Layer Of Finite Thickness Research Articles

Fatigue Wear Modeling of Elastomers

This study presents modeling results on fatigue wear of elastomers. A contact problem solution has been derived for the sliding of a system of asperities over a viscoelastic half-space. The mechanical properties of the viscoelastic half-space are described by relations between stresses and strains given by the Volterra integral operator. The contact problem is solved by the boundary element method using an iterative procedure. Stresses in the subsurface layers of the viscoelastic material are analyzed. The damage function of the surface layer is calculated using a reduced stress criterion, the parameters of which are determined on the basis of available experimental data. The wear process is studied under the assumption that the accumulated damage can be summed up. Within the applied frictional interaction model, the wear process presents the delamination of material surface layers of finite thickness at discrete points in time and continuous surface wear by fatigue mechanism. A model calculation of contact fatigue damage accumulation has shown that the time to the first material delamination (incubation period) depends on the sliding velocity and the viscoelastic properties of the material. By analyzing the dependence of the wear rate on the input parameters of the problem, it was investigated how the sliding velocity affects the time of fatigue damage initiation and the run-in and steady-state wear rates in materials with different rheological properties. Model calculations revealed that the wear rate of material surface layers after the incubation period increases smoothly and then stabilizes. The presence of the steady-state wear rate agrees well with experimental data. The developed method for studying fatigue damage accumulation in the surface layers of viscoelastic materials in frictional interaction can also be applied on the macrolevel to determine possible crack initiation sites.

One-way mixing of collinear waves in an adhesive layer

This paper studies the one-way collinear mixing of a pair of longitudinal and shear waves in an adhesive layer. The objective is to establish a theoretical framework for developing ultrasonic methods for nondestructively characterizing adhesive bonds by using only one side of the adhesive joint. The adhesive joint is modeled as a nonlinear elastic layer embedded in a linear elastic matrix of infinite extent. First, a solution is developed for the general case where the elastic impedance of the layer is different from that of the surrounding matrix. Then, a nonlinear spring model is developed that yields a reduced order solution for the one-way collinear wave mixing problem at hand. It is shown that in the limit of vanishing layer thickness, the solution to a layer of finite thickness reduces to that of the spring model, provided that a proper relationship is used between the properties of the nonlinear layer and the nonlinear spring. In other words, a very thin layer can be effectively replaced by a nonlinear spring. Finally, numerical analyses show that such effective replacement is valid when the layer thickness is less than a few percent of the shortest wavelength used in the measurement.

Improvement of Calculation of Stresses in the Earth Bed and Layers of Road Clothes from Granulated Materials. Part 1. Analysis of Decisions and a New Method

The bases of road clothes made of discrete materials have become widespread in the practice of building roads throughout the world. Experimental studies of various loads have shown that an adequate calculation of stresses by formulas in the mechanics of a continuous medium is practically impossible. The article presents a method for modifying stress calculation models, the application of which allows supplementing the solutions of granular medium mechanics and engineering methods with dependencies for calculating the minimum main stress σ3. Following this method, some solutions have been modified, and modified models are given. These models make it possible to calculate the main stresses in a layer of finite thickness in the section on the axis of symmetry of the load distributed along the circular platform. In accordance with this method, in the section along the axis of symmetry of the load at the point z=0 compression pressure occurs, that is ε2=ε3=0. Within the limits of depth change 0<z<∞ the soil operates under conditions of triaxial compression, experiencing lateral expansion strains ε2=ε3<0. At the point z=∞ the ground undergoes uniaxial compression σ2=σ3=0 and ε2=ε3=−μ·ε1.

