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We establish the uniformity of stresses and strains inside an imperfectly bonded elastic ellipsoidal inhomogeneity embedded within an infinite elastic matrix subjected to uniform remote stresses and strains. Both the inhomogeneity and the matrix can be either isotropic elastic or generally anisotropic elastic. The imperfect interface is described by a spring-type imperfect interface characterized by a single imperfect interface function. The same degree of imperfection of the ellipsoidal interface is realized in both the normal and tangential directions. We identify the imperfect interface function leading to an internal uniform field. The internal uniform strains and stresses within the ellipsoidal inhomogeneity are obtained with the aid of Eshelby’s equivalent inclusion method.

We consider a transversely isotropic piezoelectric spheroidal inhomogeneity embedded in an infinite transversely isotropic piezoelectric matrix subjected to a uniform remote axisymmetric electromechanical loading. The inhomogeneity-matrix interface is spring-type in elasticity and weakly conducting in dielectricity. The same degree of interface imperfection in elasticity is realized in both the normal and tangential directions and the interface is characterized by two imperfect interface functions. We identify the two interface functions leading to a uniform interior electroelastic field within the spheroidal inhomogeneity. Explicit expressions for the internal uniform stresses and electric displacement within the inhomogeneity are presented and illustrated. The uniformity property within an imperfectly bonded spheroidal piezoelectric inhomogeneity under a uniform remote antisymmetric electromechanical loading is also proved and illustrated.

In this study, a poor/imperfect interphase is assumed to express the effective interphase thickness, operative filler concentration, percolation onset and volume share of network in graphene–polymer systems. Additionally, a conventional model is advanced by the mentioned terms for conductivity of samples by the extent of conduction transference between graphene and polymer medium. The model predictions are linked to the experimented data. Likewise, the mentioned terms as well as the conductivity of nanocomposites are expressed at dissimilar ranges of various factors. The novel equations successfully predict the percolation onset and conductivity in the samples containing a poor/imperfect interphase. Thin and long nanosheets with high conduction transportation desirably govern the percolation onset and nanocomposite conductivity, but a bigger tunneling distance causes a lower conductivity.

In this investigation, the non-reciprocal transmission in a nonlinear elastic metamaterial with imperfect interfaces is studied. Based on the Bloch theorem and stiffness matrix method, the band gaps and transmission coefficients with imperfect interfaces are obtained for the fundamental and double frequency cases. The interfacial influences on the transmission behaviour are discussed for both the nonlinear phononic crystal and elastic metamaterial. Numerical results for the imperfect interface structure are compared with those for the perfect one. Furthermore, experiments are performed to support the theoretical analysis. The present research is expected to be helpful to design tunable devices with the nonreciprocal transmission and diode behaviour of the elastic metamaterial.

In this work, the effective behavior of viscoelastic composites with ellipsoidal reinforcements and imperfect interface or degraded interphase is investigated through the inclusion replacement concept. The concentration equations have been reformulated as to define the equivalent inclusion’s behavior with imperfect interface or thin coating allowing to evaluate the effective behavior through different homogenization schemes. The correlation between interface and interphase descriptions is formulated in the context of anisotropic behavior of the inclusion and the matrix and for ellipsoidal inclusion shape. In the case of isotropic elasticity, the exact analytical solutions agree with the literature references for spherical and cylindrical inclusion morphologies and linear spring interface model. The replacement procedure was extended to viscoelastic behavior of the components with imperfect interface and/or interphase. Alternative descriptions of the interface behavior are proposed through Maxwell and Kelvin–Voigt models. The combined influence of shape of inclusions and interface parameters is analyzed on the effective relaxation modulus.

We study the interaction of in-plane elastic waves with imperfect interfaces composed of a periodic array of voids or cracks. An effective model is derived from high-order asymptotic analysis based on two-scale homogenization and matched asymptotic technique. In two-dimensional elasticity, we obtain jump conditions set on the in-plane displacements and normal stresses; the jumps involve in addition effective parameters provided by static, elementary problems being the equivalents of the cell problems in classical two-scale homogenization. The derivation of the model is conducted in the transient regime and its stability is guarantied by the positiveness of the effective interfacial energy. Spring models are envisioned as particular cases. It is shown that massless-spring models are recovered in the limit of small void thicknesses and collinear cracks. By contrast, the use of mass-spring model is justified at normal incidence, otherwise unjustified. We provide quantitative validations of our model and comparison with spring models by means of comparison with direct numerical calculations in the harmonic regime.

