Magnetoelectric effects in multiferroic laminated plates with imperfect interfaces

Two-dimensional （2D） equations for multiferroic （MF） laminated plates with imperfect interfaces are established in this paper. The interface between two adjacent sublayers, which are not perfectly bonded together, is modeled as a general spring-type layer. The mechanical displacements, and the electric and magnetic potentials of the two adjacent layers are assumed to be discontinuous at the interface. As an example, the influences of imperfect interfaces on the magnetoelectric （ME） coupling effects in an MF sandwich plate are investigated with the established 2D governing equations. Numerical results show that the imperfect interfaces have a significant impact on the ME coupling effects in MF laminated structures.

Band gaps of elastic waves in 1-D phononic crystals with imperfect interfaces

Band gaps of elastic waves in 1-D phononic crystals with imperfect interfaces were studied. By using the transfer matrix method （TMM） and the Bloch wave theory in the periodic structure, the dispersion equation was derived for the periodically lami- nated binary system with imperfect interfaces （the traction vector jumps or the displacement vector jumps）. The dispersion equation was solved numerically and wave band gaps were obtained in the Brillouin zone. Band gaps in the case of imperfect interfaces were compared with that in the case of perfect interfaces. The influence of imperfect interfaces on wave band gaps and some interesting phenomena were discussed.

Fracture analysis of magnetoelectroelastic bimaterials with imperfect interfaces by symplectic expansion

A Hamiltonian-based analytical method is used to study the mode Ⅲ interface cracks in magnetoelectroelastic bimaterials with an imperfect interface. By introducing an unknown vector, the governing equations are reformulated in sets of first-order ordinary differential equations. Using separation of variables, eigensolutions in the symplectic space are obtained. An exact solution of the unknown vector is obtained and expressed in terms of symplectic eigensolutions. Singularities of mechanical, electric, and magnetic fields are evaluated with the generalized intensity factors. Comparisons are made to verify accuracy and stability of the proposed method. Numerical examples including mixed boundary conditions are given.

DIFFERENTIAL GEOMETRICAL METHOD IN ELASTICCOMPOSITE WITH IMPERFECT INTERFACES

A differential geometrical method is for the first time used to calculate the effective moduli of a two-phase elastic composite materials with imperfect interface which the inclusions are assumed to be ellipsoidal of revolutions. All of the interface integral items participating in forming the potential and complementary energy functionals of the composite materials are expressed in terms of intrinsic quantities of the ellipsoidal of revolutions. Based on this, the upper and the lower bound for the effective elastic moduli of the composite materials with inclusions described above have been derived. Under three limiting conditions of sphere, disk and needle shaped inclusions, the results of this paper will return to the bounds obtained by Hashin([6]) (1992).

A coupled Legendre-Laguerre polynomial method with analytical integration for the Rayleigh waves in a quasicrystal layered half-space with an imperfect interface

The Laguerre polynomial method has been successfully used to investigate the dynamic responses of a half-space.However,it fails to obtain the correct stress at the interfaces in a layered half-space,especially when there are significant differences in material properties.Therefore,a coupled Legendre-Laguerre polynomial method with analytical integration is proposed.The Rayleigh waves in a one-dimensional(1D)hexagonal quasicrystal(QC)layered half-space with an imperfect interface are investigated.The correctness is validated by comparison with available results.Its computation efficiency is analyzed.The dispersion curves of the phase velocity,displacement distributions,and stress distributions are illustrated.The effects of the phonon-phason coupling and imperfect interface coefficients on the wave characteristics are investigated.Some novel findings reveal that the proposed method is highly efficient for addressing the Rayleigh waves in a QC layered half-space.It can save over 99%of the computation time.This method can be expanded to investigate waves in various layered half-spaces,including earth-layered media and surface acoustic wave(SAW)devices.

