Anisotropic Multilayers Research Articles

Electromechanical coupling optimization for a sandwich beam activation using piezoceramics

Sandwich beams composed of two stiff carbon fiber skins and a viscoelastic core are often used to passively dissipate energy through the activation of shearing in a specific frequency range. Semi-active or active energy dissipation can be made possible on those structures adding piezoelectric patches, coupling mechanical vibration energy and electrical energy. J.L. Guyader et al. [jsv, 1978] theorized a frequency dependent equivalent dynamic model of a sandwich structure, recently extended to the homogenization of anisotropic multi-layers by F.Marchetti et al. [jsv, 2020]. This frequency-dependent stiffness of the beam has to be taken into account in the piezoceramic thickness definition in order to optimize the global electromechanical coupling coefficient. An analytical model is derived from the works of F.Marchetti et al. and adapted to predict the first vibration mode of a finite cantilever beam instrumented with a piezoelectric patch. The electromechanical coupling evolution is then calculated with the proper boundary conditions and for different PZT ceramic thicknesses. This model is furtherly used to define the best transducer configuration for a given sandwich structure beam.

Optical second harmonic generation in anisotropic multilayers with complete multireflection of linear and nonlinear waves using ♯SHAARP.ml package

Optical second harmonic generation (SHG) is a nonlinear optical effect widely used for nonlinear optical microscopy and laser frequency conversion. Closed-form analytical solution of the nonlinear optical responses is essential for evaluating materials whose optical properties are unknown a priori. A recent open-source code, ♯SHAARP.si, can provide such closed form solutions for crystals with arbitrary symmetries, orientations, and anisotropic properties at a single interface. However, optical components are often in the form of slabs, thin films on substrates, and multilayer heterostructures with multiple reflections of both the fundamental and up to ten different SHG waves at each interface, adding significant complexity. Many approximations have therefore been employed in the existing analytical approaches, such as slowly varying approximation, weak reflection of the nonlinear polarization, transparent medium, high crystallographic symmetry, Kleinman symmetry, easy crystal orientation along a high-symmetry direction, phase matching conditions and negligible interference among nonlinear waves, which may lead to large errors in the reported material properties. To avoid these approximations, we have developed an open-source package named Second Harmonic Analysis of Anisotropic Rotational Polarimetry in Multilayers (♯SHAARP.ml). The reliability and accuracy are established by experimentally benchmarking with both the SHG polarimetry and Maker fringes using standard and commonly used nonlinear optical materials as well as twisted 2-dimensional heterostructures.

Determination of elastic characteristics for a package of monolayers thin-walled plates from composite fibrous materials

An analytical method for calculating the equivalent elastic characteristics of anisotropic multilayer plates made of composite fibrous materials is laid out. The main assumptions taken into consideration when calculating elastic moduli and Pousson's coefficients are that fibers are elastic materials with orthotropic mechanical characteristics that deform together when multilayer plates are loaded. Analytical methods for calculating effective modulus of elasticity most common in practical applications of applied mechanics are laid out in the list of cited publications. These include the rules of the mixture, the model proposed by Hill and Khashin, the model of Kilchinsky, the methods of Vanin and L.P. Khoroshun. Numerical methods for determining the elastic mechanical properties of reinforced unidirectional and layered composite materials are based on information technologies of finite-element modeling of representative volumes of composite materials and solving a number of boundary value problems for them. For the constructions of thin-walled plates with composite fibrous materials, traditional calculation schemes are used, for which the plane stress state is typical. The stress-strain relationship for a monolayer of plates loaded at an arbitrary angle is presented in the form of Hooke's law for aniotropic materials. Deformations of a package of monolayers with composite fibrous materials in a plane elastic-deformed state are determined, as for a monolayer, by four independent elastic constants. With the use of a universal calculation model based on the equations of applied mechanics, the results of the calculations of elastic moduli and Poisson's coefficients were obtained for a package of monolayers of thin-walled plates with composite fibrous materials made of carbon fiber and carbon fiber. Research results are presented in an analytical and graphic form. The influence of the construction structure of composite fibrous materials of thin-walled plates on its mechanical properties and their dependence on the angle of the force load vector is presented. The research results can be used to determine the rational mechanical properties of multilayer composite plates, taking into account their structural and technological purpose in various industries.