Numerical modelling of wave scattering by local inhomogeneities in elastic waveguides embedded into infinite media

This paper proposes a numerical method to model wave scattering by local inhomogeneities in elastic open waveguides. The damaged zone of the waveguide and its vicinity are described by a finite-element model. This model is coupled on the cross-section boundaries to a modal representation of the field propagating along the waveguide axis in the undamaged parts, yielding transparent boundary conditions. However, open waveguides are unbounded in the transverse direction, which complicates both the numerical resolution and the physical analysis. Theoretically, the wave fields are described by a discrete sum of trapped modes and two continuous sums on radiation modes. The latter is sometimes approximated by a discrete sum of leaky modes, which grow at infinity in the transverse direction. In this paper, a Perfectly Matched Layer (PML) of finite thickness is introduced to absorb outgoing waves in the transverse direction, yielding three types of discrete modes: trapped modes, leaky modes and PML modes (PML modes oscillate mainly inside the layer and are non-intrinsic to the physics). Two numerical test cases are considered: the scattering at the junction between a closed and an open cylindrical waveguides and the scattering by an axisymmetrical notch. Good agreement with literature results is found. In particular, the influence of PML modes on the scattered field is highlighted through numerical tests. Due to the lack of power orthogonality of leaky modes, it is also shown that the modal cross power can become significant, which complicates the scattering analysis of open waveguides. Finally, the generality of the proposed method is discussed through a three-dimensional test case considering an embedded bar with an oblique break.

Three-dimensional instabilities and negative eddy viscosity in thin-layer flows

The stability of flows in layers of finite thickness H is examined against small-scale three-dimensional (3D) perturbations and large-scale two-dimensional (2D) perturbations. The former provide an indication of a forward transfer of energy while the latter indicate an inverse transfer and the possibility of an inverse cascade. The analysis is performed using a Floquet-Bloch code that allows examination of the stability of modes with arbitrary large-scale separation. For thin layers, the 3D perturbations become unstable when the layer thickness H becomes larger than H>c1(νℓU/U)1/2=c1ℓURe−1/2, where U is the rms velocity of the flown, ℓU is the correlation length scale of the flow, ν is the viscosity, and Re=ℓUU/ν is the Reynolds number. At the same time, large-scale 2D perturbations also become unstable by an eddy viscosity mechanism when Re>c2, where c1,c2 are order 1 nondimensional numbers. These relations define different regions in parameter space where 2D and 3D instabilities can (co)exist and this allows us to construct a stability diagram. Implications of these results for fully turbulent flows that display a change of direction of cascade as H is varied are discussed.3 MoreReceived 1 June 2018DOI:https://doi.org/10.1103/PhysRevFluids.3.114601©2018 American Physical SocietyPhysics Subject Headings (PhySH)Research AreasFlow instabilityTurbulenceFluid Dynamics

Effect of initial stress on the propagation and attenuation characteristics of Rayleigh waves

The present investigation deals with the mathematical modelling and analytical thinking to uncover the various facets of the propagation of Rayleigh waves in an Earth’s crustal layer. This work has been carried out when the wave is passing through a pre-stressed anisotropic layer of finite thickness, lying over a semi-infinite medium with void pores. The upper boundary plane of the crustal layer has been thought to be a free surface. Displacement components of the wave for both the media have been derived analytically. Appropriate boundary conditions have been well satisfied with the aid of displacement and stress factors in order to get the desired dispersion relation. A comparative study has been performed graphically taking anisotropic, orthotropic and isotropic strata, in order to show the impact of initial stress and thickness on the propagation characteristics of Rayleigh waves. The present work may establish a program to connect theoretical results with subject area applications.

Thermodynamics and kinetics of nucleation in binary solutions

A new approach that is a combination of classical thermodynamics and macroscopic kinetics is offered for studying the nucleation kinetics in condensed binary solutions. The theory covers the separation of liquid and solid solutions proceeding along the nucleation mechanism, as well as liquid-solid transformations, e.g., the crystallization of molten alloys. The cases of nucleation of both unary and binary precipitates are considered. Equations of equilibrium for a critical nucleus are derived and then employed in the macroscopic equations of nucleus growth; the steady state nucleation rate is calculated with the use of these equations. The present approach can be applied to the general case of non-ideal solution; the calculations are performed on the model of regular solution within the classical nucleation theory (CNT) approximation implying the bulk properties of a nucleus and constant surface tension. The way of extending the theory beyond the CNT approximation is shown in the framework of the finite-thickness layer method. From equations of equilibrium of a surface layer with coexisting bulk phases, equations for adsorption and the dependences of surface tension on temperature, radius, and composition are derived. Surface effects on the thermodynamics and kinetics of nucleation are discussed.

