Dynamic surface tension of complex fluid-fluid interfaces: A useful concept, or not?

Dilatational moduli are typically determined by subjecting interfaces to oscillatory area deformations, and are often defined in terms of the difference between the dynamic or transient surface tension of the interface (the surface tension in its deformed state), and the surface tension of the interface in its non-deformed state. Here we will discuss the usefulness of the dynamic surface tension concept in the characterization of dilatational properties of complex fluid-fluid interfaces. Complex fluid-fluid interfaces are interfaces stabilized by components which form mesophases (two-dimensionional gels, glasses, or (liquid) crystalline phases), as a result of in-plane interactions between the components. We will show that for such interfaces dilatational properties are not exclusively determined by the exchange of surface active components between interface and adjoining bulk phases, but also by in-plane viscoelastic stresses. The separation of these contributions remains a challenging problem which remains to be solved.     

Surface deformation induced by a variation in surface stresses in anisotropic half-regions

The deformations and the stresses in anisotropic half-regions taking into account surface stresses originating from surface energy, which exists originally at surfaces and interfaces dividing phases, are analysed theoretically. In the present paper, the equilibrium equation of force considering surface stresses is used to calculate the inelastic deformation induced by a variation in surface stresses. The problem of varying surface stresses in a half-surface of a half-infinite anisotropic domain is analysed using the theory of elasticity. This problem is related to the occurrence of cracks in contaminated, oxidized or chemisorbed surfaces. Stress analysis on the basis of continuum mechanics is performed precisely under the boundary condition taking into account surface stresses. The Fourier transform technique is applied to perform the analysis, and the components of stress and displacement are expressed in an explicit form. The shear component of bulk stress attains infinity at the edge of discontinuity of the surface stresses, and the free surface deforms like an edge dislocation. This result suggests that cracking in a chemically contaminant surface is easier than in a clean surface.     

Vibration and damping analysis of multilayered rectangular plates with constrained viscoelastic layers

Governing equations of motion for vibrations of a general multilayered plate consisting of an arbitrary number of alternate stiff and soft layers of orthotropic materials are derived by using variational principles. Extension, bending and in-plane shear deformations in stiff layers and only transverse shear deformations in soft layers are considered as in conventional sandwich structural analysis. In addition to transverse inertia, longitudinal translatory and rotary inertias are included, as such analysis gives higher order modes of vibration and leads to accurate results for relatively thick plates. Vibration and damping analysis of rectangular simply supported plates consisting of alternate elastic and viscoelastic layers is carried out by taking a series solution and applying the correspondence principle of linear viscoelasticity. The damping effectiveness, in term of the system loss factor, for all families of modes for three-, five- and seven-layered plates is evaluated and its variations with geometrical and material property parameters are investigated.     

Rubber friction on smooth surfaces

We study the sliding friction for viscoelastic solids, e.g., rubber, on hard flat substrate surfaces. We consider first the fluctuating shear stress inside a viscoelastic solid which results from the thermal motion of the atoms or molecules in the solid. At the nanoscale the thermal fluctuations are very strong and give rise to stress fluctuations in the MPa-range, which is similar to the depinning stresses which typically occur at solid-rubber interfaces, indicating the crucial importance of thermal fluctuations for rubber friction on smooth surfaces. We develop a detailed model which takes into account the influence of thermal fluctuations on the depinning of small contact patches (stress domains) at the rubber-substrate interface. The theory predicts that the velocity dependence of the macroscopic shear stress has a bell-shaped form, and that the low-velocity side exhibits the same temperature dependence as the bulk viscoelastic modulus, in qualitative agreement with experimental data. Finally, we discuss the influence of small-amplitude substrate roughness on rubber sliding friction.     