Layer-resolved resonance intensity of evanescent polariton modes in anisotropic multilayers

Layer-resolved resonance intensity of evanescent polariton modes in anisotropic multilayers

A Novel Optical-Based AC Calorimetry Method to Measure In-Plane Thermal Conductivity of Small-Scale Samples

Conventional ac-calorimetry method could accurately measure the in-plane thermal diffusivity of suspended thin films but cannot be applied to small-scale samples due to the large sample size required by this method. This work proposes a novel optical-based ac-calorimetry method that circumvents the limitations of the conventional ac-calorimetry method. This new method uses a modulated continuous-wave laser to heat the sample periodically, and another continuous-wave laser to detect the sample’s temperature response on the surface at different distances from the heating spot via the principle of thermoreflectance. Since this method uses highly focused laser beams with micrometer-scale spot diameters for optical heating and temperature sensing, and this method uses the state-of-the-art thermal model of 3D anisotropic multilayers for signal processing, this method can accurately measure the in-plane thermal conductivity of suspended and supported thin films and bulk materials with sub-millimeter-scale lateral sizes, with a typical measurement uncertainty of less than 5%. This paper describes the details of this technique, including the basic principle, test device, signal acquisition, data processing, and uncertainty analysis. This technique is demonstrated through measurements of a standard sapphire sample, with the phase and amplitude approaches of ac-calorimetry compared. This technique is also compared with some other related optical-based thermal methods for their pros and cons in the end.

Reflectionless anisotropic multilayers for both polarisations at grazing incidence

We find a method for designing anisotropic multilayer profiles that are reflectionless at grazing incidence, for both electromagnetic polarisations. The Helmholtz equation for grazing incidence propagation through an anisotropic multilayer can be factorised into a pair of equations of the form [see formula in PDF]. Solutions of [see formula in PDF] then determine two of the three principal values of the permittivity. Imposing the additional constraint of uniaxial anisotropy, we find a pair of coupled equations for the profile of both permittivity components such that neither polarisation is reflected.

A Fast Computational Method for the Optimal Thermal Design of Anisotropic Multilayer Structures with Discrete Heat Sources for Electrified Propulsion Systems

This work investigates the effect of the anisotropy on the heat transfer properties of layered composite materials with discrete heat sources, that are used in the power electronics of hybrid-electric propulsion systems. An analytical method, based on closed-form expressions structured on Fourier expansion series, is proposed for the solution of the Laplace’s steady-state anisotropic heat equation. The physical presence of electrical components is replaced by externally applied power sources. The method provides an accurate prediction of the temperature distribution and of the heat transfer across perfect layer-to-layer adhesion or finite conductance interfaces; its use is therefore encouraged for the optimization of composite substrates. Code verification has been employed on test cases for which the analytical solution was available.

Optimization of coupled Lamb wave parameters for defect detection in anisotropic composite three-layer with Kelvin-Voigt viscoelasticity using Legendre polynomial method

An extension of the Legendre polynomial method is proposed, which allows to model coupled Lamb wave propagation in anisotropic multilayers with Kelvin-Voigt viscoelastic properties in a carbon-epoxy-layer sequence [0/ϕ/0]. In spite of complicated nonlinear dependences of the constituent equations on the viscoelastic properties, a linear relationship is found between the attenuation curves calculated by Hysteretic model, and the attenuation curves calculated by the Kelvin-Voigt model. In view of verifying the feasibility of using wave propagation analysis for non-destructive testing of composite materials, predictions are made concerning the dependence of the experimentally accessible phase velocities and attenuation coefficients of the modes on (virtual, defect induced, changes of) the viscoelastic constants in general and the fiber orientation in particular. In order to get a deeper insight in the material property sensitivity of the waves and in how to excite and detect them efficiently, also the through-thickness of displacements and energies profiles of different wave modes and frequencies are investigated, and how these depend on the viscoelastic moduli Cij.