Surface Pressure of Charged Colloids at the Air/Water Interface.

Charged colloidal monolayers at the interface between water and air (or oil) are used in a large number of chemical, physical, and biological applications. Although considerable experimental and theoretical effort has been devoted in the past few decades to the investigation of such monolayers, some of their fundamental properties are not yet fully understood. In this article, we model charged colloidal monolayers as a continuum layer of finite thickness, with a separate charge distribution on the water and air sides. The electrostatic surface free energy and surface pressure are calculated via the charging method and within the Debye-Hückel approximation. We obtain the dependence of surface pressure on several system parameters: the monolayer thickness, its distinct dielectric permittivity, and the ionic strength of the aqueous subphase. The surface pressure scaling with the area per particle, a, is found to be between a-2 in the close-packing limit and a-5/2 in the loose-packing limit. In general, it is found that the surface pressure is strongly influenced by charges on the air side of the colloids. However, when the larger charge resides on the water side, a more subtle dependence on salt concentration emerges. This corrects a common assumption that the charges on the water side can always be neglected due to screening. Finally, using a single fit parameter, our theory is found to fit the experimental data well for strong- to intermediate-strength electrolytes. We postulate that an anomalous scaling of a-3/2, recently observed in low ionic concentrations, cannot be accounted for within a linear theory, and its explanation requires a fully nonlinear analysis.

Design and Performance of a Single Axis Shake Table and a Laminar Soil Container

Correct evaluation of shear modulus and damping characteristics in soils under dynamic loading is one of the most important topics in geotechnical engineering. Shaking tables are used for physical modelling in earthquake geotechnical engineering and is key to the fundamental understanding and practical application of soil behaviour. The shaking table test is realistic and clear when the response of geotechnical problems such as liquefaction, post-earthquake settlement, foundation response and soil-structure interaction and lateral earth pressure problems, during an earthquake is discussed. This paper describes various components of the uniaxial shaking table at university of Guilan, Iran. Also, the construction of the laminar shear box is described. A laminar shear box is a flexible container that can be placed on a shaking table to simulate vertical shear-wave propagation during earthquakes through a soil layer of finite thickness. Typical model tests on sandy soil conducted on the shaking table and the results obtained are also presented. Appropriate evaluation of shear modulus and damping characteristics of soils subjected to dynamic loading is key to accurate seismic response analysis and soil modelling programs. The estimated modulus reduction and damping ratio were compared to with Seed and Idriss’s benchmark curves.

Kelvin–Helmholtz instability of two finite-thickness fluid layers with continuous density and velocity profiles

The effect of density and velocity gradients on the Kelvin–Helmholtz instability (KHI) of two superimposed finite-thickness fluid layers are analytically investigated. The linear normalized frequency and normalized growth rate are presented. Then, their behavior as a function of the density ratio of the light fluid to the heavy one (r) was analyzed and compared to the case of two semi-infinite fluid layers. The results showed that the values of normalized frequency of KHI for two finite-thickness fluid layers are less than their counterparts for two semi-infinite fluid layers. The behavior of normalized growth rate as a function of the velocity and density gradients capitulates to the effect of velocity gradient at the large values of (r).

