Magnetoelectroelastic Properties Research Articles

Thermal and mechanical vibration response of auxetic core sandwich smart nanoplate

This study explores a new nanoplate design’s thermal and mechanical properties, including an auxetic core with a negative Poisson ratio. The core is between face plates made of Barium‐Cobalt, which possess magneto‐electroelastic properties. The analysis centers on the parameters θ, β 1 , and β 2 to clarify their influence on the nanoplate’s performance. The evaluations of the nanoplate’s thermal, electrical, and magnetic properties showcase its remarkable versatility and sensitivity. Incorporating magneto‐electroelastic face plates improves the multifunctionality of the nanoplate, making it a highly promising option for use in smart technologies. The findings offer valuable insights into the distinctive features of auxetic core structures, significantly enhancing the comprehension of these materials. This research emphasizes the potential for creating groundbreaking applications in fields like aerospace engineering and advanced electronics, where versatile and adaptable materials play a vital role. This study contributes to the broader knowledge of auxetic materials and their practical implementation in cutting‐edge technological solutions by exploring the interplay between thermal, mechanical, and magneto‐electroelastic properties.This article is protected by copyright. All rights reserved.

Interaction integral method for crack-tip intensity factor evaluations of magneto-electro-elastic materials with residual strain

Magneto-electro-elastic (MEE) materials generally consist of piezoelectric and piezomagnetic constituent phases so that the residual strain often occurs during the manufacturing process. The distributed residual strain and complex interfaces between constituents cause a great challenge to the fracture analysis of MEE materials. Considering the effect of the residual strain, this paper develops an interaction integral (I-integral) method for the extraction of the fracture parameters of an impermeable crack in nonhomogeneous MEE materials. The I-integral method has several merits: 1) it can decouple stress intensity factors (SIFs), electric displacement intensity factor (EDIF) and magnetic induction intensity factor (MIIF); 2) the I-integral is independent of the size of the integration domain, even when the integration domain contains nonhomogeneous and discontinuous material properties. Combined with the extended finite element method (XFEM), the I-integral is adopted to investigate several crack problems subjected to homogeneous, nonhomogeneous and discontinuous residual strains. The I-integral values calculated by different integration domains agree well with each other (relative deviation < 1%) for nonhomogeneous and discontinuous MEE properties. Then, single-crack and multi-crack problems are studied to show the influences of residual strain distributions on the intensity factors. Homogeneous residual strain affects the SIFs dramatically but has a slight influence on the EDIF and MIIF. By comparison, nonhomogeneous residual strains affect the SIFs, EDIF and MIIF significantly. In addition, the residual strain gradients affect the variations of intensity factors with crack location extremely.

Three-dimensional modeling of static deformation of arbitrary functionally graded multilayered multiferroic composites plates with weakly and highly conducting imperfect interfaces

In this paper, a three-dimensional static deformation of arbitrary functionally graded multilayered multiferroic composites plates with weakly and highly conducting imperfect interfaces is derived. The magnetoelectroelastic properties of each layer of the composite plates have been assumed varying throughout the thickness direction. The imperfect interfaces between the layers are assumed to be mechanically compliant, dielectrically and magnetically weakly or highly conducting. In each layer, the state-space approach is firstly applied leading to space variable. Cauchy’s problem and adapted Runge-Kutta numerical procedure is used to solve the established state-space equation. The elaborated semi-analytical solution has been propagated throughout the multilayered multiferroic composites plates using the propagator matrix method and accounting the transfers matrices at each imperfect interface. The developed formulas have been programmed and the numerical obtained results have been well compared with available ones. For the computation process, the piezoelectric material [Formula: see text] and piezomagnetic material [Formula: see text] are used. In addition, these numerical tests showed that the proposed solution is in good agreement with the available 3D asymptotic approach, the modified Pagano method, the pseudo-Stroh formalism, the finite elements method and the Peano series solution. Furthermore, the effects of mechanically compliant, dielectrically and magnetically weakly or highly conducting imperfect interface on the static response and the magnetoelectric coupling coefficient of the functionally graded multilayered multiferroic composites plates for various configurations have been also analyzed. It has been carried out that, the bending response and the magnetoelectric coupling coefficient of the multiferroic composites plates remarkably depend on the kind of imperfect interface, the used sequences as well as on the loadings conditions namely mechanical, electric or magnetic, respectively.

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.

