Magnetoelectroelastic Composites Research Articles

Micromechanical modeling of magnetoelectroelastic composite materials with multicoated inclusions and functionally graded interphases

In this article, micromechanical modeling of magnetoelectroelastic composites with multicoated inclusions and functionally graded interphases are elaborated. The integral equation taking into account the continuously varying interphase properties as well as the multifunctional coating effects is introduced based on Green’s tensors and interfacial operators. Magnetoelectroelastic composites with functionally graded interphases are analyzed, and the effective properties are derived. Based on the Mori–Tanaka, Self-Consistent, and Incremental Self-Consistent models, the numerically predicted effective properties of magnetoelectroelastic composites are presented with respect to the volume fractions, shapes of the multicoated inclusions, and the thickness of the coatings. The multicoating and functionally graded interphase concepts can be used to optimize the effective properties of multifunctional composites. This can be used to design new multifunctional composite materials with higher coupling coefficients.

Unified series solution for the anti-plane effective magnetoelectroelastic moduli of three-phase fiber composites

The anti-plane magnetoelectroelastic behavior of three-phase magnetoelectroelastic composites (fiber/interphase/matrix) with doubly periodic microstructures is dealt with. With the aid of the matrix notation, the anti-plane magnetoelectroelastic coupling problem is formulated as same as the anti-plane piezoelectric coupling problem. And then the eigenfunction expansion-variational method (EEVM) is extended to solve such a problem. Series solutions for the effective magnetoelectroelastic moduli are presented, which are in a unified form for generally periodic fiber arrays, different unit cell shapes as well as different constituent properties, and are applicable for high volume fraction of fibers. With the present solution, it is found that the effective magnetoelectric coefficient of a two-phase composite may have two local extrema rather than only one extremum predicted by the Mori-Tanaka method. By optimizing the volume fraction, permutation and the choice of the constituent phases, the maximum magnitude of the effective magnetoelectric coefficient of a three-phase composite can be much larger than that of any of the two-phase composites, and the sign of the magnetoelectric coefficient can be changed, which is not observed in a two-phase composite. For composites with a generally periodic array of fibers, the effective magnetoelectric moduli can be anisotropic.

Multi-coated magnetoelectroelastic composites with functionally graded interphases

The aim of this work is to develop a micromechanical modeling to predict the effective properties of multi-coated magnetoelectroelastic composites with functionally graded interphases. The localization equations are derived based on the integral equation and on the interfacial operators. Magnetoelectroelastic composites with functionally graded interphases are analyzed and the effective properties are obtained. Based on different micromechanical models, the effects of the volume fractions, shapes of the multi-coated inclusions, thickness of the coatings and graded interphase on the effective properties are deeply analyzed.

Transient dynamic analysis of cracked magnetoelectroelastic composites by a hypersingular time‐domain BEM

Michael Wunsche1,∗, Chuanzeng Zhang1,∗∗, Andres Saez2,∗∗∗, and Felipe Garcia-Sanchez3,† 1 University of Siegen, Department of Civil Engineering, D-57068 Siegen, Germany 2 Departamento de Mecanica de Medios Continuos, Universidad de Sevilla, Camino de los Descubrimientos s/n, 41092-Sevilla, Spain 3 Departamento de Ingenieria Civil, de Materiales y Fabricacion, Universidad de Malaga, C/ Dr. Ortiz Ramos s/n, 29071-Malaga, Spain

Layout design optimization for magneto-electro-elastic laminate composites for maximizedenergy conversion under mechanical loading

Magneto-electro-elastic (MEE) laminate composites with piezoelectric and piezomagneticphases can be utilized as materials providing energy conversion among magnetic, electricand mechanical energies. This work is concerned with the development of a systematicdesign method of MEE composites with maximized conversion of mechanical energy toelectric and/or magnetic energy. To predict the energy conversion phenomena,a fully coupled MEE theory is employed. A composite plate is assumed to besimply supported and is discretized into a number of laminates for analysis using asemi-analytic finite element method. Since the optimal stacking sequences forpiezoelectric/piezomagnetic phases and the optimal thickness for each phase must besimultaneously determined, we propose formulating the design problem as a topologyoptimization problem. To implement the topology optimization, two interpolationmodels, the standard SIMP (solid isotropic material with penalization) modeland the micromechanics model, are investigated. After solving benchmark testproblems, design examples dealing with multifunctional composites are considered.

Transient fracture of a layered magnetoelectroelastic medium

Most magnetoelectroelastic composites were developed in the form of a composite laminate by alternating the ferromagnetic layers and ferroelectric layers during stacking. Presence of interfacial crack may influence the magneto-electro-mechanical coupling behavior of magnetoelectroelastic materials considerably. This paper describes a method to analyze the transient response of a layered magnetoelectroelastic medium of finite size with an interface crack. Based on Fourier and Laplace transforms, the boundary value problem is reduced to a system of generalized singularity integral equations in the Laplace transform domain. By utilized numerical Laplace inversion, the time-dependent full field solutions are obtained in the time domain. Effects of medium size, crack-face electric and magnetic boundary conditions on the dynamic crack tip fields are studied. By investigating an interface notch of finite gap thickness, the electric and magnetic properties of the medium inside the notch are included in the analytical model so that the applicability of crack-face electric and magnetic boundary conditions on the transient response of the magnetoelectroelastic medium can be investigated.