Reflection and Transmission of P-Waves in an Intermediate Layer Lying Between Two Semi-infinite Media

With a motivation to gain physical insight of reflection as well as transmission phenomena in frozen (river/ocean) situation for example in Antarctica and other coldest place on Earth, the present article undertakes the analysis of reflection and transmission of a plane wave at the interfaces of layered structured comprised of a water layer of finite thickness sandwiched between an upper half-space constituted of ice and a lower isotropic elastic half-space, which may be useful in geophysical exploration in such conditions. A closed form expression of reflection/transmission coefficients of reflected and transmitted waves has been derived in terms of angles of incidence, propagation vector, displacement vector and elastic constants of the media. Expressions corresponding to the energy partition of various reflected and transmitted waves have also been established analytically. It has been remarkably shown that the law of conservation of energy holds good in the entire reflection and transmission phenomena for different angles of incidence. A numerical examples were performed so to graphically portray the analytical findings. Further the deduced results are validated with the pre-established classical results.

Love-type wave propagation in a hydrostatic stressed magneto-elastic transversely isotropic strip over an inhomogeneous substrate caused by a disturbance point source

Propagation of Love-type waves emanating due to a disturbance point source in a transversely isotropic layer of finite thickness laid over a semi-infinite half-space is investigated. The layer is assumed under the influence of magnetic field and hydrostatic state of stress, while the half-space is inhomogeneous. The source point is situated at the common interface of the layer and half-space. Maxwell’s equation and generalized Ohm’s law have been taken into account to calculate the Laurent force induced in the layer. Green’s function technique and Fourier transform are used as a powerful tool to calculate the interior deformations of the model; consequently, we obtain a closed-form dispersion relation for the wave. Six numerical examples for the transversely isotropic layer, namely, beryl, magnesium, cadmium, zinc, cobalt, and simply isotropic, have been considered. The role of magneto-elastic coupling parameter, hydrostatic stress, inhomogeneity, the order of the depth variation in inhomogeneity function, and different examples of the layer on the propagation of Love-type wave has been observed by numerical examples and graphical demonstrations.

Thickness shear vibration of a ZnO film structure covered with magnetic fluid

This paper aims to reveal the effect of magnetic liquid on the resonant frequency shift and the output impedance. For this purpose, a thin film sensor was designed with a finite-thickness layer of magnetic fluid, and the thickness shear vibration of the film was analysed in details. The main findings are as follows. First, the relative resonance frequency is positively correlated with the intensity of magnetic field, and the viscosity coefficient, density and volume fraction of magnetic fluid. The effect of magnetic field on the shift of the relative resonant frequency depends on various parameters of magnetic liquid. With the increase of the volume fraction, density and viscosity coefficient, the resonant frequency plunges, but the output impedance peak grows in size. Therefore, the relative resonant frequency shift and the output impedance are sensitive to various parameters in the design. The research findings shed new light on the application of thin piezoelectric film in sensors.

Selectively enhanced near-field radiative transfer between plasmonic emitter and GaSb with nanohole and nanowire periodic arrays for thermophotovoltaics

To design a nano-gap thermophotovoltaic device with selectively enhanced radiative transfer above the cell’s bandgap, this work theoretically investigated the near-field radiative transfer from a plasmonic Drude emitter to a nanostructured GaSb absorber, with a finite-thickness surface layer of nanowire or nanohole arrays, across a 200 nm vacuum gap. The Fourier Modal method (FMM) is used to rigorously characterize the radiative transfer involving diffractive periodic structures. The results showed that the added nanostructure, especially nanowires, effectively and selectively enhanced the near-field radiative transfer above the bandgap, with a maximum of three times the spectral radiative heat flux when compared to the unstructured GaSb case. By considering periodic structures in two dimensions, this work revealed the difference between the nanowire and nanohole absorbers in manipulating of the radiative heat flux, showing that the nanowire array offers largely enhanced radiative heat transfer compared with the nanohole arrays with similar geometric parameters, which cannot be quantitatively characterized by effective medium theories even though the structural size is much smaller than the studied wavelength. The results proved that nanohole and nanowire structures can be used to significantly enhance the power and efficiency of a nano-gap thermophotovoltaic device, for which the equivalent of anti-reflection structures of the semiconductor cells have seldom been studied.

