Isotropic Layer Research Articles

Coupled Vibrations of Viscoelastic Three-Layer Composite Plates. 1. Formulation of the Problem

A mathematical model of damped vibrations of three-layer plates formed by two rigid anisotropic layers and a soft middle isotropic viscoelastic polymer layer is proposed in this paper. The model is based on the Hamilton’s variational principle, the refined theory of first-order plates, the model of complex modules, and the principle of elastic-viscoelastic correspondence in the linear theory of viscoelasticity. The frequency-temperature dependence of the elastic-dissipative characteristics is considered negligible for rigid layer materials; however, this dependence is taken into account for the viscoelastic polymer of the soft layer. By minimizing the Hamilton functional we reduce the problem of damped vibrations of anisotropic structures to the algebraic problem of complex eigenvalues. The Rietz method using the Legendre polynomials as coordinate functions is applied to form the system of algebraic equations. The real solutions are found. When determining the complex natural frequencies of the plate, real natural frequencies obtained are used as their initial values, and then the complex frequencies are calculated by the third-order iteration method. The results of the study of the convergence of the numerical solution are discussed. The estimation of reliability of the mathematical model and the numerical solution method obtained by comparing the calculated and the experimental values of natural frequencies and loss factors is presented.

Axisymmetric Wave Propagation in Functionally Grade Cylinder with Isotropic Concentric Layers

The axisymmetric wave propagation is investigated in coaxially layered isotropic functionally graded cylinders with different mass and stiffness properties of the layers. Exact solutions of the governing equations of the wave propagation in the cylinders exist only for isotropic, transversely isotropic and piezoelectric transversely isotropic cylinders. In the case of the functionally graded cylinders exact solutions are not known. The authors developed a method of exact solution of the problem, which is based on matching of continuity and boundary conditions on junctions of the layers. The continuity and boundary conditions are formulated in terms of exact solutions for displacements and stresses in the layers obtained in Bessel functions. The spectral diagrams of the dispersion curves of frequencies versus wave numbers are plotted for both propagating and evanescent waves and graphs of the phase and group velocities are obtained from these diagrams.

NONSTATIONARY HEAT CONDUCTION IN MULTILAYER GLAZING SUBJECTED TO DISTRIBUTED HEAT SOURCES

A method for calculation of nonstationary thermal fields in a multilayer glazing of vehicles under the effect of impulse film heat sources is offered. The glazing is considered as a rectangular multilayer plate made up of isotropic layers with constant thickness. Film heat sources are arranged on layers' interfaces. The heat conduction equation is solved using the Laplace transformation, series expansion and the second expansion theorem. The method offered can be used for designing a safe multilayer glazing under operational and emergency thermal and force loading in vehicles.

Асимптотическое поведение решения осесимметричной динамической задачи теории упругости для трансверсально-изотропного сферического слоя малой толщины

In this paper, we study the axisymmetric dynamic problem of the theory of elasticity for the transversely isotropic spherical layer of small thickness that does not contain any of the poles 0 and π. It is assumed that the lateral surface of the sphere is free of stresses, and boundary conditions are set on conical sections. Using the method of asymptotic integration of equations of the theory of elasticity, the dynamic problem of this theory is analyzed for the transversely isotropic spherical layer as the thin-walled parameter tends to zero. A possible form of wave formation in the transversely isotropic spherical layer has been studied depending on the frequency of the influencing forces. Homogeneous solutions are constructed and their classification is given. Asymptotic expansions of the homogeneous solutions are obtained, which make possible to calculate the stress-strain state for various values of the frequency of the influencing forces. It is shown that for the high-frequency oscillations in the first term of the asymptotics, the dispersion equation coincides with the well-known Rayleigh-Lamb equation for the elastic band. In the general case of loading on the sphere using the Hamilton variational principle, the boundary-value problem is reduced to the solving infinite systems of linear algebraic equations.

