Imperfect Interface Conditions Research Articles

Mechanical Analysis of Functionally Graded Multilayered Two-Dimensional Decagonal Piezoelectric Quasicrystal Laminates with Imperfect Interfaces

Quasicrystals have a wide range of applications due to their unique multi-field coupling effects and distinctive physical and mechanical characteristics. In this paper, the static and dynamic problems of imperfectly bonded, multilayered, functionally graded, two-dimensional decagonal piezoelectric quasicrystal laminates under mixed boundary conditions are investigated. The state equations in a concise and compact matrix form can be expressed by using differential quadrature regional discrete point expansions in any layer of the laminate. This allows for the representation of displacement, stress, electric potential, and electric displacement components. Then, different imperfect interface conditions are introduced to characterize specific structural and electric contact properties at the bounding interfaces, which are further converted to the interface propagator matrix. Numerical examples are carried out to investigate the impact of varying interface compliances, load types, and functional gradient factors on the static bending and vibration phenomena of QC laminates. These results can be used as references to validate existing or future numerical work on QC laminates and could further guide the design of related QC laminate structures.

Influence of Homo- and Hetero-Junctions on the Propagation Characteristics of Radially Propagated Cylindrical Surface Acoustic Waves in a Piezoelectric Semiconductor Semi-Infinite Medium

This paper theoretically investigates the influence of homo- and hetero-junctions on the propagation characteristics of radially propagated cylindrical surface acoustic waves in a piezoelectric semiconductor semi-infinite medium. First, the basic equations of the piezoelectric semiconductor semi-infinite medium are mathematically derived. Then, based on these basic equations and the transfer matrix method, two equivalent mathematical models are established concerning the propagation of radially propagated cylindrical surface acoustic waves in this piezoelectric semiconductor semi-infinite medium. Based on the surface and interface effect theory, the homo- or hetero-junction is theoretically treated as a two-dimensional electrically imperfect interface in the first mathematical model. To legitimately confirm the interface characteristic lengths that appear in the electrically imperfect interface conditions, the homo- or hetero-junction is equivalently treated as a functional gradient thin layer in the second mathematical model. Finally, based on these two mathematical models, the dispersion and attenuation curves of radially propagated cylindrical surface acoustic waves are numerically calculated to discuss the influence of the homo- and hetero-junctions on the dispersion and attenuation characteristics of radially propagated cylindrical surface acoustic waves. The interface characteristic lengths are legitimately confirmed through the comparison of dispersion and attenuation curves calculated using the two equivalent mathematical models. As piezoelectric semiconductor energy harvesters usually work under elastic deformation, the establishment of mathematical models and the revelation of physical mechanisms are both fundamental to the analysis and optimization of micro-scale surface acoustic wave resonators, energy harvesters, and acoustic wave amplification based on the propagation of surface acoustic waves.

On the imperfect interface of a functionally graded thermoelectric layered structure

This paper investigates the frictionless contact problem of a functionally graded thermoelectric (FGTE) layered half-plane under the action of a rigid flat punch. The punch is an electrical and thermal conductor. The electro-thermo-elastic properties of the FGTE materials vary exponentially with thickness. Especially, the imperfect interface conditions are taken into account. The problem is reduced to a pair of Cauchy singular integral equations using the Fourier integral transform technique, which are numerically solved to yield the surface normal electric current density, the surface normal energy flux, and the surface normal contact pressure. The asymptotic analysis of the kernel function is supplied. The intensity factors are provided to characterize the singularity at the punch ends. The contact behavior of the FGTE coating-TE substrate systems is significantly influenced by the imperfect interface condition and the material property gradient according to numerical results. The design of thermoelectric coating structures may benefit from the theoretical research done here.

Effective properties of centro-symmetric micropolar composites with non-uniform imperfect contact conditions

In this work, the homogenization theory is addressed within the framework of three-dimensional linear micropolar composite materials with centro-symmetric constituents and non-uniform imperfect interface conditions. The imperfect contact conditions are modeled like a generalization of the spring model, where tractions and coupled stresses are continuous, but displacements and microrotations are discontinuous across the interface. The jumps in displacement and microrotation components are proportional to the interface traction and coupled stress components in terms of a partition of different spring-factor-type interface parameters, respectively. The two-scale asymptotic homogenization method (AHM) is developed, through series expansions for displacements and micro-rotations, to find the analytical statement of the local problems on the periodic cell and the corresponding effective coefficients. In particular, centro-symmetric multi-laminated micropolar composites with non-uniform imperfect contact conditions are studied, and their corresponding effective properties are explicitly declared. Numerical results show the effects of the interface partition lengths, the non-uniform imperfection values, and the constituent’s fraction volumes on the effective properties of centro-symmetric bi-laminated composite with isotropic constituent materials. We also analyze and discuss the effective behaviors illustrated in the results. In general, the effective properties are always affected by a non-uniform imperfect interface, and they are bounded between those achieved when the contact conditions are perfect and imperfect uniform. The reported formulas and data may be helpful as benchmarks for checking other experimental and numerical results.