Purpose This research aims to explore the transmission of seismic surface waves through a two magneto-strictive materials i.e. cobalt ferrite and Terfenol-D when embedded in a plate-substrate configuration with non-ideal interface. The study focuses on understanding the impact of width of the plates, imperfect parameter, heterogeneity parameter on both the materials cobalt ferrite and Terfenol-D under magnetically open and short conditions. Methodology To achieve this, the study employs a variable-separable technique following Direct Sturm-Liouville method and appropriate boundary conditions to derive frequency relations for both magnetically open and short circuit scenarios. Numerical simulations are conducted to investigate the effects of width of the plates, imperfect parameter, heterogeneity parameter on both the materials cobalt ferrite and Terfenol-D under magnetically open and short conditions. Findings The research findings indicate that the phase velocity is increasing more in Terfenol-D as compared to Cobalt ferrite, either the case magnetically open or closed. Graphical comparisons highlight the impact of width plates, imperfect parameter, heterogeneity parameter on the characteristics on wave propagation clearly. Research limitations The study is confined to linear wave propagation and does not consider nonlinear effects. Additionally, the analysis is based on idealized material properties and interface conditions. Practical implications The results of this research can contribute to the design and optimization of sensors, energy harvesters, and wave manipulation devices utilizing piezomagnetic materials. Understanding the behaviour of surface waves in these structures is crucial for their effective application. Originality This study offers a comprehensive analysis of surface wave propagation in two different types of piezomagnetic composite structure by considering heterogeneity and interface conditions. The comparative study of different piezomagnetic models and the incorporation of heterogeneity and interface conditions contribute to the originality of the research.

In this work, the concept of high-frequency homogenization is extended to the case of one-dimensional periodic media with imperfect interfaces of the spring-mass type. In other words, when considering the propagation of elastic waves in such media, displacement and stress discontinuities are allowed across the borders of the periodic cell. As is customary in high-frequency homogenization, the homogenization is carried out about the periodic and antiperiodic solutions corresponding to the edges of the Brillouin zone. Asymptotic approximations are provided for both the higher branches of the dispersion diagram (second-order) and the resulting wave field (leading-order). The special case of two branches of the dispersion diagram intersecting with a non-zero slope at an edge of the Brillouin zone (occurrence of a so-called Dirac point) is also considered in detail, resulting in an approximation of the dispersion diagram (first-order) and the wave field (zeroth-order) near these points. Finally, a uniform approximation valid for both Dirac and non-Dirac points is provided. Numerical comparisons are made with the exact solutions obtained by the Bloch–Floquet approach for the particular examples of monolayered and bilayered materials. In these two cases, convergence measurements are carried out to validate the approach, and we show that the uniform approximation remains a very good approximation even far from the edges of the Brillouin zone.

We study the design of a neutral spheroidal piezoelectric inhomogeneity that does not disturb the prescribed uniform axisymmetric electromechanical loading in a piezoelectric matrix. Both the inhomogeneity and the matrix are transversely isotropic. Our design methodology is based on an imperfect interface model with infinitesimal thickness that is spring-type in elasticity and weakly conducting in dielectricity, and is characterized by two non-negative imperfect interface functions which are determined for given material properties of the composite and given geometry of the spheroid. The inhomogeneity is neutral to either a hydrostatic or non-hydrostatic stress field through the interface design. Of particular note is that for the first time, we have achieved the neutrality of a three-dimensional anisotropic piezoelectric inhomogeneity through interface design.

The research presented in this paper aims to demonstrate how imperfect interfaces influence the behavior of a multilayered structure. To achieve this, a dynamic equivalent model for multilayered panels is used, enabling the characterization of these interfaces using experimental data. This model, known as the Layer Wise (LW) model, incorporates imperfections in the interfaces through sliding displacement. To effectively validate the model against experimental measurements, an equivalence with a thin beam is established. Then the experimental methodology used for characterization is outlined, including the setup, considered samples, and data processing techniques. Specifically, the Corrected Force Analysis Technique (CFAT) is used, which is a robust method based on the equations of motion for thin plates or beams. This method, for the first time, allows obtaining broadband frequency results, facilitating dynamic monitoring of interface states in multilayers. The concurrently developed model enables the quantification of an interface parameter through experimental measurements. Finally, a detailed analysis of the results obtained through this methodology is provided, emphasizing the significant influence of imperfect interfaces on the dynamics of multilayered structures.