Fast multipole boundary element analysis of 2D viscoelastic composites with imperfect interfaces

A fast multipole boundary element method(FMBEM)is developed for the analysis of 2D linear viscoelastic composites with imperfect viscoelastic interfaces.The transformed fast multipole formulations are established using the time domain method. To simulate the viscoelastic behavior of imperfect interfaces that are frequently encountered in practice,the Kelvin type model is introduced.The FMBEM is further improved by incorporating naturally the interaction among inclusions as well as eliminating the phenomenon of material penetration.Since all the integrals are evaluated analytically,high accuracy and fast convergence of the numerical scheme are obtained.Several numerical examples,including planar viscoelastic composites with a single inclusion or randomly distributed multi-inclusions are presented.The numerical results are compared with the developed analytical solutions,which illustrates that the proposed FMBEM is very efficient in determining the macroscopic viscoelastic behavior of the particle-reinforced composites with the presence of imperfect interfaces.The laboratory measurements of the mixture creep compliance of asphalt concrete are also compared with the prediction by the developed model.

Guided Wave Propagation in Multilayered Two-dimensional Quasicrystal Plates with Imperfect Interfaces

An analytical solution of the guided wave propagation in a multilayered twodimensional decagonal quasicrystal plate with imperfect interfaces is derived.According to the elastodynamic equations of quasicrystals(QCs),the wave propagating problem in the plate is converted into a linear control system by employing the state-vector approach,from which the general solutions of the extended displacements and stresses can be obtained,These solutions along the thickness direction are utilized to derive the propagator matrix which connects the physical variables on the lower and upper interfaces of each layer.The special spring model,which describes the discontinuity of the physical quantities across the interface,is introduced into the propagator relationship of the multilayered structure.The total propagator matrix can be used to propagate the solutions in each interface and each layer about the multilayered plate.In addition,the traction-free boundary condition on the top and bottom surfaces of the laminate is considered to obtain the dispersion equation of wave propagation,Finally,typical numerical examples are presented to illustrate the marked influences of stacking sequence and interface coeficients on the dispersion curves and displacement mode shapes of the QC laminates.

Transient response of a concrete tunnel in an elastic rock with imperfect contact

The two-dimensional transient response of an imperfect bonded circular lined pipeline lying in an elastic infinite medium is investigated.Imperfect boundary conditions between the surrounding elastic rock and the tunnel are modelled with a two-linear-spring design.The novelty of the manuscript consists in studying at the same time transient regimes and imperfect bonded interfaces for simulating the dynamic response of a tunnel embedded in an elastic infinite rock.Wave propagation fields in tunnel and rock are expressed in terms of infinite Bessel and Hankel series.To solve the transient problem,the Laplace transform and the associated Durbin’s algorithm are performed.To exhibit the dynamic responses,influences of various parameters such as the quality of the interface conditions and the thickness of the lining are presented.The dynamic hoop stresses and the solid displacements of both the tunnel and the rock are also proposed.

Band structures of transverse waves in nanoscale multilayered phononic crystals with nonlocal interface imperfections by using the radial basis function method

A radial basis function collocation method based on the nonlocal elastic continuum theory is developed to compute the band structures of nanoscale multilayered phononic crystals. The effects of nonlocal imperfect interfaces on band structures of transverse waves propagating obliquely or vertically in the system are studied. The correctness of the present method is verified by comparing the numerical results with those obtained by applying the transfer matrix method in the case of nonlocal perfect interface. Furthermore, the influences of the nanoscale size, the impedance ratio and the incident angle on the cut-off frequency and band structures are investigated and discussed in detail. Numerical results show that the nonlocal interface imperfections have significant effects on the band structures in the macroscopic and microscopic scale.

Modeling Piezoelectric Interfacial Wave Near an Imperfect Interface

The interface wave propagating along an imperfect interface between two piezoelectric half spaces is derived firstly. The wave equations based on the interface modeled, called ＂spring model＂, are presented. The micro-scale structures of the interface for connecting the spring constant with the interface micro-structures are examined. For some simple interface micro-structure, exact dynamic solution is available, and the spring constant is obtained by comparing solutions. For the complex micro structures, it remains as a challenge of micro-mechanics modeling to connect the ＂spring constant＂ and micro-structure.