Piezoelectric performance of lead-free PDMS/CNT/BaTiO3 piezocomposites with imperfect interphases and CNT agglomerations

Three-dimensional (3D) printable lead-free piezocomposites offer scalable and environmentally friendly solutions in many engineering applications. Typically, the composite system consists of polymeric matrices reinforced with active polycrystalline particles, and possibly nanoadditives. The presence of interfacial inclusion/matrix damage could not only compromise the structural integrity of the component but also significantly alter its ability to act as functional smart materials. In addition, both the agglomeration of the nanoadditives, such as carbon nanotubes (CNTs), and the degree of polarization could also affect the electromechanical behavior of the composite. In this paper, we develop a computational micromechanical model for the study of the influence of three types of internal defects on the piezoelectric performance of such composites. We investigate the influence of (a) the texture of the active phase, which is linked to the degree of polarization; (b) the effect of agglomerations of the CNTs; and (c) the presence of damage in the inclusion/matrix interphase region. Performance is assessed through the macroscopic response in various figures of merit. This work provides numerical evidence that the effective piezoelectric constants related to normal strain modes are strongly affected by the presence of damage in the interphase. Instead, the piezoelectric constant related to the shear strain remains unchanged by interfacial damage. Near the percolation threshold of the CNTs, piezocomposites exhibit a notable improvement in the piezoelectric response compared to the composite without nanomodification, as noted in previous works. Interestingly, this trend also applies in the presence of interfacial damage, and it is described in this work. The piezoelectric performance also depends on the texture of the active particles. We find, under some simplifications, the optimal orientation for the crystallites, and we find how the texture changes the performance in the presence of damage. Regarding energy harvesting applications, optimal energy conversion efficiency has been observed for polycrystalline inclusions that resembles a highly oriented single crystal and CNT volume fraction of 60 of percolation threshold. This is a quite surprising result since the optimal is usually expected for volume fractions very close to percolation and active inclusions with some orientational dispersion. The optimal CNT volume fraction depends on the presence of interfacial damage. Under perfect interface conditions, the energy conversion efficiency is improved with the presence of CNT agglomerations. Under imperfect interface conditions, there is no enhancement due to the addition of CNT.

Semi-analytical solution for mixed supported and multilayered two-dimensional thermo-elastic quasicrystal plates with interfacial imperfections

The tremendous attention of researchers has been attracted to the unusual properties of quasicrystals (QCs). In this article, the thermo-elastic problems of imperfectly bonded, multilayered, two-dimensional decagonal QC plates with mixed boundary conditions are investigated based on the QC linear elasticity theory. The temperature, heat flux, displacement, and stress components are expressed in terms of differential quadrature regional discrete point expansions in any rectangular plate, from which the state equations with thermomechanical coupling effects in a concise and compact matrix form is obtained. The different imperfect interface conditions are introduced to characterize specific structural and thermal contact properties at the interfaces and are further converted into the interface propagator matrix. Different from the conventional propagator matrix method, the new global propagator relation for the composite laminate with the presence of perfect/imperfect interfaces is recursively obtained by means of the reduced propagator distance and the exponential term between the layer to layer propagator matrix. The numerical examples indicate that numerical results are stability and precision, different boundary conditions have hardly influenced temperature and heat fluxes, and interlaminar thermal stresses strengthen with increasing interface coefficients. The methods and results can also serve as a reference for verifying existing or future QC laminate theories.