Heat dissipation model and temperature distribution of Yb-doped double-clad fiber in the composite system

Abstract To address the thermal effect of 3000 W Yb-doped double-clad fiber (YDCF), a double-layer substrate is designed to encapsulate a high power fiber laser. A thermal resistance model is proposed where the contact between the layers is ideal, and the thermal conductivity and thickness, as well as the position of the additional layer, are considered. The axial temperature of the fiber is the lowest, and the temperature uniformity the best, in an Hm-Al system. In addition, the thermal resistance model is also established where the contact between the layers is nonideal. The influence of the interfacial heat transfer coefficient and the thickness of the isotropic and orthotropic layers on the temperature distribution of the fiber are considered. The average temperature of the fiber is the lowest, and the temperature uniformity the best, in an Iso-Ortho system. Numerical simulations are used to verify the two thermal resistance models. The results show that the trend of the change in the analytical value is consistent with that of the simulation value. These thermal resistance models are reasonable and accurate and can be used to analyze more complex fiber laser packaging structures.

Cracked elastic layer with surface elasticity under antiplane shear loading

A mode-III crack embedded in a homogeneous isotropic elastic layer of nanoscale finite thickness is studied in this article. The classical elasticity incorporating surface elasticity is employed to reduce a nonclassical mixed boundary value problem, where the layer interior obeys the traditional constitutive relation and the surfaces of the layer and the crack are dominated by the surface constitutive relation. Using the Fourier transform, we convert the problem to a hypersingular integro-differential equation for the out-of-plane displacement on the crack faces. By expanding the out-of-plane displacement as series of Chebyshev polynomials, the Galerkin method is invoked to reduce the singular integro-differential equation with Cauchy kernel to a set of algebraic linear equations for the unknown coefficients. An approximate solution is determined, and the influences of surface elasticity on the elastic field and stress intensity factor are examined and displayed graphically. It is shown that surface elasticity decreases the bulk stress and its intensity factor near the crack tips for positive surface shear modulus and gives rise to an opposite trend for a negative surface shear modulus.

Switchable Lens Design for Multi-View 2D/3D Switching Display with Wide-Viewing Window

We improved the three-dimensional (3D) crosstalk level of multi-view 3D displays using a lens array with small f-number, thereby facilitating a wide 3D viewing window. In particular, we designed a polarization-dependent-switching liquid crystal (LC)-based gradient refractive index (GRIN) lens array that could be switched between 2D and 3D viewing modes. For the GRIN lens with a small f-number (1.08), we studied the effect of the interfacial curvature between the plano-concave isotropic polymer layer and the plano-convex birefringent LC layer on the aberration properties. We examined the conventional spherical, quadratic polynomial aspherical, and a high-order (fourth-order) polynomial aspherical curvature. For the high-order polynomial aspherical curvature, the achievable transverse spherical aberration (TSA = 10.2 µm) was considerably lower than that with the spherical (TSA = 100.3 µm) and quadratic polynomial aspherical (TSA = 30.4 µm) curvatures. Consequently, the angular luminance distributions for each view were sharper for the high-order polynomial interfacial curvature. We designed multi-view (43-view) 3D displays using the arrays of switchable LC lenses with different curvatures, and the average adjacent crosstalk levels within the entire viewing window (50°) were 68.5%, 73.3%, and 60.0% for the spherical, quadratic polynomial aspherical, and high-order polynomial aspherical curvatures, respectively.

Influence of concrete age on the behavior of ultrasonic waves in interfaces (concrete–steel–concrete)

This paper presents the influence of the composite age on the variation of the transmission and reflection coefficients. The composite is the concrete in our case. The studied structure is a multilayer structure composed of two elastic and isotropic layers where each one is characterized by its own physical properties. The problem is simplified in two-dimensional plane waves, and the influence of the attack angle on the acoustic impedances is also examined. Moreover, an experimental study is realized in the formulation of concrete and the measurement of waves propagation velocity. In this work, during the concrete formulation, three different types of concrete were developed: sand concrete, ordinary concrete, and high-performance concrete. The results of simulation and experiments demonstrate that the age of concrete and the internal concrete structure have a direct influence on the evolution of the acoustic parameters as well as the angle of incidence, which has considerably changed the behavior of the transmission and reflection coefficients. This internal structure is directly related to the age of the concrete where its maturity is not reached until after a certain age, which influences the behavior of the waves through the layers of the multilayer structure.