Single molecule characterization of anomalous transport in a thin, anisotropic film

The diffusion of small, charged molecules incorporated in an anisotropic polyelectrolyte multilayer (PEM) was tracked in three dimensions by combining single-molecule fluorescence localization (to characterize lateral diffusion) with Förster resonance energy transfer (FRET) between diffusing molecules and the supporting surface (to measure diffusion in the surface-normal direction). Analysis of the surface-normal diffusion required model-based statistical analysis to account for the inherently noisy FRET signal. Combining these distinct single-molecule methods, which are inherently sensitive to different length-scales, permitted simultaneous characterization of severely anisotropic diffusion, which was more than three orders of magnitude slower in the surface-normal direction. We hypothesize that the anomalously slow surface-normal diffusion was related to the periodic distribution of charge in the PEM, which created electrostatic barriers. The motion was strongly subdiffusive, with anomalous temporal scaling exponents in lateral and normal directions, suggesting a connection to the transient, random fractal conformation of polymer chains in the film’s matrix.

A Novel Analytical Study of Anisotropic Multi-Layer Elliptical Structures Containing Graphene Layers

This article aims to propose a novel analytical model for anisotropic multi-layer elliptical structures incorporating graphene layers. The multi-layer structure is formed of various magnetic materials, and each one has the permittivity and permeability tensors of ε̅̅ and μ̅, respectively. An external magnetic bias has been applied in the axial direction. A graphene layer, with isotropic surface conductivity of o, has been sandwiched between the two adjacent anisotropic materials. A novel matrix representation has been derived to find the propagation parameters of the multi-layer structure. Two exemplary important cases of the proposed general structure, as waveguides, have been investigated to show, first, the validity of our proposed analytical model and second, the richness of the general structure. The analytical and simulation results show an excellent agreement. A very large value of figure of merit (FOM), e.g., FOM = 110, is achieved for the second structure for the chemical potential and external magnetic bias of μ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">c</sub> = 0.9 eV and B <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> = 1 T, respectively. Our general structure and its analytical model can be exploited to design innovative terahertz devices such as absorbers, couplers, and cloaks.

Coercivity mechanism and effect of Dy element in anisotropic LaPrFeB multilayers with Dy diffusion

In composite magnets, an in-depth understanding of magnetization reversal behaviors promotes optimizing the structure design of a magnet and improving its performance. In this work, the perpendicular magnetic anisotropic Ta/La–Pr–Fe–B/Dy/La–Pr–Fe–B/Ta multilayers have been prepared by adjusting the thickness of the Dy layer. The domain reversal evolutionary procedure has been investigated in different aspects including the characterization of domain morphology, micromagnetic analysis, and irreversible reversal distribution. It is confirmed that the nucleation mechanism is dominant in determining the coercivity of the multilayers with Dy diffusion. Dy diffusion helps to enhance the coercivity of the multilayers. The formation of Dy-containing hard magnetic phases and rare-earth-rich grain boundary phases by adding the Dy element leads to a strong nucleation field and isolation of hard magnetic phase grains, respectively. Our results aid in the understanding of magnetization reversal behaviors and enhance the magnetic properties of highly abundant rare-earth permanent magnetic multilayer films with the doping element.