Numerical simulation of micro-scratch tests for coating/substrate composites

In this paper the micro-scratch test is simulated by ANSYS finite element code for thin hard coating on substrate composite material system. Coulomb friction between indenter and material surface is considered. The material elastic-plastic properties are taken into account. Contact elements are used to simulate the frictional contact between indenter and material surfaces, as well as the frictional contact after the detachment of coating/substrate interfaces has taken place. In the case of coating/substrate interfaces being perfectly bonded, the distributions of interfacial normal stress and shear stress are obtained for the material system subjected to normal and tangential loading. In the case of considering the detachment of interfaces, the length of interfacial detachment and the redistribution of stresses because of interfacial detachments are obtained. The influences of different frictional coefficients and different indenter moving distances on the distributions of stresses and displacements are studied. In the simulation, the interfacial adhesion shear strength is considered as a main adhesion parameter of coating/substrate interfaces. The critical normal loading from scratch tests are directly related to interfacial adhesion shear strengths. Using the critical normal loading known from experiments, the interfacial adhesion shear strength is obtained from the calculation. When the interfacial adhesion shear strength is known, the critical normal loading is obtained for different coating thicknesses. The numerical results are compared with the experimental values for composite materials of thin TiN coating on stainless steel substrate.     

A fixture for interfacial dilatational rheometry using a rotational rheometer

In characterizing complex fluid-fluid interfaces, interfacial rheometry has become an important tool to indirectly probe the interfacial microstructure and molecular interactions. It can also be useful to obtain the constitutive properties of an interface for calculating the interfacial flows of complex fluid-fluid interfaces. A number of devices for measuring interfacial shear rheology have been designed and have been thoroughly validated. However, although a range of devices for measuring interfacial dilatational rheology exist, they do not always allow for a proper separation of the effects of dynamic surface tension, curvature elasticity, Marangoni stresses, bulk flow effects and the desired dilatational rheological material functions. In the present work it is investigated if a fixture for a standard rotational rheometer can be designed which probes the dilatational viscoelastic properties of a planar complex fluid-fluid interface. A modification of the double wall ring geometry for shear rheometry is proposed, which creates a mixed but analyzable flow field. The use of a mixed flow field inherently limits the sensitivity for the dilatational properties, but some advantages over existing techniques are presented, in particular for insoluble monolayers. More importantly, the analysis illustrate some generic aspects on the use of mixed interfacial flow fields for measuring the surface rheological properties.     

Refined vibration and damping analysis of multilayered rectangular plates

Refined vibration and damping analysis of a general multilayered rectangular plate consisting of an arbitrary number of layers of orthotropic materials has been developed by considering extension, bending, in-plane shear and transverse shear deformations in all the layers and taking into account the rotary and longitudinal translatory inertias along with the transverse inertia of the plate. The solution for a multilayered plate with simply supported edges has been taken in series summation form and resonating frequencies and associated loss factors for plates with alternate elastic and viscoelastic layers have been evaluated by application of the correspondence principle of linear viscoelasticity. Results for three-, five- and seven-layered plates obtained by the present refined analysis are compared with the results obtained by conventional analysis of multilayered plates.     

On the use of acoustic birefringence to determine components of plane stress

To assess the integrity of a structure containing a (known) flaw, it is necessary to know the stresses acting on the flaw. Many common structural elements (e.g. beams and plates) are subjected to either true plane stress or generalized plane stress. For either of these cases, there are three in-plane stresses (one shear stress and two normal stresses) to be determined in general.In this paper, we consider the application of the acoustic birefringence method to generalized plane stress states, where the thickness-averaged values of the shear and normal stresses are sought. It is shown that the times-of-flight are thickness-averaged effects, whereas the polarization directions depend upon local values of stress. Consequently, when the symmetric (axial) component of the stresses dominates the antisymmetric (bending) component, the acoustic birefringence method can be used to determine all three stresses, if the boundary conditions are known. For unknown boundary conditions, the normal stresses can be determined to within arbitrary functions.Problems arise in using the normal incidence technique when either the shear stress vanishes, or the symmetric (membrane) components of generalized plane stress do not dominate the bending components. In the former case, the thickness-averaged difference in normal stresses can be obtained, provided that the birefringence in the unstressed state is known. In the latter case, the (averaged) difference in normal stresses can be obtained by measuring time-of-flight differences of off-axis SH-waves propagating in the planes of material symmetry of the plate.     

