Nonhomogeneous Layer Research Articles

A New Finite Element Formulation for Thin Non-Homogeneous Heat-Conducting Adhesive Layers

A thin heat-conducting adhesive layer is considered in a two-dimensional approach. The material of the adhesive layer exhibits an arbitrary non-homogeneous thermal conductivity which is a function of the spatial coordinate perpendicular to the interface. Based on the weighted residual method, a new finite element formulation for a four-node, rectangular element is derived which is able to easily incorporate high conductivity gradients in the new thermal conductivity matrix. The approach is not based on any assumptions of the temperature distribution (e.g. linear or cubic) but considers that the heat flux must be constant in the case that no heat sources or sinks are present. A numerical example of a simple bonded joint illustrates the implementation into the commercial finite element code MSC.Marc due to special user subroutines. The numerical results are compared to a classical approach based on standard elements and the differences are discussed.

Nonhomogeneous Spectral Element for Wave Motion in Multilayer Systems

This contribution deals with the use of the computationally efficient spectral element technique as a means of analyzing the dynamic behavior of axisymmetric multilayer systems consisting of homogenous and nonhomogeneous material layers and subjected to a stationary but transient force. Focus is placed on the mathematical formulation and numerical verification of a nonhomogeneous spectral element for soil material. The general solution of the wave equations and the boundary value problem are achieved by triple summation over fast Fourier, Fourier–Bessel, and Frobenius series. Practical utilization of the model is presented via a numerical example, which simulates a pavement structure subjected to the dynamic action of a falling weight deflectometer test as typically utilized for pavement structural evaluation.

Formation of Viscoelastic Protein Droplets on a Chemically Functionalized Surface

Droplet formation during adsorption of the protein lactoferrin from an aqueous solution on a surface functionalized by plasma deposited poly(acrylic acid) is studied using quartz crystal microbalance and atomic force microscopy. The formation of protein droplets is particularly favored at pH values close to the isoelectric point of lactoferrin, where the molecules carry little excess charge and intermolecular attraction exceeds the molecule-surface interaction. By combining topographic data with information on the system dynamics, it is possible to describe the viscoelastic properties of the adsorbate within a quantitative model for nonhomogeneous layers.

Magnetothermoelastic transient response of a multilayered hollow cylinder subjected to magnetic and vapor fields

This paper deals with one-dimensional axisymmetric quasi-static coupled magnetothermoelastic problems subjected to magnetic and vapor fields. Laplace transform and finite difference methods are used to analyze the problems. Using the Laplace transform with respect to time, the general solutions of the governing equations are obtained in the transform domain. The solution is obtained by using the matrix similarity transformation and inverse Laplace transform. We obtain solutions for the temperature and thermal deformation distributions for a transient and steady state. It is demonstrated that the computational procedures established in this paper are capable of solving the generalized magnetothermoelasticity problem of a hollow cylinder with nonhomogeneous layers.

Modeling method for a crack problem of functionally graded materials with arbitrary properties—piecewise-exponential model

A new model, piecewise-exponential model (PE model), is developed to investigate the crack problem of the functionally graded materials (FGMs) with arbitrary properties. In the PE model, the functionally graded material is divided into some nonhomogeneous layers along the gradient direction of the properties, with each layer’s properties varying exponentially. By this way, the real material properties can be approached by a series of exponential functions. Since the real material properties are used on both surfaces of each nonhomogeneous layer, the nature of continuously varying properties of FGMs can be approached accurately. The influences of the local nonhomogeneity on the crack-tip fields can be fully considered. By using the new model, the fracture problem of a functionally graded strip with arbitrary properties and a crack vertical to the free surfaces is studied. The integral transform method, the theory of residues and the theory of singular integral equation are applied. Some representative samples with different kinds of nonhomogeneous properties are analyzed and the corresponding stress intensity factors (SIFs) are presented. It is shown that the PE mode is effective for investigating the crack problems of the FGMs with arbitrary properties.

Two-dimensional determination of dissolved iron and sulfur species in marine sediment pore-waters by thin-film based imaging. Thau lagoon (France)