Elastic Properties of Particulate Composites with Imperfect Interface

An effective analytical approach is developed for the problem of pardculate composites containing spherical inclusion with imperfect interface between the matrix and spherical inclusions. In this paper, a general interface model for a variety of interfaced defects has been presented, in which both displacement discontinuity across the interface and the elastic moduli varing with radius outside of the inclusion are considered, The imperfect interface conditions are appropriate in the case of thin coatings on the inclusion. Furthermore, in the case of thin elastic interphase, the displacement field and the stress field in the inclusion and matrix are exactly solved for the boundary problem of hydrostatic compression of an infinite spherical symmetrical body by Frobenius series , and the expression of the normal interface parameter, Dr, is derived. In addition, it has been proved that two previous results derived in some literatures by considering the interface to be a thin interphase with displacement jump or with some variance in its moduli can be reverted from the present formula, respectively. Numerical results are given to demonstrate the significance of the general imperfect interface effects.

Rayleigh-Type Wave in A Rotated Piezoelectric Crystal Imperfectly Bonded on a Dielectric Substrate

Propagation characteristics of Rayleigh-type wave in a piezoelectric layered system are theoretically investigated.The piezoelectric layer is considered as a cubic crystal with finite thickness rotated about Y-axis and is imperfectly bonded onto a semi-infinite dielectric substrate.The imperfect interface between the two constituents is assumed to be mechanically compliant and dielectrically weakly conducting.The exact dispersion relations for electrically open or shorted boundary conditions are obtained.The numerical results show that the phase velocity of Rayleigh-type wave is symmetric with respect to the cut orientation of 45°and can achieve the maximum propagation speed in this orientation.The mechanical imperfection plays an important role in the dispersion relations,further the normal imperfection can produce a significant reduction of phase velocity comparing with the tangential imperfection.Comparing with the mechanical imperfection the electrical imperfection makes a relatively small reduction of phase velocity of Rayleigh-type wave.The obtained results can provide some fundamentals for understanding of piezoelectric semiconductor and for design and application of piezoelectric surface acoustic wave devices.

Fracture analysis of mode-II crack perpendicular to imperfect bimaterial interface

The problem of a mode-II crack interface of two bonded dissimilar materials close to and perpendicular to an imperfect is investigated. The imperfect interface is modelled by a linear spring with the vanishing thickness. The Fourier transform is used to solve the boundary-value problem and to derive a singular integral equation with the Cauchy kernel. The stress intensity factors near the left and right crack tips are evaluated by numerically solving the resulting equation. SeverM special cases of the mode-II crack problem with an imperfect interface are studied in detail. The effects of the interfacial imperfection on the stress intensity factors for a bimaterial system of aluminum and steel are shown graphically. The obtained observation reveals that the stress intensity factors are dependent on the interface parameters and vary between those with a fully debonded interface and those with a perfect interface.

Efficient model for the elastic load of film-substrate system involving imperfect interface effects

In this paper,an efficient calculation method based on discrete Fourier transformation is developed for evaluating elastic load induced elastic deformation fields of film-substrate system.Making use of 2 D discrete Fourier transformation,the elastic fields induced by Hertz load is harvested in frequency domain,and the displacement and stress fields across the interface are enforced to satisfy the elasticity conditions for each Fourier modes.Given arbitrary distributed stress field at free surface plane of the three types of film-substrate systems,unique resultant elastic field within the can be harvested.Hertz load of half space,elastic film on elastic substrate,elastic film on rigid substrate system and elastic film-substrate system with three types of imperfect interface models are investigated:(1)the spring-like imperfect interface model which can be described as:u^fk|zf=-h-u^sk|z^s=0=KTσKZ and u^fz|zf=-h-u^sz|z^s=0=KNσZZ;(2)the dislocation-like interface model,where interface displacement and stress components relation can be described as:u^fi|zf=0=k^uiju^si|z^s=0 andσ^fiz|z^f=0=σ^siz|zf=0=σ^siz|z^s=0;(3)the force-like interface model,where interface displacement and stress components relation can be described as:u^fi|z^f=0=u^si|z^s=0 andσ^fiz|z^f=0=k^tijσ^siz|z^s=0 respectively.Finally,several simulation examples are performed for verification of the reliability and efficiency of the proposed semi-analytical methods.