An analytical study of transient thermo-viscoelastic responses of viscoelastic laminated sandwich composite structure for vibration control

Viscoelastic laminated sandwich composite structure has been used as a new class of high-efficient structural damping in the passive vibration control systems. This work aims to investigate transient thermo-viscoelastic responses of viscoelastic laminated sandwich composite structure. The effects of fractional order parameters and material constants ratio on the structural transient thermo-viscoelastic responses are evaluated and discussed. For each homogeneous isotropic layer, the governing equations are formulated and solved by Laplace transformation techniques. The results are expected to provide new insights on the vibration control and thermal management of viscoelastic laminated sandwich composite structure under extreme non-isothermal conditions.

Second-harmonic generation of two-dimensional elastic wave propagation in an infinite layered structure with nonlinear spring-type interfaces

The two-dimensional elastic wave propagation in an infinite layered structure with nonlinear interlayer interfaces is analyzed theoretically to investigate the second-harmonic generation due to interfacial nonlinearity. The structure consists of identical isotropic linear elastic layers that are bonded to each other by spring-type interfaces possessing identical linear normal and shear stiffnesses but different quadratic nonlinearity parameters. Explicit analytical expressions are derived for the second-harmonic amplitudes when a single monochromatic Bloch mode propagates in the structure in arbitrary directions by applying the transfer-matrix approach and the Bloch theorem to the governing equations linearized by a perturbation method. The second-harmonic generation by a single nonlinear interface and by multiple consecutive nonlinear interfaces are shown to be profoundly influenced by the band structure of the layered structure, the fundamental Bloch wave mode, and its propagation direction. In particular, the second harmonics generated at multiple consecutive interfaces are found to grow cumulatively with the propagation distance when the phase matching occurs between the Bloch modes at the fundamental and double frequencies.

Hybrid Self-Reinforced Composite Materials Based on Ultra-High Molecular Weight Polyethylene.

The properties of hybrid self-reinforced composite (SRC) materials based on ultra-high molecular weight polyethylene (UHMWPE) were studied. The hybrid materials consist of two parts: an isotropic UHMWPE layer and unidirectional SRC based on UHMWPE fibers. Hot compaction as an approach to obtaining composites allowed melting only the surface of each UHMWPE fiber. Thus, after cooling, the molten UHMWPE formed an SRC matrix and bound an isotropic UHMWPE layer and the SRC. The single-lap shear test, flexural test, and differential scanning calorimetry (DSC) analysis were carried out to determine the influence of hot compaction parameters on the properties of the SRC and the adhesion between the layers. The shear strength increased with increasing hot compaction temperature while the preserved fibers’ volume decreased, which was proved by the DSC analysis and a reduction in the flexural modulus of the SRC. The increase in hot compaction pressure resulted in a decrease in shear strength caused by lower remelting of the fibers’ surface. It was shown that the hot compaction approach allows combining UHMWPE products with different molecular, supramolecular, and structural features. Moreover, the adhesion and mechanical properties of the composites can be varied by the parameters of hot compaction.

Numerical modeling of wave propagation in anisotropic viscoelastic laminated materials in transient regime: Application to modeling ultrasonic testing of composite structures

SummaryComposite laminate structures remain an important family of materials used in cutting‐edge industrial areas. Building efficient numerical modeling tools for high‐frequency wave propagation in order to represent ultrasonic testing experiments of these materials remains a major challenge. In particular, incorporating attenuation phenomena within anisotropic plies, and thin intermediate isotropic layers between the plies often represent significant obstacles for standard numerical approaches. In our work, we address both issues by proposing a systematic study of the fully discrete propagators associated to the Kelvin‐Voigt, Maxwell, and Zener models, and by incorporating effective transmission conditions between plies using the mortar element method. We illustrate the soundness of our approach by proposing intermediate one‐dimensional and two‐dimensional numerical evidence, and we apply it to a more realistic configuration of a curved laminate composite structure in a three‐dimensional setting.

