Magnetoelectroelastic Materials Research Articles

Mechanical-electric-magnetic-thermal coupled enriched finite element method for magneto-electro-elastic structures

Abstract Magneto-electro-elastic (MEE) materials possess the ability to convert mechanical, electrical, and magnetic energies, playing a critical role in smart devices. To improve the accuracy and efficiency of solving the mechanical properties of MEE structures in mechanical-electrical-magnetic-thermal (MEMT) environments, an MEMT coupled multiphysics enriched finite element method (MP-EFEM) is proposed. Based on the fundamental equations and boundary conditions of MEE materials, the interpolation coverage function is introduced into the MEMT coupled finite element method (FEM) to construct higher-order approximate interpolation displacement shape functions, electric potential shape functions, and magnetic potential shape functions. Combined with the variational principle, MP-EFEM is proposed, and the governing equations of MP-EFEM are derived. Numerical examples validate the accuracy and high efficiency of MP-EFEM in solving the mechanical properties of MEE structures in MEMT environments. When compared to the MEMT coupled FEM (MEMT-FEM), the results show that this method offers higher accuracy and efficiency. Therefore, MP-EFEM can effectively analyze the mechanical properties of MEE structures under multiphysics coupling, providing a new method for the design and development of smart devices.

Fracture Mechanics of Magnetoelectroelastic Materials and Structures: State of the Art and Prospects

Fracture Mechanics of Magnetoelectroelastic Materials and Structures: State of the Art and Prospects

Frictional contact analysis between two-dimensional deformable anisotropic magneto-electro-elastic bodies via a semi-analytical method

In this paper, we utilize the surface Green's function of a magneto-electro-elastic (MEE) half-plane as a general analytical kernel to develop a semi-analytical method (SAM). This SAM is designed to solve the two-dimensional contact problems of two dissimilar deformable anisotropic MEE bodies. Using the surface Green's function, the associated influence matrices in SAM can be obtained in a closed mathematical form and then computed analytically, offering significant benefits in terms of computational efficiency and accuracy. This method can be applied to general contact problems where the contact surface is frictional sliding and subjected to four different electric and magnetic conditions. By assuming the elastic and piezoelectric materials as uncoupled MEE materials, the method can also be applied to contact problems in which anisotropic elastic and piezoelectric materials are involved. To demonstrate the accuracy and applicability of the proposed SAM, four different numerical examples are provided, and their results are compared with those obtained by using other approaches, such as analytical solutions and the previous SAM in the literature. Through the numerical results, parametric studies are also performed, allowing us to explore the influences of material properties, loadings, frictional coefficient, and contact surface profile on mechanical/electrical/magnetic contact behaviors.

Shear horizontal wave dispersion in two phase magneto-electro-elastic material loaded with viscoelastic fluid layer

In the present work, an exact analytical approach has been used to study the dispersive behavior of the shear horizontal (SH) wave in magneto-electro-elastic (MEE) material loaded with a viscoelastic fluid. Complex dispersion equations are derived in the cases of electric short magnetic short (ESMS), electric short magnetic open (ESMO), electric open magnetic short (EOMS), and electric open magnetic open (EOMO) boundary conditions by solving the equilibrium equations of MEE material and the Stokes equation of viscoelastic fluid. To validate the present outcomes, the MEE material is changed into piezoelectric and piezomagnetic materials by taking some theoretical assumptions and the outcomes are matched with preexisting results. Effect of volume fraction, wave frequency, substrate thickness and thickness of the fluid layer on phase velocity and attenuation of SH wave have studied. This study may find its applications in better understanding of the surface acoustic wave devices incorporated with viscoelastic fluid layer.

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.

A semi-analytical approach for two-dimensional frictional contact of anisotropic magneto-electro-elastic solids

In this work, we present a semi-analytical modeling approach for solving the frictional contact of two-dimensional anisotropic magneto-electro-elastic (MEE) solids. The method is established in a broad framework in which the contact body is made of generally anisotropic MEE materials, the punch head can be arbitrary, and the punch can be subjected to generalized loading conditions including mechanical forces and electric and magnetic charges. An analytical solution of generalized distributed load along the half-plane surface is derived and utilized to formulate the semi-analytical equations governing the relation between the generalized displacements and tractions. Based upon the semi-analytical equations, the semi-analytical model in which the influence matrices can be calculated explicitly and its effectiveness is established. An iterative procedure is then used for determining the contact region, contact status, generalized surface deformation and the distribution of contact tractions, as well as the punch’s indentation depth and electric and magnetic potentials. The present approach is verified by comparing its numerical results with those obtained by the existing analytical solutions and boundary element method. The influences of different factors, such as punch profile, mechanical load, electric and magnetic charges, friction coefficient and material properties, are also analyzed. The capability of this method to handle complicated geometry, such as rough surfaces, is finally discussed, showing the potential performance of the developed method for practical engineering applications.