Dislocation stability in three-phase nanocomposites with imperfect interface

Interface imperfection can significantly affect the mechanical properties and failure mechanisms as well as the strength and toughness of nanocomposites. The elastic behavior of a screw dislocation in nanoscale coating with imperfect interface is studied in the three-phase composite cylinder model. The interface between inner nanoin- homogeneity and intermediate coating is assumed as perfectly bonded. The bonding between intermediate coating and outer matrix is considered to be imperfect with the assumption that interface imperfection is uniform, and a linear spring model is adopted to describe the weakness of imperfect interface. The explicit expression for image force acting on dislocation is obtained by means of a complex variable method. The analytic results indicate that inner interface effect and outer interface imperfection, simultaneously taken into account, would influence greatly image force, equilibrium position and stability of dislocation, and various critical parameters that would change dislocation stability. The weaker interface is a very strong trap for glide dislocation and, thus, a more effective barrier for slip transmission.

Multiphysical contact of functionally graded magneto-electroelastic material with imperfect bonding interface

Three-dimensional(3D)frictional contact model of functionally graded magneto-electro-elastic(FGMEE)material with a conducting spherical punch under electromagnetic fields is presented.Two types of imperfect bonding interface of layers,dislocation-like interface and force-like interface,are considered.Frequency response functions(FRFs)for multilayered MEE material with imperfect interface subjected to unit mechanical,electric,and magnetic loads are derived.The FRFs are used with the semi-analytical method(SAM)to solve present multiphysical contact problem.The present model is verified by comparing with literatures and the finite element method(FEM)and used to study the contact problem of FGMEE film imperfectly bonded on homogenous MEE half-space under electromagnetic fields.Parametric studies are conducted to reveal the effects of imperfect interfaces and also film properties including gradient index and thickness.

Viscoelastic micromechanical model for dynamic modulus prediction of asphalt concrete with interface effects

A viscoelastic micromechanical model is presented to predict the dynamic modulus of asphalt concrete （AC） and investigate the effect of imperfect interface between asphalt mastic and aggregates on the overall viscoelastic characteristics of AC. The linear spring layer model is introduced to simulate the interface imperfection. Based on the effective medium theory, the viscoelastic micromechanical model is developed by two equivalence processes. The present prediction is compared with available experimental data to verify the developed framework. It is found that the proposed model has the capability to predict the dynamic modulus of AC. Interface effect on the dynamic modulus of AC is discussed using the developed model. It is shown that the interfacial bonding strength has a significant influence on the global mechanical performance of AC, and that continued improvement in surface fimctionalization is necessary to realize the full potential of aggregates reinforcement.

Surface wave transference in a piezoelectric cylinder coated with reinforced material

The present study deals with the propagation of a polarized shear horizontal(SH)wave in a pre-stressed piezoelectric cylinder circumscribed by a self-reinforced cylinder.The interface of the two media is assumed mechanically imperfect.For obtaining the dispersion relation,the mathematical formulation has been developed and solved by an analytical treatment.The effects of various parameters,i.e.,the thickness ratio,the imperfect interface,the initial stress,the reinforcement,and the piezoelectric and dielectric constants,on the dispersion curve are observed prominently.The dispersion curves for different modes have been also plotted.The consequences of the study may be used for achieving optimum efficiency of acoustic wave devices.

THE VALIDITY OF THE MODIFIED MORI-TANAKA METHOD FOR COMPOSITES WITH SLIGHTLY WEAKENED INTERFACE

This paper presents a direct Mori-Tanaka approach to calculate the effective moduli of particle-reinforced composites and fiber-reinforced composites with spring-like imperfect interfaces. By a comparison between these results and those obtained from the approximate Mori-Tanaka method developed by Qu for composites with slightly weakened interface, the validity of the Qu's method is revealed.