Semicoherent heterophase interfaces with core-spreading dislocation structures in magneto-electro-elastic multilayers under external surface loads

Using the extended Stroh formalism combining with the Fourier-transform and dual variable and position techniques, semicoherent interfaces are introduced to simulate the appropriate structural interface conditions in three-dimensional magneto-electro-elastic (MEE) multilayered composites under external loads. The field solutions caused by both internal and external actions are expressed in terms of biperiodic Fourier series expansions in multilayered systems that are made of dissimilar, linear and anisotropic plates with planar lattice mismatches. For non-perfectly bonded internal interfaces, the semicoherent heterophase interfaces are atomistically described by infinitely-long, parallel, periodically-spaced, and core-spreading intrinsic dislocation structures in free-standing multilayers. On the other hand, subsequent solutions for general loads on the external surfaces with coherent interfacial conditions are consistently derived and superposed to the former dislocation-induced fields.Three application examples in bi-, tri-, and six-layered MEE systems are investigated. The first bilayered case illustrates the significant effects of the semicoherent interface with dislocation core-spreading widths on the elastic, electric, and magnetic fields in the CoFe2O4/BaTiO3 composite materials. The second example is a trilayered system made of A/B/A with two discrete sets of intrinsic dislocation dipoles on their semicoherent interfaces, analyzed by proposing a novel energy based criterion. Critical dislocation spacings and thicknesses of capped interlayers are quantified in nanoscale MEE heterostructures with different stacking sequences, providing possible guides for stable growth of layered nanostructures. Finally, the complex distribution of field solutions in a six-layered MEE system with a prescribed externally mechanical load shows the crucial role played by the topological defects in localizing the coupled electric and magnetic components at the semicoherent interfaces, which indicates the important interplay between the internal and external actions. These resulting features open up novel opportunities for designing atomic-scale heterostructures with unprecedented MEE properties by engineering the interfacial dislocation patterns when the multilayered structures are free or under external action.

Bending, buckling, and forced vibration analyses of nonlocal nanocomposite microplate using TSDT considering MEE properties dependent to various volume fractions of CoFe2O4-BaTiO3

In this article, the bending, buckling, free and forced vibration behavior of a nonlocal nanocomposite microplate using the third order shear deformation theory (TSDT) is presented. The magneto-electro-elastic (MEE) properties are dependent on various volume fractions of CoFe2O4-BaTiO3. According to Maxwell’s equations and Hamilton’s principle, the governing differential equations are derived. These equations are discretized by using Navier’s method for an MEE nanocomposite Reddy plate. The numerical results show the influences of elastic foundation parameters such as aspect ratio, length to thickness ratio, electric and magnetic fields and various volume fractions of CoFe2O4-BaTiO3 on deflection, critical buckling load and natural frequency. The natural frequency and critical buckling load increases with the increasing volume fraction of CoFe2O4-BaTiO3, also the amplitude vibration decreases with an increase in the volume fraction. This model can be used for various nanocomposite structures. Also, a series of new experiments are recommended for future work.

Effective properties of coated fiber composites with piezoelectric and piezomagnetic phases

The finite element method is proposed to analyze coated fiber composites with piezoelectric and piezomagnetic phases. The computational homogenization technique is applied for fiber composites with magnetoelectroelastic properties to determine effective material parameters. The evolution of the magnetoelectroelastic fields at the macroscopic level is resolved through the incorporation of the microstructural response. The microstructural analyses are performed on the representative volume element, where essential physical geometrical information about the microstructural components is included. Circular cross section of fibers is considered in numerical analyses. A thin coating layer is considered on the surface of the piezoelectric fiber which is embedded in the piezomagnetic matrix. Influence of the coating layer on the effective material properties is analyzed.

Complex variable step method for sensitivity analysis of effective properties in multi-field micromechanics

This paper shows an approach to computing the effective properties of multi-field composite materials and their first-order sensitivities. The approach is based on the application of the complex variable step method for the micromechanical Mori–Tanaka scheme; hence, the first-order sensitivities can be computed in the same analysis. Numerical results are presented for magnetoelectroelastic properties of piezoelectric–piezomagnetic composite materials. A comparison of the results to those obtained by other methods shows that the presented sensitivity analysis gives highly accurate and stable results, but the values of the results are dependent on the applied micromechanical model. The presented approach may be used to solve ill-posed problems of optimal design or identification in coupled fields micromechanics.

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.

Shear horizontal surface acoustic waves in functionally graded magneto-electro-elastic half-space

The propagation of shear horizontal surface acoustic waves (SHSAWs) in an inhomogeneous magneto-electro-elastic (MEE) half-space with 6-mm symmetry is studied. By virtue of both the direct approach and Stroh-formalism, the dispersion relations corresponding to two general cases of material properties variation are obtained. In the first case, it is assumed that all material properties involving the MEE properties and density vary similarly in depth, whereas, the second case considers identical variation for the MEE properties, which differs from the variation of the density. The non-dispersive SHSAW velocities pertinent to the homogeneous MEE media are obtained under eight different surface electromagnetic boundary conditions as the limiting cases of the current study. The dispersion curves corresponding to eleven inhomogeneity profiles of practical importance are presented in an effective dimensionless format, and the effects of different types of inhomogeneity functions describing the composition of the functionally graded magneto-electro-elastic (FGMEE) half-space on the dispersion relation are discussed.