Alternative Solutions for Consolidation Problems in Isotropic Clay Stratum Using Laplace Heaviside’s Theorem

This study offers an alternative analytical solution, for one and two-dimensional consolidation problem, for functionally-homogenous isotropic clay layer. The fundamental analytical solution presented in this study is derived based on the Laplace transform which eliminates the time-dependent and Heaviside's inversion theorem to extract the inverse. The alternative solutions have been derived based on the governing available fundamental consolidation equations solution. The derived solutions have shown good estimation with the exact solution. The two dimensions of isotopic permeability expressed significant influence on the accumulated excess pore water pressure and approximate time for full consolidation. The analytical solution shows identical results with the numerical one.

Designing anisotropic microstructures with spectral density function

Materials’ microstructure is a critical aspect in design of functional materials as it links processing conditions to material performance. Previous efforts on microstructure mediated design mostly assume isotropy, which is not ideal for applications where material properties along specific directions must be tailored to meet performance requirements, such as those associated with transport phenomena. In this article, we propose an anisotropic microstructure design strategy that leverages Spectral Density Function (SDF) for rapid reconstruction of high resolution, two phase, isotropic or anisotropic microstructures in 2D and 3D. We demonstrate that SDF microstructure representation provides an intuitive method for quantifying anisotropy through a dimensionless scalar variable termed anisotropy index. The computational efficiency and low dimensional microstructure representation enabled by our method is demonstrated through an active layer design case study for Bulk Heterojunction Organic Photovoltaic Cells (OPVCs). Results indicate that optimized design, exhibiting strong anisotropy, outperforms isotropic active layer designs.

Dynamic response of an irregular heterogeneous anisotropic poroelastic composite structure due to normal moving load

The present study is concerned with the dynamic response of an anisotropic composite structure due to a normal moving load on its irregular rough surface. The composite structure is comprised of an irregular incompressible heterogeneous transversely isotropic fluid-saturated poroelastic layer lying over a transversely isotropic substrate. The mathematical formulation of this structure gives rise to a boundary value problem with specified boundary conditions, and the perturbation method has been used to tackle the irregular surface problem. The expressions for the induced shear and normal stresses in layer and substrate of the composite structure are derived analytically in closed form due to the moving load. As a special case of the problem, the deduced expressions of the induced stresses are validated with the pre-established and standard results. The effect of several substantial parameters such as vertical depth, heterogeneity parameter, porosity parameter, frictional coefficient, irregularity depth, and irregularity factor on the induced shear as well as normal stresses of the layer and substrate has been delineated graphically by the numerical computation. Moreover, a comparative study of the various types of irregularity, namely rectangular irregularity, parabolic irregularity and no irregularity (regular boundary surface) on the induced shear and normal stresses in the layer and, substrate, is carried out by means of graphs, and some considerable peculiarities are outlined.

The Eshelby problem of the confocal N-layer spheroid with imperfect interfaces and the notion of equivalent particle in thermal conduction

The solution to the generalized conduction Eshelby problem of a confocal N-layer spheroid with low or highly conducting interfaces between isotropic layers is provided thanks to a decomposition in series of harmonics. A generic workflow is detailed for practical numerical implementation including a fine analysis to assess the influence of the level of truncation of the infinite series. The case of perfect interfaces presents a particular interest insofar as it is characterized by an equivalent conductivity tensor obtained from a recursive procedure. The notion of equivalent conductivity is then investigated and applied to a uniform spheroid surrounded by an imperfect interface. Some approximated models are developed, either based on a surface description of the interface or on a thin interphase, casting a new light on published models and proposing a unified framework for new ones. These approximated models are finally analyzed by comparison to the exact solution.