Nonlinear low-velocity impact of magneto-electro-elastic plates with initial geometric imperfection

Magneto-electro-elastic (MEE) materials are widely used in the aviation and spaceflight area, attributed to magneto-electric coupling effect of MEE materials which can achieve mutual energy conversion in complex physical fields. This article takes the imperfect MEE plate as the research object to explore the nonlinear low-velocity behaviors, and the influence of multiple physical fields such as electric, magnetic and temperature fields are taken into account. Based on Maxwell's equations and first-order shear deformation theory (FSDT), the constitutive equation of MEE plate is obtained, and the nonlinear motion equations are derived using the Euler-Lagrange principle. Subsequently, with the aid of the Galerkin method, the ordinary differential equations are obtained by discretizing the partial differential equations. Then the low-velocity impact problem is solved using the Runge-Kutta method. Finally, the impacts of unknown factors upon the dynamic behaviors of the MEE plate are illustrated particularly. It can be found that the magnetic and electric potentials have opposite effects on the impact displacement of the plate, and the MEE plate with the lowest volume fraction of BaTiO3 has the smallest center displacement and the shortest contact time, but has the maximum contact force.

Investigation of Properties and Application of Magneto Electro Elastic Materials and Analysis of Piezoelectric Smart Shells

Investigation of Properties and Application of Magneto Electro Elastic Materials and Analysis of Piezoelectric Smart Shells

High frequency multi-field continualization scheme for layered magneto-electro-elastic materials

Magneto-electro-elastic (MEE) heterogeneous materials with periodic microstructure are investigated, with special focus on the particular case of a layered MEE material. By exploiting the transfer matrix method in combination with the Floquet–Bloch boundary conditions, the frequency dispersion spectrum can be derived by solving an eigenproblem, involving a 12 × 12 transfer matrix with palindromic characteristic polynomial. In particular, by assuming the cubic symmetry of layers, the problems involving longitudinal and transverse elastic waves are uncoupled. This circumstance has the advantage of simplifying the treatment and the size of the subproblems to be solved, corresponding to a 4 × 4 transfer matrix for the longitudinal case, and a 8 × 8 transfer matrix of the transverse problem, both characterized by palindromic characteristic polynomials. Afterward, a dynamic multi-field continualization approach is proposed to investigate wave propagation in MEE layered periodic material by matching the Z-transform of the vector collecting the nodal fields to the two-sided Laplace transform of the same vector at the macroscale. The continualization technique allows identifying multi-field integral-type non-local continua as well as multi-field generalized gradient-type (higher-order) non-local continua. Finally, to verify the accuracy of the proposed approach, the dispersion curves derived from the continualization technique are compared with the curves provided by the Floquet–Bloch theory.

A size-dependent meshfree approach for magneto-electro-elastic functionally graded nanoplates based on nonlocal strain gradient theory

In this paper, we introduce a novel size-dependent meshfree approach for analyzing free vibrations of magneto-electro-elastic (MEE) functionally graded (FG) nanoplates. This approach combines the nonlocal strain gradient theory (NSGT), the higher-order shear deformation theory (HSDT), and meshfree method for the first time. MEE materials are essentially mixed by the barium titanate and cobalt ferrite which are definitely coupled by both piezoelectric and piezomagnetic effects. Our approach captures both the nonlocal and strain gradient effects in nanoplates, which result in the reduced stiffness and increased stiffness, respectively, by adjusting two parameters. The kind of effective material properties of MEE-FG nanoplates are expressed using a power-law scheme. The coupled governing equations, based on the principle of extended virtual displacement, are solved using the moving Kriging (MK) meshfree method. Numerical examples are given to investigate the effect of geometrical parameters, initial electric voltage, power index, initial magnetic potential, strain gradient parameter, and nonlocal parameter on the natural frequency of MEE-FG nanoplates.

