We can manipulate the electrons to assemble in multiple local regions in the MCS fiber by setting the exciting frequency to a specific higher natural frequency. This provides a new way to explore multi-tunnel electronic devices through the dynamic contactless magnetic control approach.

Microstructural and viscous liquid loading effects on the propagation of love waves in a piezomagnetic layered structure

The gist of the present study is to unfold the veiled characteristics of the Love-type wave propagation through a piezomagnetic (PM) material overlying a semi-infinite couple stress substrate, under the viscous liquid (Newtonian) loading. Dispersion equations are obtained for magnetically open and short conditions. Possible particular cases are discussed. Dispersion equation is reduced to the classical Love wave equation for validation. Graphical representations reveal that the phase velocity of Love-type wave is remarkably affected by viscous liquid loading, microstructural parameter and PM parameters. This study has meaningful practical applications toward the fabrication and enhancement of PM sensors and transducers.

Effects of electric/magnetic impact on the transient fracture of interface crack in piezoelectric-piezomagnetic sandwich structure: anti-plane case

Due to the incompatibility of the interlaminar deformations, the interface debonding or cracking usually happens in a layered magnetoelectric (ME) structure under an applied load. In this paper, the transient responses of the anti-plane interface cracks in piezoelectric (PE)-piezomagnetic (PM) sandwich structures are studied by the standard methods of the integral transform and singular integral equation. Discussion on the numerical examples indicates that the PE-PM-PE structure under electric impact is more likely to fracture than the PM-PE-PM structure under a magnetic impact. The dynamic stress intensity factors (DSIFs) are more sensitive to the variation of the active layer thickness. The effects of the material constants on the DSIFs are dependent on the roles played by PE and PM media during the deformation process.

Magnetically Controllable Piezotronic Responses in a Composite Semiconductor Fiber with Multiferroic Coupling Effects

Herein, a multiferroic composite semiconductor (MCS) fiber, in which the carriers transport behaviors can be effectively controlled by applying a magnetic field, is proposed. The fiber consists of two outer piezomagnetic (PM) layers, two piezoelectric (PE) layers, and a semiconducting core, and hence exhibits the comprehensive magneto–electro–semiconductive (MES) coupling effects. Based on the basic equations of multiferroic composites and the drift‐diffusion model of currents in semiconductor physics, a 1D theoretical model for the laminated MCS fiber with the MES coupling effects is presented, and an analysis of the extensional deformation induced by a magnetic field is conducted. The electrons move toward one end of the fiber under the PE field resulting from the MES coupling mechanism. As a result, this leads to the redistribution of electrons in the fiber. Theoretical results show that the magnetic field as well as the initial concentration of carriers and the volume fraction of the PM or PE layer have obvious effects on the carriers transport properties and mechanical behaviors of the MCS fiber. Compared with the mechanical tuning method of piezotronics, such a magnetic field based tuning method via the MES coupling effects has some advantages because it is remote and contactless.

Interfacial imperfection study in pres-stressed rotating multiferroic cylindrical tube with wave vibration analytical approach

In the present paper, two distinct multiferroic composites are taken into account, i.e., PE (piezoelectric)/PM (piezomagnetic). An analytical technique is applied to study the shear horizontal (SH) wave propagation in a layered pre-stressed rotating cylindrical tube structure consisting of a PE material layer which is wrapped on PM material having an imperfect interface. It is assumed that consider interface is mechanical, electrically and magnetically damaged. Dispersion relations are obtained for electrical-magnetic open/short boundary conditions. Distinct graphs are drawn (numerically) to exhibit the influence of parameters like rotation, initial stress and imperfect parameters (mechanical, electrical and magnetic) on phase velocity. Parametric results on the phase velocities yield a significant conclusion of which some are: (a) Performance has Piezo-composites have a great impact on phase velocity. (b) The mechanical imperfection affects the more on phase velocity along with the combination of thickness ratio and wave number in respect to electrical -magneto imperfection (c) The PE/PM stiffening can monotonically increase the speed of phase.

Magnetoelectric Properties of Piezoelectric–Piezomagnetic Composites with Elliptical Nanofibers

Based on the surface/interface theory, the effective magnetoelectric (ME) properties of piezoelectric (PE)–piezomagnetic (PM) composites with elliptical nanofibers are investigated analytically. Using the complex function theory, conformal mapping and the Mori–Tanaka mean-field method, the solutions of magneto-electro-elastic (MEE) fields are obtained, which satisfy both the interface and the single-valued conditions. The closed-form expression of the ME coefficient of the composites shows that the effect of ME coefficient is related to the interface parameters, elliptical aspect ratio, material properties of both fiber and matrix and the fiber volume fraction. Numerical calculation shows that by properly selecting some of these parameters, the effective ME coefficient could be substantially enhanced.

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.

An asymptotic approximation of Love wave frequency in a piezo-composite structure: WKB approach

This paper proposes an asymptotic approximation solution for the propagation of Love-type surface waves in a smart composite structure involving functionally graded piezoelectric material (FGPM). The considered structure is a three-layered system in which the uppermost piezoelectric (PE) layer is accomplished by an FGPM layer and piezomagnetic (PM) substrate. The distribution of material coefficients in FGPM layer is considered in two different manners: exponential and linear, along with the x-axis. The Wentzel-Kramers-Brillouin (WKB) asymptotic method is adopted to solve the differential equations. Frequency equations are derived for electrically and magnetically open and short circuit cases. Variation of phase velocity, group velocity and electromechanical coupling factor versus the wave number has been distinctly marked. Influence of different parameters (like layer width, material gradient) on phase velocity curve of different modes has been shown graphically. Comparison between phase velocity and group velocity has been also demonstrated through graphs. This study finds its application toward designing and optimization of Seismic Acoustic Wave (SAW) devices, ultrasonic transducer and Love wave sensors.