Analytical and experimental study of a circular membrane in adhesive contact with a rigid substrate

The problem that is addressed here is that of a pressurized circular membrane in adhesive contact with a rigid substrate. A closed-form membrane analysis is developed for the JKR, DMT and Maugis regimes, which describes the relationships between adhesion energy, pressure, contact radius and contact force. The JKR–DMT transition is studied for this case of membrane contact by introducing an appropriate dimensionless parameter. Experiments are conducted with smooth and structured acrylate layers on a PET carrier film contacting a glass substrate using an apparatus based on moiré deflectometry to measure the contact radius and slope of these thin transparent films. They demonstrate that this analysis predicts the contact radius well. The adhesion energy extracted from the analysis of the measured pressure-contact radius response is constant during unloading but appears to increase during pressurization.     

A 1-D theory for extensional deformation of a viscoelastic filament under exponential stretching

We consider a viscoelastic filament placed between two coaxial discs, with the bottom plate fixed and the top plate pulled at an exponential rate. Using a slender rod approximation, we derive a one-dimensional (1-D) model which describes the deformation of a viscoelastic filament governed by the Oldroyd-B constitutive model. It is assumed that the flow is axisymmetric and that inertia and gravity are negligible. One solution of the model equations corresponds to ideal uniaxial elongation. A linear stability analysis shows that this solution is unstable for a Newtonian fluid and for viscoelastic filaments with small Deborah number (De ≤ 0.5). For Deborah number greater than 0.5, ideal uniaxial elongation is linearly stable. Numerical solution of the nonlinear equations confirms the result of the linear stability analysis. For initial conditions close to ideal uniaxial flow, our results show that if De > 0.5, the central portion of the filament undergoes considerable strain hardening. As a result, the sample remains almost cylindrical and the deformation approaches pure uniaxial extension as the Hencky strain increases. For De ≤ 0.5, the Trouton ratio based on the effective extension rate at the mid-plane radius gives a much better approximation to the true extensional viscosity than that based on the imposed stretch rate.     

Mechanics of adhesive contact at the nanoscale: The effect of surface stress

At small length scales, the adhesion and surface effect are of great significance, both of which play important roles in the contact between two elastic solids. In this study, the classical Johnson–Kendall–Roberts (JKR) adhesive contact theory is generalized to the nanoscale at which the surface effect is considered. The influence of the surface stress on the JKR adhesive contact is investigated by employing the non-classical Boussinesq fundamental solutions. It is found that, compared with the classical theory, the pull-off force increases while the critical contact radius decreases as a result of the surface effect. Numerical results show that a relative error of 10% can be introduced in the pull-off force when the indenter radius is less than 20 nm. A detailed theoretical analysis of this interesting phenomenon is presented based on dimensional analysis, and two scaling laws for the adhesive contact at the nanoscale are constructed. These two new scaling laws reveal that the pull-off force is relevant to the elastic properties of the bulk materials, which is different from the classical adhesive contact theory. The present work is promising for the engineering applications in micro-electro-mechanical systems (MEMS) and nano-intelligent devices.     

Effect of elastic anisotropy on surface pattern evolution of epitaxial thin films

Stress-induced surface instability and evolution of epitaxial thin films leads to formation of a variety of self-assembled surface patterns with feature sizes at micro- and nanoscales. The anisotropy in both the surface and bulk properties of the film and substrate has profound effects on the nonlinear dynamics of surface evolution and pattern formation. Experimentally it has been demonstrated that the effect of anisotropy strongly depends on the crystal orientation of the substrate surface on which the film grows epitaxially. In this paper we develop a nonlinear model for surface evolution of epitaxial thin films on generally anisotropic crystal substrates. Specifically, the effect of bulk elastic anisotropy of the substrate on epitaxial surface pattern evolution is investigated for cubic germanium (Ge) and SiGe films on silicon (Si) substrates with four different surface orientations: Si(0 0 1), Si(1 1 1), Si(1 1 0), and Si(1 1 3). Both linear analysis and nonlinear numerical simulations suggest that, with surface anisotropy neglected, ordered surface patterns form under the influence of the elastic anisotropy, and these surface patterns clearly reflect the symmetry of the underlying crystal structures of the substrate. It is concluded that consideration of anisotropic elasticity reveals a much richer dynamics of surface pattern evolution as compared to isotropic models.     

Computational investigation of hydrodynamics and cracking reaction in a heavy oil riser reactor

This paper presents a computational investigation of hydrodynamics, heat transfer and cracking reaction in a heavy oil riser operated in a novel operating mode of low temperature contact and high catalyst-to-oil ratio. Through incorporating feedstock vaporization and a 12-lump cracking kinetics model, a validated gas–solid flow model has been extended to the analysis of the hydrodynamic and reaction behavior in an industrial riser. The results indicate that the hydrodynamics, temperature and species concentration exhibit significantly nonuniform behavior inside the riser, especially in the atomization nozzle region. The lump concentration profiles along the riser height provide useful information for riser optimization. Compared to conventional fluid catalytic cracking (FCC) process, feedstock conversion and gasoline yield are respectively increased by 1.9 units and 1.0 unit in the new FCC process, the yield of liquefied petroleum gas is increased by about 1.0 unit while dry gas yield is reduced by about 0.3 unit.     