Ellipsoidal inhomogeneity with anisotropic incoherent interface. Multipole series solution and application to micromechanics

The ellipsoidal inhomogeneity with transversely isotropic incoherent interface is considered in the conductivity and elasticity context. The general imperfect interface is modeled by the first order approximation of thin transversely isotropic interphase layer. This model expands the Gurtin et al. (1998) theory of curved deformable interfaces in solids with a nanometer-scale microstructure to the incoherent interfaces between the dissimilar elastic materials and provides a certain insight into the interface moduli. The rigorous analytical solution to the conductivity and elasticity problems has been obtained by the multipole expansion method in terms of ellipsoidal solid harmonics. An accurate fulfillment of the imperfect interface conditions reduces the model boundary value problem to the linear algebraic system for multipole strengths. These results apply equally to the inhomogeneities with anisotropic interphases and nano level incoherent interfaces. The obtained solutions are valid for the non-uniform far loading and are readily incorporated in the many-particle (finite cluster or representative unit cell) model of heterogeneous solid with anisotropic incoherent interface. The tensors of effective conductivity and elastic stiffness of composite with ellipsoidal inhomogeneities are evaluated using Maxwell homogenization scheme. The obtained accurate numerical data indicate that the effective properties of composite may vary widely due to shape of inhomogeneities and the interface anisotropy ratio. Taking the incoherency of interface into account may increase reliability of predicting the behavior of nanostructured solids.

Theoretical analyses of magnetoelectric effects for magnetostrictive/radial mode piezoelectric transformer composite under dual ac stress and magnetic field modulation

Magnetoelectric (ME) composite based on the converse magnetoelectric (CME) effect is promising for the high sensitivity dc and low-frequency magnetic field detection application, however, the performance is restricted by the stress modulation ability of piezoelectric phases and the narrow bandwidth. This work presents a nonlinear equivalent circuit model to design a new ME composite consisting of magnetostrictive layers/radial mode piezoelectric transformer/magnetostrictive layers under dual ac magnetic field and stress modulation. The theoretical model is based on the nonlinear constitutive relationships of magnetostrictive material, motion equation with imperfect interface condition, and improved ME equivalent circuit. This model cannot only predict the resonant ME effects of electrically modulated ME composite under the dual ac stress and magnetic field drive, but can also predict the conventional CME and mutual inductance effects separately. Specifically, the theoretical prediction indicates that with negligible extra power consumption, the dual modulated ME composite provides higher dc and low-frequency magnetic field sensitivity with frequency conversion method and significantly wider bandwidth compared to the conventional CME effect. Such theoretical predictions are further verified by the experimental results of Metglas/piezoelectric transformer/Metglas and Terfenol-D/piezoelectric transformer/Terfenol-D laminate. The theoretical study plays a guiding role in designing the new ME magnetometer with low power consumption, high sensitivity, and wide bandwidth.

A method for dynamic response of a multilayered pavement loaded by FWD

AbstractThe dynamic response of a viscoelastic multilayered pavement under falling weight deflectometer (FWD) loading is an attractive topic for the pavement engineers. Starting from the governing equations, the Laplace transform is first applied to suppress the time variable. The ordinary differential equations (ODE) of the governing equations in Laplace domain are derived by the cylindrical vector functions systems. On the basis of the facts that the top and bottom boundary conditions dual appear, a novel analytical method called dual variable and dual boundary (DVDB) for the ODE is proposed combined with dual variable and position method (DVP). The final solution in time domain is obtained by the inverse Laplace transform that is accelerated by Epsilon algorithm. The solutions of the thin layer issues and imperfect interface conditions are also investigated. Some numerical results from DVDB for the dynamic response of multilayered pavement loaded by FWD discrete pulse series are compared and discussed. It can be concluded that the DVDB combined with Laplace transform can efficiently solve the dynamic response of multilayered pavement in time domain. Furthermore, it can also be suited for some cases, such as material anisotropy properties, thin layers in the structure and interface conditions.

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.

Free vibration of fully coupled thermoelastic multilayered composites with imperfect interfaces

A fully coupled thermoelastic framework is formulated to cope with the free vibration response of anisotropic multilayered plates in three dimensions. The laminated structure consists of homogeneous laminae of arbitrary thickness and width under simply supported edge conditions in thermal environment. The general and exact field expressions of the temperature, heat flux, displacement and stress components are expressed in terms of double Fourier series expansions in any rectangular plate, which lead to the extended Stroh formalism with thermomechanical coupling effects in a concise and compact matrix form. Different imperfect interface conditions are introduced to characterize specific structural and thermal contact properties at the bounding interfaces, and further to determine the finite complex valued coefficients in the suitable series relations. The complete time-harmonic solutions in the laminated composites in the presence of perfect/imperfect interfaces are recursively obtained by means of the modified dual variable and position technique with explicit layer-to-layer transfer matrices. Results are obtained for different layups, length-to-thickness ratios and interfacial boundary conditions for two application examples, namely the graphite/epoxy cross-ply composites and the thermal barrier coatings on superalloys, without suffering from numerical exponential instability. These investigations reveal that the natural frequencies and first and higher vibration mode shapes of the multilayered structures can be considerably affected by increasing the environmental temperature and the severity of the interfacial imperfections. Since the through-thickness stress distribution in 2, 5, and 10 layered composites appears to be strongly correlated to the layups, such modal stress analysis could be exploited to locate the fatigue hotspots operated in dynamic structures and to guide the structural design of aircraft and spacecraft composite laminates subjected to residual vibrations.