Modeling and numerical study of the influence of imperfect interface properties on the reflectance function for anisotropic multilayered structures

The demand for the development of non-destructive techniques aiming to assess the reliability of adhesively bonded structures has greatly increased these recent years. The multilayered plates investigated can suffer from different defects, such as delaminations, inclusions and microcracks at interfacial areas. The aim of this paper is to study the effect of imperfect interfaces on the wave propagation in multilayered structures that represent the typical architecture of components present in several industrial fields. This study is based on the calculation of both the reflectance function and the guided waves dispersion curves for an anisotropic multilayer where two metallic layers are bonded together by an adhesive layer made of an epoxy resin. Comparisons were performed in order to evaluate numerically the influence of several properties of the adhesive layer on the resonance modes of the multilayer. In addition, an imperfect porous interface layer model is implemented in order to simulate different adherence qualities between the metallic layers.

The Scattering of Electromagnetic Fields from Anisotropic Objects Embedded in Anisotropic Multilayers

This article presents an efficient method for calculating the scattered electromagnetic (EM) fields from anisotropic objects embedded in general anisotropic multilayers, both with arbitrary anisotropy. The electric field integral equation (EFIE) is derived based on the electric dyadic Green’s functions for general anisotropic multilayers. The volume integral equation (VIE) involves a convolution form between the dyadic Green’s function and equivalent sources. To accelerate the integral computation, the fast Fourier transform technique (FFT) is adopted which reduces the computational cost from $O(N^{2})$ to $O (N \log N)$ . The biconjugate gradient stabilized method (BiCGSTAB) is then applied to solve the EFIE efficiently to calculate the total electric fields in the computational domain. In order to validate the algorithm, several examples are modeled for anisotropic objects embedded in both isotropic and anisotropic multilayers. The modeled scattered fields are compared with the finite-element method (FEM) results. The good agreement between the two results shows the algorithm works properly.

Size effect of layer thickness on stress fields due to interface core-spreading dislocation arrays in multilayers

The elastic fields due to interface dislocation arrays with spreading core in multilayers are derived analytically by means of the superposition of Green function of individual compact dislocations. The numerical results for Cu-Nb multilayers with dislocation arrays demonstrate that: (1) There exists a critical layer thickness (CLT) in describing interface shear stress. The maximum interface shear stress (MISS) increases with the layer thickness as it exceeds CLT; while the MISS decreases rapidly with the layer thickness as it is thinner than CLT. (2) Both the density and core width of interface dislocations have salient effect on the stress fields. The overall stress field is confined by high density of dislocations, and the stress singularity is released by core spreading. (3) A new dislocation prefers to glide in the middle region between the two adjacent interface dislocations by means of Peach-Kohler (P-K) force acting on the dislocation and elastic energy of dislocations. These findings would provide foundations to deepen the understanding of microscopic plastic deformation mechanisms and their related macroscopic mechanical properties of metallic anisotropic multilayers.

Electric field-controlled transformation of the eigenmodes in a twisted-nematic Fabry\u2013P\xe9rot cavity

The polarized optical states in the transmission spectrum of a twisted-nematic Fabry–Pérot cavity with the distinctly broken Mauguin’s waveguide regime have been theoretically and experimentally investigated. Specific features of the electric field-induced transformation of the polarization and spectral characteristics of eigenmodes of the neighboring series at the overlap resonant frequencies have been examined. It is demonstrated that the linear polarizations of eigenmodes at the cavity boundaries remain nearly orthogonal and their frequency trajectories reproduce the avoided crossing phenomenon. The experimental data are confirmed analytically and by the numerical simulation of light transmission through the investigated anisotropic multilayer with the use of a Berreman matrix method. The results obtained can be generalized to any materials with the helix response.