Surface characteristics of spruce veneers and shear strength of plywood as a function of log temperature in peeling process

The objective of this study was to determine the effect of temperature of spruce (Picea orientalis L.) logs during peeling process on surface roughness, adhesive wettability, colour variation of veneer, and shear strength of plywood made from these veneer sheets. Veneer samples were manufactured from the logs after they were kept for 3 h and 24 h to reach to average temperatures of 52 °C and 32 °C, respectively. A fine stylus method was used for surface roughness evaluation of the veneer produced from two types of the logs and it was found that the samples peeled from the logs with a temperature of 52 °C had significantly better roughness values than those of manufactured from the logs with 32 °C at a 95% confidence level. Wettability of veneer samples was determined with contact angle measurements according to the sessile drop method. Urea formaldehyde (UF) and phenol formaldehyde (PF) resin drops were used in contact angle measurements. Contact angles of PF resin drops on veneers were similar for each peeling temperature while the contact angles of UF glue resin on veneers produced from the logs with 32 °C were lower than those of produced from the logs with 52 °C. Small colour difference was measured (indicated by a low ΔE value) on veneer samples depending on the log temperature. The highest shear strength value was determined for the plywood manufactured from veneers obtained from the logs with 52 °C by using UF glue.     

CFD based mini- vs. micro-system delineation in elongated bubble flow regime

Delineation of mini- and micro-scale channels with respect to two-phase flow has been the subject of many research papers. There is no consensus on when the small channel can be characterized as a mini-channel or micro-channel. The idea proposed by this paper is to use the normalized bubble nose radius, liquid film thickness top over bottom ratio, and bubble shape contour, which are found under normal gravity conditions in slug flow through a horizontal adiabatic channel, as the delineation criteria. The input parameters are bubble nose radius and bubble nose velocity as the characteristic length scale and characteristic velocity scale respectively. 3D numerical simulation with ANSYS FLUENT was used to obtain the necessary data. Following CFD practice, a mesh independence study and a numerical model validation against published experimental data were both conducted. Analysis of the numerical simulation results showed that channels with D ⩽ 100 μm can be characterized as a micro-system, while channels with D ⩾ 400 μm belong to mini-systems. The region 200 μm ⩽ D ⩽ 300 μm represents a transition from the micro-scale to mini-scale.     

On the impacts of coarse-scale models of realistic roughness on a forward-facing step turbulent flow

The present work explores the impacts of the coarse-scale models of realistic roughness on the turbulent boundary layers over forward-facing steps. The surface topographies of different scale resolutions were obtained from a novel multi-resolution analysis using discrete wavelet transform. PIV measurements are performed in the streamwise–wall-normal (x–y) planes at two different spanwise positions in turbulent boundary layers at Re_h = 3450 and δ/h = 8, where h is the mean step height and δ is the incoming boundary layer thickness. It was observed that large-scale but low-amplitude roughness scales had small effects on the forward-facing step turbulent flow. For the higher-resolution model of the roughness, the turbulence characteristics within 2h downstream of the steps are observed to be distinct from those over the original realistic rough step at a measurement position where the roughness profile possesses a positive slope immediately after the step’s front. On the other hand, much smaller differences exist in the flow characteristics at the other measurement position whose roughness profile possesses a negative slope following the step’s front.     

Oscillatory motions of a prestrained compliant membrane caused by fluid–membrane interaction

Flow over a compliant membrane is a complex problem where the interaction between fluid and membrane determines the nature of the aerodynamic characteristics of the membrane wing. This investigation is concerned with the deformation and oscillatory motion of a membrane under aerodynamic loading. The approach is computational, but the analytical solution is also presented for a constant pressure loading. The computational results are compared with the experimental data available in the literature as well as with the present analytical solution. In this study, the values of Reynolds number are 38 416 and 141 500, and the angle of attack and prestrain range from 10° to 40° and from 0 to 0.074, respectively. This range of parameters makes the outcome of the investigation more relevant to applications involving the flight of micro air vehicles and the membrane wings of flying mammals such as bats. The computations indicate a mostly asymmetric deflection with the point of maximum camber located nearly at 40% of the chord length from the leading edge. The deflection is decreased with prestrain, and it is increased with Reynolds number. Moreover, the lift coefficient generally increases with the angle of attack. However, for Re=141 500, it increases first to a peak at 20–30° angle of attack, and then decreases. The drag coefficient is much higher than that of conventional airfoils. The membrane oscillates in the streamwise and vertical directions. The largest amplitude of oscillations is observed at 40° for Re=38 416. The oscillations are caused by the oscillatory nature of the flow due to fluid–membrane interaction and the formation of the leading edge and trailing edge vortices. Compared with a rigid membrane of the same camber, the compliant membrane has a smaller recirculation region which may lead to a delayed stall.     