A simplified shear and normal deformations nonlocal theory for bending of nanobeams in thermal environment

This article presents a simplified three-unknown shear and normal deformations nonlocal beam theory for the bending analysis of nanobeams in thermal environment. Eringen's nonlocal constitutive equations are considered in the analysis. Governing equations are derived according to the present refined theory using Hamilton's principle. Central deflections of nanobeams under uniform and point loads are given and compared with the available ones in the literature. Additional results of displacement and stresses are presented for future comparison. The effects of nonlocality, temperature parameters, length of beam, length-to-depth ratio as well as shear and normal strains are all investigated.     

Principal component analysis of shear strain effects

Shear stresses are always present during quasi-static strain imaging, since tissue slippage occurs along the lateral and elevational directions during an axial deformation. Shear stress components along the axial deformation axes add to the axial deformation while perpendicular components introduce both lateral and elevational rigid motion and deformation artifacts into the estimated axial and lateral strain tensor images. A clear understanding of these artifacts introduced into the normal and shear strain tensor images with shear deformations is essential. In addition, signal processing techniques for improved depiction of the strain distribution is required. In this paper, we evaluate the impact of artifacts introduced due to lateral shear deformations on the normal strain tensors estimated by varying the lateral shear angle during an axial deformation. Shear strains are quantified using the lateral shear angle during the applied deformation. Simulation and experimental validation using uniformly elastic and single inclusion phantoms were performed. Variations in the elastographic signal-to-noise and contrast-to-noise ratios for axial deformations ranging from 0% to 5%, and for lateral deformations ranging from 0 to 5° were evaluated. Our results demonstrate that the first and second principal component strain images provide higher signal-to-noise ratios of 20 dB with simulations and 10 dB under experimental conditions and contrast-to-noise ratio levels that are at least 20 dB higher when compared to the axial and lateral strain tensor images, when only lateral shear deformations are applied. For small axial deformations, the lateral shear deformations significantly reduces strain image quality, however the first principal component provides about a 1–2 dB improvement over the axial strain tensor image. Lateral shear deformations also significantly increase the noise level in the axial and lateral strain tensor images with larger axial deformations. Improved elastographic signal and contrast-to-noise ratios in the first principal component strain image are always obtained for both simulation and experimental data when compared to the corresponding axial strain tensor images in the presence of both axial and lateral shear deformations.     

Influence of Adhesive Characteristics on the Interfacial Stress Concentrations in Externally FRP Plated Steel Beams

This paper deals with the influence of adhesive properties on the interlaminar stress in externally FRP plated steel beams. The analysis provides efficient calculations for both shear and normal interfacial stresses in steel beams strengthened with composite plates, and accounts for various effects of Poisson's ratio and Young's modulus of adhesive. Such interfacial stresses play a fundamental role in the mechanics of plated beams, because they can produce a sudden and premature failure. The analysis is based on equilibrium and deformations compatibility approach developed by Tounsi [1]. In the present theoretical analysis, the adherend shear deformations are taken into account by assuming a parabolic shear stress through the thickness of both the steel beam and bonded plate. The paper concludes with a summary and recommendations for the design of the strengthened beam.     

Vibration analysis of laminated cross-ply oval cylindrical shells

Here, free vibrations and transient dynamic response analyses of laminated cross-ply oval cylindrical shells are carried out. The formulation is based on higher order theory that accounts for the transverse shear and the transverse normal deformations, and includes zig-zag variation in the in-plane displacements across the thickness of the multi-layered shells. The contributions of inertia effect due to in-plane and rotary motions, and the higher order function arising from the assumed displacement models are included. The governing equations obtained using Lagrangian equations of motion are solved through finite element approach. A detailed parametric study is conducted to bring out the influence of different shell geometry, ovality parameter, lay-up and loading environment on the vibration characteristics related to different modes of vibrations of oval shell.     