Dynamic Green's functions for multiple elliptical inclusions with imperfect interfaces

The problem of an unbounded elastic solid with multiple elliptical inclusions subjected to a time-harmonic anti-plane concentrated force is semi-analytically solved by using the collocation multipole method. The displacement of matrix and inclusion are represented by angular and radial Mathieu functions. The imperfect interface between the matrix and the inclusion is characterized as a linear spring model with vanishing thickness. It is the derivative that the imperfect condition is involved. The addition theorem of Mathieu function is frequently used to solve multiply-connected domain problems in the traditional multipole method. An alternate here is a direct computation. The associated normal derivative with respect to a non-local elliptical coordinate system is developed by means of directional derivative. Besides simple computation, no truncation error is caused. The displacement field is determined by using the imperfect interface conditions through collocating points along the interface. Several numerical experiments are done to investigate the effects of the driving frequency of the concentrated force, imperfect interface and the convexity of elliptical inclusions on the dynamic Green's functions. © 2020 The Authors. Published by Elsevier Ltd.

Surface Finite Element for Imperfect Interface Modeling in Elastic Properties Homogenization

The paper presents a mathematical model of a finite element for modeling imperfect interface conditions for two contacting surfaces. The element is used in the numerical implementation of the Asymptotic Averaging Method (AAM) for the determination of effective elastic properties of composite materials under investigation. Numerical experiments are carried out to calculate the elastic properties taking into account the adhesion layer using a displacements field jump condition at the phase boundary. Results are compared with adhesion modeling using an additional bulk phase.

SH waves in multilayered piezoelectric semiconductor plates with imperfect interfaces

In this paper, analytical solutions for SH waves in transversely isotropic multilayered piezoelectric semiconductor (PSC) plates with imperfect interfaces are obtained. The extended displacements and stresses are expressed in terms of the eigenvalues and eigenvectors by introducing the extended Stroh formalism. Making use of the dual variable and position (DVP) method and the imperfect interface conditions, the transfer matrix which relates the extended displacement and traction on the lower and upper interfaces of the multilayered plates is derived. Then the dispersion relation is obtained by using the boundary conditions on the top and bottom surfaces of the multilayered plates. Effect of the steady-state carrier density in single-layer ZnO plate, and effect of stacking sequences and imperfect interfaces in sandwich plates are discussed via numerical examples. Particularly, the critical elastic (E), piezoelectric (PE), and PSC wave domains are identified for the given carrier density, plate thickness and frequency, which could be very helpful as theoretical guidance for the design of PSC devices.

Effective Elastic Properties of Laminated Composite Materials with Interfacial Defects

The problem of effective elastic properties of stochastic laminated composite is solved. The imperfect interface conditions between the reinforcement and the matrix are assumed to have the form of porous interlayers between the matrix and reinforcement, which are considered as the third component. These layers are perfectly bonded to the matrix and reinforcement, which is expressed as continuity of displacements and surface stresses. The approach is based on the stochastic equations of elasticity for a structurally inhomogeneous material, where the tensor of elastic moduli is a random function of one coordinate and the problem of effective elastic properties has an exact solution. The dependence of the effective elastic properties on the volume fraction of the reinforcement and the porosity of the interlayers is studied.

Mechanically, electrically and magnetically imperfect interface conditions via first-order plate theory

We show systematically that when an interface between two materials is treated as a thin layer modelled by the first-order plate theory, the conventional mechanically, electrically and magnetically imperfect interface conditions can be derived from the plate theory. Specifically, the continuity of those components of the stress tensor, electric displacement vector and magnetic induction vector related to the normal of the interface are continuous at the interface as a consequence of the zero-order plate equations, but the displacement vector, electric potential and magnetic potential may have discontinuities across the interface as a consequence of the first-order plate equations. This procedure also shows the conditions or limitations of the conventional imperfect interface conditions.