A device composed of a polyacrylamide gel thin-film (18 cm high, 5 cm wide and 0.4 mm thick) and a PVC (polyvinyl chloride) film was used as a sediment probe to obtain iron and S(−II) sulfur dissolved species' distributions in sediment pore waters. A porous protective membrane was set on top of hydrogel layer. Probes were deployed in May 2003 for 24–48 h in the superficial sediment of Thau lagoon (France), in a shellfish farming area. The polyacrylamide gel layer was used as a DET (Diffusive Equilibration in Thin-films) device for 2D Fe(II) concentration determination, and as the diffusive layer of a DGT-like (Diffusive Gradients in Thin-films) device for sulfur species study. The accumulation layer of the DGT device consisted in a PVC film layer underneath the polyacrylamide layer. Iron determinations were performed by colorimetric methods with Ferrozine and imaging technique. Image acquisitions were performed with a flatbed scanner. Fe(II) concentrations were deducted from densitometry analysis of the magenta zones (ImageJ software). The calibration curve was obtained by densitometry analysis of polyacrylamide gel pieces which were equilibrated in known iron (II) concentration solutions. ΣFe distribution was performed but not quantified. Analysis of gray zones on the PVC layer provided a qualitative distribution of unidentified S(−II) dissolved compounds, related to H 2S zone for which information is obtained by classical methods (peeper and colorimetric measurements). EDX (X-ray energy dispersive spectrometry) and GIXR (Grazing-Incidence X-ray Diffraction) analyses of gray zone of this PVC layer provide evidence for FeS 2 catalyzed precipitation onto this film. Dissolved Fe(II) was mainly located near the sediment–water interface (SWI), showing a nonhomogeneous layer about 10 mm thick. Small Fe rich domains appeared deeper in the sediment and likely confirm newest paradigms in the field of sediment biogeochemistry. S(−II) species are detected from 3 to 4 cm below the SWI, with a heterogeneous spatial distribution showing a burrow-like structure.

Effect of geometrical and material parameters in nanoindentation of layered materials with an interphase

Indentation models for thin layer-substrate geometry with an interphase have been developed. The interphase can be modeled either as a nonhomogeneous layer or as a homogeneous layer. Between the two models of the interphase, contact depth and critical interfacial stresses are compared to find the effect of indentation area, film and substrate Young’s moduli, and the interphase and film thicknesses. Although contact depth is found not to be sensitive to the type of interphase model used, critical interfacial stresses are significantly different (up to 15%) for film to substrate elastic Young’s moduli ratios of more than 25. A formal sensitivity analysis based on design of experiments shows that on critical interfacial stresses, interphase to film thickness ratio and film to substrate Young’s moduli ratio has the most impact, while type of elastic moduli variation in the interphase and indentor width to film thickness ratio has the least impact.

Transient dynamic stress intensity factors around two rectangular cracks in a nonhomogeneous interfacial layer between two dissimilar elastic half-spaces under impact load

Transient dynamic stresses around two rectangular cracks in a nonhomogeneous interfacial layer sandwiched between two dissimilar elastic half-spaces are examined. The material properties vary continuously in the layer within a range from those of the upper half-space to those of the lower half-space. An incoming shock stress wave impinges perpendicular on the crack surfaces. In order to solve the problem, the interfacial layer is divided into several homogeneous layers that have different material properties. Application of Laplace and Fourier transforms reduces the problem to the solution of a pair of dual integral equations. To solve the equations, the differences in the crack surface displacements are expanded into a series of functions that vanish outside the crack. The unknown coefficients in the series are solved using the Schmidt method. The stress intensity factors are defined in the Laplace transform domain and these are inverted numerically in physical space. Numerical calculations are carried out for composite materials made of a ceramic half-space and a steel half-space.

Nondestructive Microscopic and Spectroscopic Methods for Depth Profiling of Ink Jet Prints

The binding process of printing inks on the printing substrate is one of the final phases in the creative chain of a new product formation-the print. It is not only the expected mechanism of ink drying that influences the ink distribution on the substrate surface, but also the properties of the substrate itself. Many factors, like hydrophobicity, roughness, and porosity influence the ink distribution on both coated and uncoated papers. The aim of this study was to evaluate the applicability of several nondestructive methods in the analysis of vertical and radial ink distribution on diverse ink jet prints. What are the limits and the extent of confocal Raman, ultraviolet (UV) Raman, CLSM and Fourier-transform infrared (FTIR) PAS in the analysis of ink jet ink distribution in the z direction of the print? In the experiment, both dye- and pigment-based ink jet inks were printed on different types of coated and uncoated papers. The results show a correlation between the confocal Raman and CLSM methods for depth profiling. UV Raman proved useful in the surface analysis of prints while FTIR PAS was useful for measurements at low depth in the z direction. The applied microscopic and spectroscopic methods provide a precise distinction between the upper homogeneous and the inside nonhomogeneous ink layers. Sporadic streams of deeply penetrated ink jet ink were also detected.