Heterogeneity and the role of normal stresses during the extensional thinning of non-Brownian shear-thickening fluids

We contrast the extensional and shear dynamics of non-Brownian suspensions as a function of particle concentration. We show that the thinning rate selected during the viscoelastic pinch-off of a liquid bridge is related to the shear rate at which normal stresses become positive, which differs from the shear rate at the onset of shear thickening. By tracking particles, we demonstrate that the extensional flow is heterogeneous, with local variations of the volume fraction consistent with self-dilution. This nonuniform structure is the cause of the buckling of the threads formed after breakup.     

Radiation impedance of a finite circular piston on a viscoelastic half-space with application to medical diagnosis

In a recent study a new analytical solution was developed and validated experimentally for the problem of surface wave generation on a linear viscoelastic half-space by a rigid circular disk located on the surface and oscillating normal to it. The results of that study suggested that, for the low audible frequency range, some previously reported values of shear viscosity for soft biological tissues may be inaccurate. Those values were determined by matching radiation impedance measurements with theoretical calculations reported previously. In the current study, the sensitivity to shear viscoelastic material constants of theoretical solutions for radiation impedance and surface wave motion are compared. Theoretical solutions are also compared to experimental measurements and numerical results from finite-element analysis. It is found that, while prior theoretical solutions for radiation impedance are accurate, use of such measurements to estimate shear viscoelastic constants is not as precise as the use of surface wave measurements.     

Effectiveness of multilayer viscoelastic insulators to prevent occurrences of brake squeal: A numerical study

The purpose of this publication is to give an overview of the actual role of multi-layered viscoelastic parts, so called “shims”, to prevent squeal noises of automotive brake systems. Since shear stress is usually used to damp thin structures in their bending modes it is commonly believed to be the largest underwent by shims. To check this assumption and considering that stresses underwent by shims cannot be measured experimentally, the authors have computed them with the help of a detailed and realistic finite element model. Contrary to what shims manufacturers say, this study exhibits the fact that shims are almost uniquely solicited in their normal direction in brake systems. Secondly, the study focuses on the added damping and stiffening induced by the viscoelastic materials. In order to take into account these materials, a realistic frequency dependent viscoelastic behavior has been integrated in the simulations. Finally, the study shows certains eigenmodes for which the viscoelastic behavior of the shims reveals instabilities that would not exist without it. It is shown that this is due to coalescence phenomenon.     

Analysis of Laser-generated Rayleigh wave on viscoelastic materials

In order to understand the viscoelasticity of material, this research has been conducted to study the propagation characteristics of viscoelastic Rayleigh wave theoretically. A model is presented for the pulsed laser generation of ultrasound on viscoelastic medium surface. Referred to the Kelvin model, the frequency equation and the normal displacement of viscoelastic Rayleigh wave were derived, the influence of the viscoelastic modulus on dispersion and attenuation was discussed. From the theoretical calculation, it is shown that the effect of viscoelasticity on the attenuation of Rayleigh wave is more than that on its dispersion. In the case of a weak viscosity, the attenuation of viscoelastic Rayleigh wave is directly proportional to viscosity modulus; the effect of shear viscosity on the attenuation is much more than that of bulk viscosity. The transient response of viscoelastic Rayleigh wave was also simulated using Laplace and Hankel inversion transform, which are showed in good agreement with the theoretic predictions. The model provides a useful tool for the determination of viscoelastic parameters of medium.     