Analysis of cracked magnetoelectroelastic composites under time-harmonic loading

This paper presents a numerical model for the analysis of cracked magnetoelectroelastic materials subjected to in-plane mechanical, electric and magnetic dynamic time-harmonic loading. A traction boundary integral equation formulation is applied to solve the problem in combination with recently obtained time-harmonic Green’s functions ( Rojas-Diaz et al., 2008). The hypersingular boundary integral equations appearing in the formulation are first regularized via a simple change of variables that permits to isolate the singularities. Relevant fracture parameters, namely stress intensity factors, electric displacement intensity factor and magnetic induction intensity factor are directly evaluated as functions of the computed nodal opening displacements and the electric and magnetic potentials jumps across the crack faces. The method is checked by comparing numerical results against existing solutions for piezoelectric solids. Finally, numerical results for scattering of plane waves in a magnetoelectroelastic material by different crack configurations are presented for the first time. The obtained results are analyzed to evaluate the dependence of the fracture parameters on the coupled magnetoelectromechanical load, the crack geometry and the characteristics of the incident wave motion.

Effect of Interfacial Cracks on the Effective Properties of Magnetoelectroelastic Composites

An impermeable interfacial crack problem in two dissimilar magnetoelectroelastic half planes has been solved in a compact form by Stroh formulism. The expression for energy release rate has been derived. By using the expression, the overall average properties of the composite have been established in relation to the interface crack density. Results indicate that the presence of interface cracks, as a whole, would deteriorate the coupling effects in the magnetoelectroelastic composites.

Effective properties of magnetoelectroelastic materials with aligned ellipsoidal voids

The presence of defects may influence the behavior of magnetoelectroelastic materials. The present work considers the influence of aligned ellipsoidal voids on the effective properties of magnetoelectroelastic composites. By treating the voided composite as consisting of a matrix and two kinds of inclusions, the effective properties can be obtained based on Eshelby’s equivalent inclusion principle. The effects of both density and orientation of voids are studied in particular. The results indicate that the deterioration of effective properties largely depends on the void volume fraction and void orientation.

Dynamic behavior of two parallel symmetry cracks in magneto-electro-elastic composites under harmonic anti-plane waves

The dynamic behavior of two parallel symmetry cracks in magneto-electroelastic composites under harmonic anti-plane shear waves is studied by Schmidt method. By using the Fourier transform, the problem can be solved with a pair of dual integral equations in which the unknown variable is the jumps of the displacements across the crack surfaces. To solve the dual integral equations, the jumps of the displacements across the crack surface were expanded in a series of Jacobi polynomials. The relations among the electric filed, the magnetic flux and the stress field were obtained. From the results, it can be obtained that the singular stresses in piezoelectric/piezom agnetic materials carry the same forms as those in a general elastic material for the dynamic anti-plane shear fracture problem. The shielding effect of two parallel cracks was also discussed.

Micromechanics predictions of the effective moduli of magnetoelectroelastic composite materials

In this paper, the self-consistent, generalized Mori–Tanaka and dilute micromechanics theories are extended to study the coupled magnetoelectroelastic composite materials. The heterogeneous inclusion problem of magnetoelectroelastic behavior is formulated in terms of five interaction tensors related to the Green's functions for an infinite three-dimensional transversely isotropic magnetoelectroelastic solid. These tensors are then used to predict the effective moduli of the magnetoelectroelastic solid based on the self-consistent, Mori–Tanaka and the dilute approaches. Numerical results are obtained for various types of inclusions. These results are employed to study the effects of the inclusion properties, such as moduli, volume fractions, shapes, etc., on the effective moduli of magnetoelectroelastic composites, in particular, the related magnetic properties. The results obtained using the self-consistent model, the generalized Mori–Tanaka's model and the dilute approach are compared with the existing experimental and theoretical results.

Crack initiation behavior in magnetoelectroelastic composite under in-plane deformation

While the method of solution for crack problems in anisotropic elasticity and magnetoelectroelasticity is nearly identical, the prediction of crack initiation and/or growth behavior based on the asymptotic stress fields can differ widely depending on the chosen failure criterion. The latter has no haven to hide. Avoidance of contraction and satisfaction of the first law of thermodynamics are the rules that need to be observed. A negative crack tip energy release rate would infer the creation of energy and a negative strain energy density would imply the non-uniqueness of solution in classical linear continuum mechanics theories. Under these conditions, the crack initiation and growth behavior in a magnetoelectroelastic material will be examined. For the sake of notation and continuity, this work gives a brief account of the well-known solution for a line crack in a magnetoelectroelastic medium. Not to be underestimated is the derivation of the asymptotic form of the strain energy density function that was first given for the piezoelectroelastic crack problem. The equivalent expression for the magnetoelectroelastic case is given here. This sets the stage for a physical interpretation of how a crack would behave in a composite possessing the mixed properties of piezoelectric and piezomagnetic materials. The individual terms in the strain energy density function shows how the applied electric and magnetic field would affect the critical applied mechanical normal and shear stress to trigger crack initiation, respectively. When both normal and shear action prevail, the direction of crack initiation is no longer obvious and it needs to be determined since the energy stored ahead of the crack depends on the direction of prospective crack initiation. Numerical results are given for a BaTiO 3–CoFe 2O 4 composite. The inclusion is the piezoelectric BaTiO 3 material and the matrix is the magnetostrictive CoFe 2O 4 material. The proportion of the two phases can be varied by adjusting the volume fraction of the inclusions upon which the fluctuation of the energy density field near the crack depends and the material properties of the constituents. Directions of the applied electric and magnetic field can also be changed; their effects on crack initiation are discussed using the strain energy density criterion. Indeed, the additional magnetostrictive effect can have an influence on crack initiation as the applied field directions are altered. Possible behavior of crack initiation can be made for design-specific magnetoelectroelastic composites.