Dynamic Green's functions for multiple circular inclusions with imperfect interfaces using the collocation multipole method

This paper presents a semi-analytical approach to solve anti-plane dynamic Green's functions for an elastic infinitely extended isotropic solid (matrix) containing multiple circular inclusions with imperfect interfaces. A linear spring model with vanishing thickness is employed to character the imperfect interface. The multipole expansions of anti-plane displacement of the matrix and inclusion, induced by a time-harmonic anti-plane line force located in the matrix or in the inclusion, are expanded by using Hankel and Bessel functions, respectively. The imperfect interface condition is satisfied by uniformly collocating points along the interface of each inclusion. For the imperfect interface condition, the normal derivative of the anti-plane displacement with respect to a non-local polar coordinate system is developed without any truncation error for multiply-connected domain problems. For the case of one circular inclusion, the proposed quasi-static stress field matches well with the analytical static solution. The proposed quasi-static stress fields containing two and three circular inclusions are critically compared with those calculated by static analysis using the finite element method. Finally, extensive studies are presented to investigate the effects of the frequency of excitation, imperfect interface and separation between inclusions on the dynamic Green's functions.

Multilayer multiferroic composites with imperfect interfaces

We study the macroscopic behaviors of multilayered multiferroic composites with interface imperfections by a direct micromechanical approach. Both generalized interface stress type and generalized linear spring type imperfect interfaces are considered. Concise matrix expressions of the overall behaviors of the layered piezoelectric–piezomagnetic composite with contact imperfection are presented. The key step is to observe that the two types of imperfect interface conditions are equivalent to the perfect ones due to the laminated geometry. Numerical calculations are demonstrated for BaTiO3–CoFe2O4 multilayer media, and are shown in good agreement with the more involved interphase model. Furthermore, it is observed that the interface imperfection would reduce the magnitude of the magnetoelectric voltage coefficients as compared to the corresponding perfect interface case. This feature is opposite to that predicted and observed in the corresponding cylindrical composites.

Effective elastic properties of layered composites considering non-uniform imperfect adhesion

• Analytical expressions for elastic interlayer properties of layered composites. • Two-layer model considered with non-uniform imperfect adhesion. • The three-layer model provides an excellent approximation of the two-layer model. • Effective properties for layered composites by numerical/analytical models. In this study, the effective elastic properties of layered composites are predicted by considering the influence of non-uniform imperfect adhesion. In practical terms, the influence of non-uniform imperfection on the effective properties of layers is evaluated when debonding or delamination occurs between adjacent layers. Thus, the effective properties of two- and three-layer composites with imperfect and perfect interfaces are calculated using the finite element method and an analytical technique based on the two-scale asymptotic homogenization method, respectively. In the analyses, it was used a two-layer model with imperfect interface conditions and a three-layer model with perfect conditions to derive analytical expressions of the interlayer properties, which are equivalent to the effect of the imperfection (e.g., debonding). Our numerical results demonstrate that the three-layer model provides an excellent approximation of the two-layer one and it illustrates how the effective properties of the layered composites made from titanium Ti6Al4V and ceramic AD-96 are affected by non-uniform imperfect adhesion.

Reflection and refraction of thermoelastic waves at an interface of two couple-stress solids based on Lord-Shulman thermoelastic theory

• The coupled governing equations of thermoelastic couple stress solid are derived in detail. • The thermal wave effects and the couple-stress effects are both studied. • The mechanically and thermally imperfect interface conditions are considered. • The transmission mechanism of waves across an imperfect interface is explained by three channels of energy flux. • The influences of the thermal relaxation time are discussed. The reflection and refraction of thermoelastic waves at an imperfect interface of two semi-infinite homogeneous isotropic thermoelastic couple stress solids are studied in this paper. First, the coupled governing equations and the constitutive equations of thermoelastic couple-stress medium are derived based on Lord-Shulman generalized thermoelastic theory. In contrast to the classical thermoelastic solid, there exist four kinds of wave modes (two coupled longitudinal waves and two transversal waves) in the thermoelastic couple-stress solid. Second, the reflection and refraction of these coupled thermoelastic waves across a mechanically and thermally imperfect interface are considered. The interfacial conditions result in a set of algebraic equations from which the reflection and refraction amplitudes ratios can be obtained for both incident CP-wave and incident SV-wave. The numerical results are shown graphically and the influences of the thermal relaxation time and the imperfect interface parameters are discussed. The transmission mechanism of waves across an imperfect interface is explained by three kinds of channels of energy flux.