Two-dimensional analysis of interlaminar stresses in thin anisotropic composites subjected to inertial loads by regularized boundary integral equation

Evaluation of interlaminar stresses in composites plays a crucial role to ensure structural integrity. It is quite often to have composites consisting of very thin anisotropic multilayers. Traditional domain modeling of ultra-thin multilayers usually requires a tremendous amount of refined elements that might cause computation overloading. This article proposes an efficient computational methodology for evaluation of two-dimensional interlaminar stresses in thin anisotropic composites subjected to inertial loads. This analysis is by the regularized boundary integral equation (BIE) that employs only very coarse meshes. In the present work, the directly transformed boundary integral equation is regularized using the scheme of integration by parts and analytical integration. By the proposed approach, modeling of very thin layered composites can be performed simply by very coarse mesh. The obvious advantage of the present method over conventional methods is the much less modeling efforts that are required for analyzing very thin multi-layered composites. For verifications, a few benchmark examples are presented in the end.

Non-iterative, stable analysis of surface acoustic waves in anisotropic piezoelectric multilayers using spectral collocation method

Surface acoustic waves (SAWs) enjoy profound importance across many disciplines, and one of their most prominent applications are the vast ranges of SAW devices made of piezoelectric multilayers. Thus a stable and efficient algorithm of analysing key SAW parameters in arbitrary layered media is of wide interest. This paper introduces such an algorithm based on the spectral collocation method (SCM). It firstly explains the fundamental governing equations and their numerical calculations via the SCM in a self-contained way, and then demonstrates the technique on the well-studied ZnO/diamond/Si material system, where the key factors of phase velocity, electromechanical coupling coefficient and effective permittivity are evaluated and discussed in detail. Compared to the widely employed root-finding approach, it is shown that the SCM is intuitive to formulate and code, and is highly accurate; it delivers all modes at once, and does not suffer from numerical instabilities. The establishment of the method on this simple example also implies potential applications to more general material and geometry types that could be difficult for the conventional approaches.

Numerical Shielding Analysis of Anisotropic Multilayer Materials by the Method of Moments

In this contribution, an efficient method is developed to calculate the shielding effectiveness of anisotropic conducting multilayer materials by the method of moments. An analytical solution is used to approximate the wave propagation inside the multilayer material. This solution is coupled with a method of moments implementation, allowing to numerically calculate the electromagnetic fields in exterior and interior regions of a shield. Obtained results are compared to those of alternative numerical techniques and form the basis to validate the modeling of anisotropic multilayer materials by a homogeneous material of equivalent conductivity.

Elastic-wave transmission through self-similar anisotropic Cantor-like multilayers

Through the study of elastic wave propagation in Cantor-like anisotropic multilayers, this work analyzes the influence of medium geometry on the transmission of elastic waves to yield a better understanding of the connection between topological ordering and physical properties. Cantor-like multilayers, whose homothetic dimension is modified by changing the length of the central segment, are made of one anisotropic material with two orientations. The influence of the combination of self-similarity and anisotropy on the global transmission is investigated by means of iteration order, homothetic dimension and layer orientations. The propagation is described by the stiffness matrix algorithm. The results reveal that the homothetic dimension scales the resonance frequencies and the frequency ranges of the pseudo band gaps, and that layer orientation influences the speed of quasi-transverse waves to enhance the effect of self-similarity. Finally, an extensive study on various frequency ranges is conducted. It is demonstrated that self-similarity may be used to tune the position and the width of the pseudo band gaps to minimize the global acoustic transmission.

Fast Calculation of Scattering by 3-D Inhomogeneities in Uniaxial Anisotropic Multilayers

A fast algorithm to calculate the response of uniaxial layered media on a rectilinear mesh is proposed in order to handle scattering phenomena due to inhomogeneities within them. The uniaxial layered media are with their optical axes parallel to the interfaces of the layered structure. The generalized Poisson summation formula is used to efficiently calculate the discrete Fourier transform of spatial responses of the layeredmedia from its continuous Fourier spectrum. Using the windowing technique, the integral involved in constructing the discrete Fourier spectrum can be performed in a small domain without compromising the accuracy of the result. Furthermore, a fast numerical integration method based on the recently proposed Padua points is used, which, together with the windowing technique, yields a fast solution to such scattering problems. Numerical simulations illustrate the accuracy and efficiency of the proposed algorithm.