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.

Analyses of Circular Magnetoelectroelastic Plates with Functionally Graded Material Properties

A meshless method based on the local Petrov–Galerkin approach is proposed for plate bending analysis with material containing functionally graded magnetoelectroelastic properties. Material properties are considered to be continuously varying along the plate thickness. Axial symmetry of geometry and boundary conditions for a circular plate reduces the original 3D boundary value problem into a 2D problem in axial cross section. Both stationary and transient dynamic conditions for a pure mechanical load are considered in this article. The local weak formulation is employed on circular subdomains in the axial cross section. Subdomains surrounding nodes are randomly spread over the analyzed domain. The test functions are taken as unit step functions in derivation of the local integral equations (LIEs). The moving least-squares (MLS) method is adopted for the approximation of the physical quantities in the LIEs. After performing the spatial integrations, one obtains a system of ordinary differential equations for certain nodal unknowns. That system is solved numerically by the Houbolt finite-difference scheme as a time-stepping method.

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.

Magnetoelectric effect in coated fibrous magnetic–piezoelectric composites

In this study, the magnetoelectroelastic behavior is investigated for magnetic–piezoelectric composites with coated reinforcements under antiplane mechanical and in-plane electromagnetic loads. The coating is considered as a layer with properties different from those of the inclusion and the matrix. The developed model is based on the solution of the problem of the magnetoelectroelastic coated inclusion embedded in an infinite homogeneous medium obtained from two different approaches. The first is the complex variable method integrating the Laurent expansion method, and the second is a micromechanical approach based simultaneously on Green’s function techniques and the interfacial operators. The exact solution is obtained and used as background to determine the effective magnetoelectroelastic properties of the composite containing thinly coated inclusions embedded in a matrix through Mori–Tanaka’s model. Numerical investigations into magnetoelectroelastic moduli responsible for the magnetoelectric effect are presented as functions of the volume fraction and characteristics of the coated inclusions. Comparisons with existing models are presented for various fractions of the coated inclusions.

Anti-plane shear fracture of the interface in a cylindrical smart structure with functionally graded magnetoelectroelastic properties

The purpose of the present work is to study the fracture behavior of the arc-shaped interface in a cylindrical non-homogeneous magnetoelectroelastic structure. Fracture analysis is performed by the method of Cauchy singular integral equation. Parametric studies are conducted on the stress intensity factor, and practical guidelines are given for the optimization of fracture performance. (a) The ratio between the outer and inner radii should be at least 1.1. (b) A softer inner side plus a stiffer outer side is a good non-homogeneity design for the magnetoelectroelastic layer. (c) A soft central cylinder and a stiff outer magnetoelectroelastic layer constitute a good stiffness matching on the interface.

Anti-plane crack intersecting the interface in a bonded smart structure with graded magnetoelectroelastic properties

The mechanical model is established for an anti-plane crack intersecting the interface in a bonded smart structure with graded magnetoelectroelastic properties. The purpose of the present work is to put forth a new treatment method for the fracture analysis of the interface-intersecting crack. Such a crack is equivalently divided into two special edge cracks in the two bonded strips, respectively. The problem is then formulated by Fourier integral transform and reduced into a system of singular integral equations, which are numerically solved under not only the classical single-valuedness conditions but also the continuity conditions of the two groups of auxiliary functions, and the latter is the key technique first introduced in the current work. The present treatment method is compared with the existing one in the literature. The numerical results of the energy density factor are provided to verify the validity of the present treatment and reveal the influences of the physical and geometrical parameters.

Fracture analysis and improved design for a symmetrically bonded smart structure with linearly non-homogeneous magnetoelectroelastic properties

The mechanical model was established for the anti-plane interfacial fracture problem of a symmetrically bonded smart structure with linearly non-homogeneous magnetoelectroelastic properties. The system of Cauchy singular integral equations for the interfacial crack was derived by Fourier integral transform. The numerical solutions of the Cauchy singular integral equations were obtained by the Lobatto–Chebyshev collocation method put up by Erdogan and Gupta. The mechanical strain energy release rate and the total energy release rate were chosen as fracture parameters to discuss the effect of the non-homogeneity parameter on the extension force of the crack. A conclusion was drawn that, to reduce the weak-discontinuity of the interface in the magnetoelectroelastic structure would be beneficial to decrease the extension force of the interfacial crack. Based on this conclusion, a new improved design was suggested for the symmetrically bonded linearly non-homogeneous magnetoelectroelastic composite. The enhancement of the capability of the improved structure to resist interfacial fracture was validated by comparison between the improved and unimproved structures for their fracture responses.

Yoffe–type moving crack in a functionally graded piezoelectric material

In this paper, the problem of a functionally graded piezoelectric material (FGPM) with a constantvelocity Yoffetype moving crack is considered. The strip is assumed to be under an antiplane mechani...