Evaluation of interface wave velocity, reflection coefficients and interfacial stiffnesses of contacting surfaces

The phase velocity of the antisymmetric-mode interface wave as well as the longitudinal and shear wave reflection coefficients have been measured for contacting poly(methyl methacrylate) (PMMA) surfaces subjected to different contact pressures. It has been found that while the reflection coefficients decrease as the contact pressure is increased, the phase velocity of the interface wave increases from that of the Rayleigh wave toward that of the bulk shear wave. From these measurements, the normal and tangential interfacial stiffnesses of the contacting PMMA surfaces have been evaluated as functions of the contact pressure. As a result, the two independent procedures to evaluate the tangential stiffness, namely, from the interface wave velocity and from the shear wave reflection measurements, have yielded mutually consistent results. Furthermore, it has been found that the tangential/normal stiffness ratio and the shear/longitudinal reflection ratio of the contact interface are consistent with the predictions of an existing theoretical model for kissing bond interfaces.     

Stresses and displacements for some Rayleigh-type surface acoustic waves propagating on an anisotropic half space

Specific relations between mechanical displacements and stresses for Rayleigh-type surface acoustic waves propagating on an anisotropic half space are demonstrated. For 16 symmetry configurations belonging to the orthorhombic, tetragonal, hexagonal and cubic systems, involving only two displacement and stress components, it is shown that the ratio between the shear and normal stresses inside the propagation media is equal to the ratio between the normal and in-plane displacement components at the free surface. This result generalizes the previous one obtained in the case of an isotropic solid [W. Hassan and P. B. Nagy, J. Acoust. Soc. Am. 104, 3107-3110 (1998)].     

Non-trivial effect of the in-plane shear elasticity on the phase transitions of fixed-connectivity meshwork models

We numerically study the phase structure of two types of triangulated spherical surface models, which includes an in-plane shear energy in the Hamiltonian, and we found that the phase structure of the models is considerably influenced by the presence of the in-plane shear elasticity. The models undergo a first-order collapsing transition and a first-order (or second-order) transition of surface fluctuations; the latter transition was reported to be of second-order in the first model without the in-plane shear energy. This leads us to conclude that the in-plane elasticity strengthens the transition of surface fluctuations. We also found that the in-plane elasticity decreases the variety of phases in the second model without the in-plane energy. The Hamiltonian of the first model is given by a linear combination of the Gaussian bond potential, a one-dimensional bending energy, and the in-plane shear energy. The second model is obtained from the first model by replacing the Gaussian bond potential with the Nambu-Goto potential, which is defined by the summation over the area of triangles.     

Theory of surface excess Miesowicz viscosities of planar nematic liquid crystal-isotropic fluid interfaces

An expression for the surface excess stress tensor for planar compressible interfaces between rod-like nematic liquid crystals and isotropic viscous fluids is derived using the classical surface excess theory formalism, adapted to capture the intrinsic anisotropy of the nematic orientational ordering. A required step in the theory is to find the actual stress tensor in the three-dimensional interfacial region, which is obtained by a decomposition of the kinematic fields (rate of deformation tensor and director Jaumann derivative) into tangential, normal, and mixed components with respect to the interface. The viscosity coefficients appearing in the surface excess stress tensor are expressed in terms of interfacial and bulk viscosities for planar, constant orientation, flows. The expressions are used to define the three fundamental surface excess Miesowicz shear viscosities, in analogy with the three bulk Miesowicz shear viscosities. The ordering in the magnitudes of the surface excess Miesowicz shear viscosities is shown to depend on the magnitude of the surface scalar nematic order parameter relative to that of the adjoining bulk nematic phase. When the surface scalar order parameter is greater than in the bulk, the classical ordering in terms of magnitudes of the three bulk Miesowicz shear viscosities is recovered. On the other hand, when the surface scalar order parameter is smaller than in the bulk, the classical ordering in terms of magnitudes of the three viscosities does not hold, and inequality transitions are predicted as the surface scalar order parameter increases towards the bulk value. Received 5 July 1999 and Received in final form 16 November 1999