S15 2個の長方形き裂を有する不均質層で接合される異材半無限体の衝撃応答問題(SS(5)「渥美光」記念セッション)

S15 2個の長方形き裂を有する不均質層で接合される異材半無限体の衝撃応答問題(SS(5)「渥美光」記念セッション)

Thermal Stresses Around a Crack in a Non-Homogeneous Diffusion Layer Between a Coating Plate and an Elastic Half-Plane

ABSTRACT This article proposes a method for determining the thermal stress field around a crack in a thin non homogeneous layer located between a ceramic plate and a metallic half-plane. For these calculations, the crack surfaces are assumed to be insulated and a uniform heat flux flows perpendicular to the crack. The material properties of the layer are assumed to vary continuously from those of the ceramic plate to those of the half-plane. The Fourier transform technique is employed to transform the problem into a set of integral equations. These equations are solved by expanding the differences in the crack surface temperature and the crack surface displacements in a series of functions that are automatically zero outside the crack. The Schmidt method is then used to determine the unknown coefficients in the series. Using this procedure, the stress intensity factors are calculated numerically for several ceramic plate thickness values.

Hybrid Numerical Method Applied to Multilayered Hollow Cylinder with Time-Dependent Boundary Conditions

ABSTRACT This article deals with one-dimensional axisymmetric quasi-static coupled thermoelastic problems with time-dependent boundary conditions. Laplace transform and finite difference methods are used to analyze the problems. Using the Laplace transform with respect to time, the general solutions of the governing equations are obtained in transform domain. The solution is obtained by using the matrix similarity transformation and inverse Laplace transform. We obtain solutions for the temperature and thermal deformation distributions for a transient and steady state. It is demonstrated that the computational procedures established in this article are capable of solving the generalized thermoelasticity problem of a hollow cylinder with nonhomogeneous layers.

Stress intensity factors for a moving cylindrical crack in a nonhomogeneous cylindrical layer in composite materials

Stresses are determined for a finite cylindrical crack that is propagating with a constant velocity in a nonhomogeneous cylindrical elastic layer, sandwiched between an infinite elastic medium and a circular elastic cylinder made from another material. The Galilean transformation is employed to express the wave equations in terms of coordinates that are attached to the moving crack. An internal gas pressure is then applied to the crack surfaces. The solution is derived by dividing the nonhomogeneous interfacial layer into several homogeneous cylindrical layers with different material properties. The boundary conditions are reduced to two pairs of dual integral equations. These equations are solved by expanding the differences in the crack surface displacements into a series of functions that are equal to zero outside the crack. The Schmidt method is then used to solve for the unknown coefficients in the series. Numerical calculations for the stress intensity factors were performed for speeds and composite material combinations.

Analysis of an elliptical crack parallel to graded interfacial zone of bonded bi-materials

This paper analyzes an elliptical crack parallel to the functionally graded interfacial zone between two fully bonded solids. The functionally graded interfacial zone is treated as a nonhomogeneous solid layer with its elastic modulus varying in the thickness direction. A generalized Kelvin solution based boundary element method is employed for the calculation of the stress intensity factors associated with the three-dimensional crack problem. The elliptical crack surface is subject to either uniform normal traction or uniform shear traction. The stress intensity factors are examined by taking into account the effects of the nonhomogeneity parameter and thickness of the functionally graded interfacial zone, as well as the crack distance to the zone. The numerical results are in very good agreement with the existing solutions under degenerated conditions. These stress intensity factor values can be further used to predict the crack growth in the functionally graded materials.

Elliptical crack normal to functionally graded interface of bonded solids

This paper presents an analysis of an elliptical crack that is perpendicular to a functionally graded interfacial zone between two fully bonded solids. The functionally graded interfacial zone is treated as a non-homogeneous solid layer with its elastic modulus varying in the thickness direction. A generalized Kelvin solution based boundary element method is employed for the calculation of the stress intensity factors associated with the three-dimensional crack problem. The elliptical crack surface is subject to either uniform normal traction or uniform shear traction. The stress intensity factors are examined by taking into account the effects of the non-homogeneity parameter and thickness of the functionally graded interfacial zone, as well as the crack distance to the zone. The SIF values are further incorporated into the S-criterion for prediction of crack growth. The paper presents the most possible direction and location of the elliptical crack growth under an inclined tensile (or compressive) load. The paper further presents results of the critical external loads that would cause the elliptical crack to grow at the most possible location and along the most possible direction. The paper also examines the effects of external load direction and material and geometrical parameters on the critical loads.