Effect of rotation on Rayleigh waves in a fiber-reinforced solid anisotropic magneto-thermo-viscoelastic media

ABSTRACTThe present paper deals with the of Rayleigh surface waves in fiber-reinforced solid anisotropic magneto-thermo-viscoelastic media, a pre-stressed elastic layer of finite thickness over a homogeneous, pre-stressed elastic half – space subjected to the rotation. The dispersion equation in closed form is derived for a layer over a half-space, when both media are considered as pre-stressed and the effect of rotation shown in earlier investigators, is in general not applicable to the case of pre-stressed media. In order to illustrate the analytical developments, Numerical simulated results are depicted graphically to show the effect of rotation and magnetic field on resulting quantities. Comparison was made with the results obtained in the presence and absence of the rotation and magnetic field. The study shows that there is a variation effect of magneto-thermoelasticity and rotation on the Rayleigh wave velocity. Some special cases are also deduced from the present investigation.

Thin layer model for nonlinear evolution of the Rayleigh-Taylor instability

On the basis of the thin layer approximation [Ott, Phys. Rev. Lett. 29, 1429 (1972)], a revised thin layer model for incompressible Rayleigh-Taylor instability has been developed to describe the deformation and nonlinear evolution of the perturbed interface. The differential equations for motion are obtained by analyzing the forces (the gravity and pressure difference) of fluid elements (i.e., Newton's second law). The positions of the perturbed interface are obtained from the numerical solution of the motion equations. For the case of vacuum on both sides of the layer, the positions of the upper and lower interfaces obtained from the revised thin layer approximation agree with that from the weakly nonlinear (WN) model of a finite-thickness fluid layer [Wang et al., Phys. Plasmas 21, 122710 (2014)]. For the case considering the fluids on both sides of the layer, the bubble-spike amplitude from the revised thin layer model agrees with that from the WN model [Wang et al., Phys. Plasmas 17, 052305 (2010)] and the expanded Layzer's theory [Goncharov, Phys. Rev. Lett. 88, 134502 (2002)] in the early nonlinear growth regime. Note that the revised thin layer model can be applied to investigate the perturbation growth at arbitrary Atwood numbers. In addition, the large deformation (the large perturbed amplitude and the arbitrary perturbed distributions) in the initial stage can also be described by the present model.

Finite Element Analysis of the Void Growth and Interface Failure of Ductile Adhesive Joints

Progressive failure of ductile porous adhesive joint generally includes two competitive failure modes: the void growth of ductile adhesive layer and the interface debonding between the adhesive layer and bonding plates. The damage evolution behavior and ultimate strength of ductile adhesive joint are largely dominated by their evolving interactions. However, most of the existing research failed to predict the damage evolution of these two failure modes simultaneously. After the variational weak form of dynamic equilibrium for two adhesive solids with a finite-thickness adhesive layer and two discontinuous cohesive interfaces is given, this paper studies theoretically the competition between these two failure modes using explicit finite element analysis (FEA). The finite-deformation Gurson–Tvergaard–Needleman (GTN) model is used to predict the void growth of adhesive layer, and the bilinear cohesive model as a ABAQUS module is used to simulate the interface debonding. For single-lap joint under tensile loads, effects of the cohesive strengths, the initial void volume fraction, and the thickness of adhesive layer on their interactions are explored. Besides, the ultimate strengths by FEA are also compared with analytical solutions. Numerical results show that dominating failure mode changes from the interface debonding to the failure of adhesive layer at about the cohesive strength 40 MPa and the thickness of adhesive layer 0.5 mm for FM-73 ductile adhesive joint.