Plasmonically induced transparency in in-plane isotropic and anisotropic 2D materials.

General two-dimensional (2D) material-based systems that achieve plasmonically induced transparency (PIT) are limited to isotropic graphene only through unidirectional bright-dark mode interaction. Moreover, it is challenging to extend these devices to anisotropic 2D films. In this study, we exploit surface plasmons excited at two crossed grating layers, which can be formed either by dielectric gratings or by the 2D sheet itself, to achieve dynamically tunable PIT in both isotropic and anisotropic 2D materials. Here, each grating simultaneously acts as both bright and dark modes. By taking isotropic graphene and anisotropic black phosphorus (BP) as proofs of concept, we reveal that this PIT can result from either unidirectional bright-dark or bidirectional bright-bright and bright-dark mode hybridized couplings when the incident light is parallelly/perpendicularly or obliquely polarized to the gratings, respectively. Identical grating parameters in isotropic (crossed lattice directions in anisotropic) layers produce polarization-independent single-window PIT, whereas different grating parameters (coincident lattice directions) yield polarization-sensitive double-window PIT. The proposed technique is examined by a two-particle model, showing excellent agreement between the theoretical and numerical results. This study provides insight into the physical mechanisms of PIT and advances the applicability and versatility of 2D material-based PIT devices.

A Novel Dry Selective Isotropic Atomic Layer Etching of SiGe for Manufacturing Vertical Nanowire Array with Diameter Less than 20 nm.

Semiconductor nanowires have great application prospects in field effect transistors and sensors. In this study, the process and challenges of manufacturing vertical SiGe/Si nanowire array by using the conventional lithography and novel dry atomic layer etching technology. The final results demonstrate that vertical nanowires with a diameter less than 20 nm can be obtained. The diameter of nanowires is adjustable with an accuracy error less than 0.3 nm. This technology provides a new way for advanced 3D transistors and sensors.

Thermal etching of AlF3 and thermal atomic layer etching of Al2O3

Thermal etching of AlF3 with dimethyl-aluminum chloride (DMAC) and thermal isotropic atomic layer etching (ALE) of Al2O3 with alternating anhydrous hydrogen fluoride (HF) and DMAC steps were studied. DMAC vapor etches AlF3 spontaneously at substrate temperatures above 180 °C. The thermal etching reaction of AlF3 with DMAC exhibited no self-limitation and showed a linear dependence on DMAC pressure. The authors determined an activation energy of 1.2 eV for this reaction. When Al2O3 is fluorinated, DMAC removes the fluorinated layer partially. The etch amount per cycle (EPC) in thermal isotropic ALE of Al2O3 with HF/DMAC is primarily determined by the fluorination step placing significant importance on its design. Fluorination with HF gas was found to be more effective and repeatable than with NF3. Plasma fluorination is faster and provides higher EPC, but the selectivity to Si3N4 or SiO2 mask materials is compromised. For pressures between 10 and 110 mTorr and a substrate temperature of 250 °C, thermal ALE of Al2O3 with HF/DMAC was found to have a very high selectivity to SiO2 and amorphous silicon. HfO2, however, etched with similar EPC as Al2O3.

Symmetry Breakdown in Franckeite: Spontaneous Strain, Rippling, and Interlayer Moiré.

Franckeite is a naturally occurring layered mineral with a structure composed of alternating stacks of SnS2-like and PbS-like layers. Although this superlattice is composed of a sequence of isotropic two-dimensional layers, it exhibits a spontaneous rippling that makes the material structurally anisotropic. We demonstrate that this rippling comes hand in hand with an inhomogeneous in-plane strain profile and anisotropic electrical, vibrational, and optical properties. We argue that this symmetry breakdown results from a spatial modulation of the van der Waals interaction between layers due to the SnS2-like and PbS-like lattices incommensurability.