Anti-plane fracture behavior of n nano-cracks emanating from a magnetoelectrically semi-permeable regular n-polygon nano-hole in magnetoelectroelastic materials

Based on Gurtin–Murdoch surface/interface model and complex potential theory, by constructing a new conformal mapping function, the fracture behavior on n nano-cracks emanating from a n-polygon nano-hole under far-field anti-plane mechanical load, inplane electrical load and magnetic load is studied. The analytical solutions of stress intensity factor, electric displacement intensity factor and magnetic induction intensity factor at the crack tip are given under the boundary conditions of magnetoelectrically semi-permeable. In addition, numerical examples show that when considering the surface effect, the stress field intensity factor, electric displacement intensity factor and magnetic induction intensity factor have obvious size-dependence. The results of this paper show that when the defect size increases to a certain extent, the influence of the surface effect begins to decrease, and finally tends to the results of classical elastic theory.

Fractional‐order sliding mode control for a novel magneto‐electro‐elastic microtube robot

AbstractIn this paper, a tracking controller based on a non‐integer sliding surface is proposed for a magneto‐electro‐elastic (MEE) fluid‐conveying microtube robot. The smart/adaptive MEE material enables us to control the robot with no need for external sensors and actuators. The micro‐robot lateral motion is modeled by Euler–Bernoulli beam equations. The governing equation of the robot is derived using the constitutive equations of MEE materials and Maxwell's principle followed by Hamilton's variational method. Based on the extracted dynamic model, a novel non‐integer order sliding mode controller is introduced to suppress the microtube vibration and to provide robust path following for the robot tip. This control approach is compatible with the parameter‐varying nature of the robot dynamics. Theoretical analyses, based on Lyapunov theory, are also conducted to verify the stability of the closed‐loop system. Comparative simulations are finally performed to show the efficiency of the proposed system in comparison with the conventional micro tubes made of smart materials and with an integer order sliding mode controller (SMC). The results demonstrate that the proposed robot properly meets the performance requirements in terms of vibration suppression and trajectory tracking, even in the presence of disturbances.

Improving soundproof characteristics of an FG-CNT–reinforced composite structure by adding a coating magneto-electro-elastic layer

This paper deals with sound propagation through a two-layer sandwich plate in which the carbon nanotubes with functionally graded (FG) distribution are coated by a thin layer of magneto-electro-elastic (MEE) materials. Firstly, the derivation of governing equations for each layer of the sandwich plate is followed according to the three-dimensional elasticity theory. In this regard, the relationship between the equations of motion for the layer, made of MEE materials, and the electric and magnetic potentials is established. Additionally, the effective properties of the nanocomposite layer are extracted by employing the rule of mixture. Afterward, the solution is finalized by employing the approximate layer and transfer matrix technique, in accordance with the definition of state space and sound transmission loss. In the next stage, to confirm the reliability of the derived relationships, three configurations of the panel are examined. Firstly, according to the obtained results, it is evident that adding a thin coating layer of triple-phase MEE materials effectively improves the sound insulation in the sandwich plate. Secondly, considering the electromagnetic boundary conditions can lead to a noticeable enhancement in the STL in the stiffness region. Moreover, the magnetic potential, compared to the electric one, is seen to be more effective on the acoustic radiation of the sandwich panel.

The magneto-electro-elastic coupling isogeometric analysis method for the static and dynamic analysis of magneto-electro-elastic structures under thermal loading

Many engineering problems show some degree of coupling or interaction between different physics fields. It is necessary to improve the calculation efficiency and accuracy for magneto-electro-elastic (MEE) materials in multiphysics fields. The MEE coupling isogeometric analysis method (MIGAM) is presented to explore the MEE structures and to produce superior calculations. With the usage of non-uniform rational B-spine (NURBS) functions in not only geometric models for straightforward construction but also analytical models of multiphysics coupling effects, the mesh density effect is ignored and seamless integration is achieved. The basic properties of MEE models are briefly constructed employing NURBS functions and the multiphysics coupling effect of the MEE material. Furthermore, the static and dynamic responses of the MEE structures under thermal and mechanical loading are investigated. The MIGAM achieves sufficient accuracy by applying fewer control points, thus showing higher efficiency than the finite element method (FEM) in exploring coupling multiphysics problems.

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.