Recursive geometric integrators for wave propagation in a functionally graded multilayered elastic medium

The differential equations governing transfer and stiffness matrices and acoustic impedance for a functionally graded generally anisotropic magneto-electro-elastic medium have been obtained. It is shown that the transfer matrix satisfies a linear 1st order matrix differential equation, while the stiffness matrix satisfies a nonlinear Riccati equation. For a thin nonhomogeneous layer, approximate solutions with different levels of accuracy have been formulated in the form of a transfer matrix using a geometrical integration in the form of a Magnus expansion. This integration method preserves qualitative features of the exact solution of the differential equation, in particular energy conservation. The wave propagation solution for a thick layer or a multilayered structure of inhomogeneous layers is obtained recursively from the thin layer solutions. Since the transfer matrix solution becomes computationally unstable with increase of frequency or layer thickness, we reformulate the solution in the form of a stable stiffness-matrix solution which is obtained from the relation of the stiffness matrices to the transfer matrices. Using an efficient recursive algorithm, the stiffness matrices of the thin nonhomogeneous layer are combined to obtain the total stiffness matrix for an arbitrary functionally graded multilayered system. It is shown that the round-off error for the stiffness-matrix recursive algorithm is higher than that for the transfer matrices. To optimize the recursive procedure, a computationally stable hybrid method is proposed which first starts the recursive computation with the transfer matrices and then, as the thickness increases, transits to the stiffness matrix recursive algorithm. Numerical results show this solution to be stable and efficient. As an application example, we calculate the surface wave velocity dispersion for a functionally graded coating on a semispace.

Stress intensity factors around a moving Griffith crack in a non-homogeneous layer between two dissimilar elastic half-planes

Stresses are determined in the vicinity of a propagating finite crack having a constant velocity in a non-homogeneous elastic layer sandwiched between two dissimilar elastic half-planes. The self-equilibrated system of pressure is applied to the crack surfaces. Application of the Fourier transform technique reduces the problem to that of solving dual integral equations. In order to solve the equations, the differences in the crack surface displacements are expanded in a series of functions that are equal to zero outside the crack. The unknown coefficients in the series are solved by the Schmidt method. The stress intensity factors are calculated numerically for a crack in a non-homogeneous layer between a half-plane made of epoxy resin and a half-plane made of aluminum.

Thermal stresses around a crack in the nonhomogeneous interfacial layer between two dissimilar elastic half-planes

Thermal stresses around a crack in the interfacial layer between two dissimilar elastic half-planes are solved. The surfaces of the crack are assumed to be insulated. The material constants of the interfacial layer are assumed to vary continuously from those of the upper half-plane to those of the lower half-plane. Uniform heat flows perpendicular the crack. Stress intensity factors are calculated numerically for several thicknesses of the interfacial layer.

Turbulence fields for atmospheric dispersion models in horizontally non-homogeneous conditions

When atmospheric pollutant dispersion is simulated over complex terrain, the turbulence input parameters are often prescribed according to standard parameterisation based on surface layer quantities. These last are available from literature. In the past, several different parameterisations for the first few moments of the turbulence velocity statistic and for the Lagrangian time scale have been developed and tested in different stability conditions. The main shortcomings for using these parameterisations are their inadequateness in predicting the turbulence field in horizontally non-homogeneous boundary layer (like for example in complex terrain or in urban heat island) and the essentially local nature of the prescribed turbulence. The purpose of this work is to suggest proper methods for predicting turbulence field for dispersion model over complex terrain and, more generally, in horizontally non-homogeneous conditions. The modelling system RMS (RAMS–MIRS–SPRAY) is applied to the present study. We introduced new non-local turbulence closures in the RAMS circulation model, which provides both mean wind and turbulence fields. Then, through the interface code (MIRS), the input quantities needed to the Lagrangian stochastic dispersion model (SPRAY) are computed. The model system is validated against a tracer experiment performed in a wind tunnel over a schematic two-dimensional valley.

A simplified analysis method for piled raft foundations in non‐homogeneous soils

AbstractA simplified method of numerical analysis based on elasticity theory has been developed for the analysis of axially and laterally loaded piled raft foundations embedded in non‐homogeneous soils and incorporated into a computer program “PRAB”. In this method, a hybrid model is employed in which the flexible raft is modelled as thin plates and the piles as elastic beams and the soil is treated as springs. The interactions between structural members, pile–soil–pile, pile–soil–raft and raft–soil–raft interactions, are approximated based on Mindlin's solutions for both vertical and lateral forces with consideration of non‐homogeneous soils. The validity of the proposed method is verified through comparisons with some published solutions for single piles, pile groups and capped pile groups in non‐homogeneous soils. Thereafter, the solutions from this approach for the analysis of axially and laterally loaded 4‐pile pile groups and 4‐pile piled rafts embedded in finite homogeneous and non‐homogeneous soil layers are compared with those from three‐dimensional finite element analysis. Good agreement between the present approach and the more rigorous finite element approach is demonstrated. Copyright © 2002 John Wiley & Sons, Ltd.