Dispersion of Rayleigh Waves in a Microstructural Couple Stress Substrate Loaded with Liquid Layer Under the Effects of Gravity

Bone loss is one of the serious health issues in bedridden patients or young generation due to lack of physical activities. Mechanical forces are exerted on the bones through ground reaction forces, liquid loadings and by other contraction activities of the muscles. We are assuming an isotropic half-space with mechanical properties equivalent to that of bone exhibiting microstructures. Consistent couple stress theory introduces an additional material parameter called characteristic length which accounts for inner microstructure of the material. Dispersion relations for leaky Rayleigh waves are derived by considering a model consisting of couple stress half space under the effects of gravity and loaded with inviscid liquid layer of finite thickness or a liquid half space. Impact of the gravity, liquid loadings and microstructures of the material are investigated on propagation of leaky Rayleigh type waves. Phase velocity of leaky Rayleigh waves is studied for five different values of characteristic length parameter which are of the order of internal cell size of the considered material. Variations in phase velocity of leaky Rayleigh waves are also studied under the effect of gravity parameter and thickness of liquid loadings.

Propagation characteristics of pseudo-Scholte waves at the interface between finite-thickness fluid layer and quasi-saturated porous half-space

The propagation of interface waves at the interface between a fluid-saturated porous medium and a fluid has been extensively investigated in the last three decades due to its various and wide applications in several fields including earthquake engineering and materials testing. Although the sea floor is usually covered with porous marine sediment, the previous interface wave theories are rarely used for submarine acoustic problems for the following reasons. 1) In addition to hard porous media, unconsolidated soft porous media exist widely in the seabed, which are seldom considered in previous studies. 2) The depth of seawater is limited, and in many cases it cannot be regarded as a half-space. 3) The fluid-saturated porous medium model cannot describe the effect of a small number of bubbles caused by decomposition of organic matter in the sediment. Hence, the present paper focuses on the low-frequency pseudo-Scholte waves at the interface between an overlying fluid layer of finite thickness and a quasi-saturated porous half-space. The overlying fluid is assumed to be ideal compressible water and the quasi-saturated porous media are assumed to be sandstone and unconsolidated sediment and modeled by Biot theory. A fluid equivalent model is used to analyze the effects of the bubbles in the pores. Based on the boundary conditions, the closed-form dispersion equations of far-field interface waves are derived by using classical potential function method. The velocity and attenuation of pseudo-Scholte wave are determined by Newton iteration in a reasonable rooting interval. The analytical expressions of the displacement field and fluid pressure distribution caused by pseudo-Scholte waves are also derived. Then, based on the derived theoretical formulation, the numerical examples of calculations are presented. Our calculation results show that the stiffness of porous medium significantly affects the mode, phase velocity, displacement and fluid pressure distribution of interface waves; the phase velocity of the pseudo-Scholte wave in the finite-thickness fluid/fluid-saturated porous half-space is related to the ratio of the wavelength to the thickness of the fluid layer; the phase velocity of the shear wave is insensitive to a small number of bubbles dissolved in the pores, but the existence of bubbles has a significant influence on the phase velocity of the compressional wave and the pseudo-Scholte wave. Furthermore, the existence of bubbles can significantly affect the distribution of the pore pressure.

Numerical Simulation of Grating Structures Incorporating Two-Dimensional Materials: A High-Order Perturbation of Surfaces Framework

The plasmonics of two-dimensional materials, such as graphene, has become an important field of study for devices operating in the terahertz to midinfrared regime where such phenomena are supported. The semimetallic character of these materials permits electrostatic biasing which allows one to tune their electrical properties, unlike the noble metals (e.g., gold, silver) which also support plasmons. In the literature there are two principal approaches to modeling two-dimensional materials: With a thin layer of finite thickness featuring an effective permittivity, or with a surface current. We follow this latter approach to not only derive governing equations which are valid in the case of curved interfaces, but also reformulate these volumetric equations in terms of surface quantities using Dirichlet--Neumann operators. Such operators have been used extensively in the numerical simulation of electromagnetics problems, and we use them to restate the governing equations at layer interfaces. Beyond this, we show that these surface equations can be numerically simulated in an efficient, stable, and accurate fashion using a High-Order Perturbation of Surfaces methodology. We present detailed numerical results which not only validate our simulation using the Method of Manufactured Solutions and by comparison to results in the literature, but also describe Surface Plasmon Resonances at the “wavy” (corrugated) interface of a dielectric-graphene-dielectric structure.