A Moving Kriging Meshfree Method for The Vibration Analysis of Homogenous Magneto-electro-elastic Plates

The free vibration analysis of the homogenous magneto-electro-elastic (MEE) plate based on a refined first-order shear deformation theory and moving Kriging meshfree method is presented in this paper. The refined first-order shear deformation theory (RFSDT) only includes four variables and reduces one variable when comparing to original first-order shear deformation theory. The MEE materials which are coupled between piezoelectric and piezomagnetic effects, are combined of BaTiO3 and CoFe2O4 materials. The magnetic and electric potentials satisfying to the Maxwell equations are assumed to be a combination of cosine and linear variations along the plate thickness. The coupled governing equations of motion of the MEE plates are obtained by using the principle of extended virtual displacement. These equations are solved to achieve the natural frequency of MEE plates by utilizing the moving Kriging meshfree method. Several numerical examples are examined to evaluate the influence of the geometrical parameter on the natural frequency of the MEE plates.This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium provided the original work is properly cited.

3D frictional contact of graded magneto-electro-elastic film-substrate system under electromagnetic fields

The 3D frictional contact model of graded magneto-electro-elastic (MEE) film-substrate system under electromagnetic fields is presented. The semi-analytical method (SAM) is used to solve this multi-physical contact problem. Firstly, the frequency response functions (FRFs) for every layer of MEE material subjected to unit mechanical, electric and magnetic loads are derived. Conjugate gradient method (CGM) is then employed to obtain contact responses with Discrete convolution-fast Fourier transformation (DC-FFT) speeding related calculations. Finally, multilayered model is used to approximate graded film with two types of grads, exponentially varying grad (EVG) and volume-fraction varying grad (FVG), the effects of the type and thickness of graded film and the friction coefficient are investigated. The results show that EVG film with gradient index less than one or FVG film with smaller volume fraction of piezoelectric phase at the surface are preferred for the MEE film-substrate systems.

A Domain-Independent Interaction Integral for Dynamic Fracture in Nonhomogeneous Magneto-Electro-Elastic Materials

In practice, magneto-electro-elastic (MEE) equipment are inevitably subjected to impact loading during service, resulting in fracture failure of the devices. This paper proposes a dynamic domain-independence interaction integral (DII-integral) to solve the dynamic intensity factors (IFs) at the crack tip of MEE materials. Here, this is a new expression of the interaction integral (I-integral) for dynamic crack study of nonhomogeneous MEE media, and we further extend it to MEE materials containing complex interfaces. Domain-independent property of the I-integral is theoretically demonstrated and excellent numerical results (relative deviation<1%) obtained from the various integration domains again verify the domain-independence for nonhomogeneous and multi-interface material properties without considering the material continuity requirements. Through the combination of the DII-integral and extended finite element method (XFEM), a good agreement is observed by comparing with the published data subjected to different MEE impact loadings. Typical examples reveal that the magnitude of dynamic mode-I stress intensity factor (SIF), dynamic electric displacement intensity factor (EDIF) and dynamic magnetic induction intensity factor (MIIF) decrease with the increase of the poling angle of the MEE material, while the dynamic mode-II SIF shows the opposite change. The peaks of dynamic EDIF and MIIF are more sensitive to the distance between the parallel cracks than the SIF, and all IFs are smaller than single crack due to the shielding effect. Finally, the significant difference on the dynamic IFs is observed with various material discontinuities.

Fracture analysis of circular hole edge arbitrary position crack with surface effects in magnetoelectroelastic materials

The mechanical properties of magnetoelectroelastic (MEE) materials are brittle, which is easy to produce nano-defects (hole or crack). The micro-fields of nanoscale cracks and holes are size dependent significantly. Nanoscale cracks and holes interact with each other, and the interference effect is very obvious. In this paper, the Model III fracture behavior of nanoscale circular hole edge arbitrary position radial crack is studied under anti-plane mechanical load, in-plane electric displacement load and in-plane magnetic induction load. Based on the surface elasticity theory, the conformal mapping technique and the MEE elasticity theory, the MEE fields expressions of the nano-hole and nano-crack are obtained, and the analytical solution of generalized intensity factors (stress intensity factor, electric displacement intensity factor and magnetic induction intensity factor) at crack tip is given. The comparison between the present results and the existing research shows the correctness of the present method in this paper. The influences of the microstructure and coupling loads on the generalized intensity factors are discussed.

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.