The degenerate scale problem for the Laplace equation and plane elasticity in a multiply connected region with an outer circular boundary

This paper investigates the degenerate scale problem for the Laplace equation and plane elasticity in a multiply connected region with an outer circular boundary. Inside the boundary, there are many voids with arbitrary configurations. The problem is analyzed with a relevant homogenous BIE (boundary integral equation). It is assumed that all the inner void boundary tractions are equal to zero, and tractions on the outer circular boundary are constant. Therefore, all the integrations in BIE are performed on the outer circular boundary only. By using the relation z * conjg(z) = a * a, or conjg(z) = a * a/z on the circular boundary with radius a, all integrals can be reduced to an integral for complex variable and they can be integrated in closed form. The degenerate scale a = 1 is found in the Laplace equation and in plane elasticity regardless of the void configuration.     

Quantifying the intensity of vehicle impacts using vehicle tracking devices during live training exercises

The operation of off-road vehicles during military training exercises can affect the environmental conditions of training lands by removing or disturbing vegetation. To quantify the impact of vehicle based military training, global positioning system (GPS)-based vehicle tracking systems were used to characterize the movement of vehicles during live training exercises. Methods were developed to spatially estimate the tracking intensity (number of vehicle passes per area) resulting from the training exercises. This method was then combined with previous developed methods that identified off-road trail formation and vehicle dynamic properties to quantify the overall training mission impacts of specific training events on installation resources. This approach to characterizing training impacts results in mission impact profiles that more accurately quantify live training mission impacts.Search radius and output grid size are important parameters of the proposed traffic intensity approximation method. Traffic intensities estimated using a variety of search radii and grid sizes were compared. Results indicated that a 10 m search radius and a 10-by-10 m output grid size worked the best for the study dataset. Approximately, 89% accuracy was found for traffic intensity (number of passes) estimation when using a 10 m search radius and a 10-by-10 m output grid size.     

Experimental study on the compressive behaviors of CFRP tube-encased concrete columns

Nine square concrete columns including 6 CFRP/ECCs and 3 concrete columns are prepared, which have cross-section of 200 mm × 200 mm and height of 600 mm. The CFRP tubes with fibers oriented at hoop direction were manufactured to have 3 or 5 layers of CFRP with 10 mm, 20 mm, or 40 mm rounding corner radii at vertical edges. A 100 mm overlap in the direction of fibers was provided to ensure proper bond. Uniaxial compression tests were conducted to investigate the compressive behavior. It is evident that the CFRP tube confinement can improve the behavior of concrete core, in terms of axial compressive strength or axial deformability. Test results show that the stress-strain behavior of CFRP/ECCs vary with different confinement parameters, such as the number of confinement layers and the rounding corner radius.     

Surface electro-elastic Love waves in a layered structure with a piezoelectric substrate and two isotropic layers

Propagation of electro-elastic surface Love waves in a structure consisting of a piezoelectric half-space substrate of crystal class 6, 4, 6 mm or 4 mm and two layers, one of which (adjacent to the substrate) is a conducting material and the second is either a conducting or a dielectric material, is considered. The mathematical model obtained includes all the above crystal classes i.e. the surface wave problems related to all these classes are presented in a single mathematical model. The dispersion equation for the existence of Love surface waves with respect to phase velocity is obtained. Numerical calculations are carried out for three different layered structures. The effect of the second layer on the propagation behaviour of the surface Love wave in the structure is revealed.     

Topological sensitivity to diagonal member flips of two-layered statically determinate trusses under worst loading

The paper deals with the topological sensitivity of free, unsupported, statically determinate plane trusses whose horizontal and vertical members form two horizontal layers of square cells and two or more vertical layers. The topology of a truss is decomposed into a form vector – the placement of cells containing diagonal members – and a binary vector describing the slopes of the diagonals. The construction of complete form and slope spaces is provided for any number of vertical layers. Using exhaustive search, forms with minimum and maximum sensitivity to slope change are found for trusses with 2 × 2 through 2 × 8 layers under worst static load condition, represented by the lowest eigenvalue of the least-squares equilibrium matrix. Typical features of the least and most sensitive forms and associated loads and internal forces are shown. Changes of absolute and relative topological sensitivities with increasing number of vertical layers are discussed.     

Curvature effects on axially compressed buckling of a small-diameter double-walled carbon nanotube

The curvature effects of interlayer van der Waals (vdW) forces on axially compressed buckling of a double-walled carbon nanotube (DWNT) of diameter down to 0.7 nm are studied. Unlike most existing models which assume that the interlayer vdW pressure at a point between the inner and outer tubes depends merely on the change of the interlayer spacing at that point, the present model considers the dependence of the interlayer vdW pressure on the change of the curvatures of the inner and outer tubes at that point. A simple expression is derived for the curvature-dependence of the interlayer vdW pressure in which the curvature coefficient is determined. Based on this model, an explicit formula is obtained for the axial buckling strain. It is shown that neglecting the curvature effect alone leads to an under-estimate of the critical buckling strain with a relative error up to −7%, while taking the average radius of two tubes as the representative radius and the curvature effect leads to an over-estimate of the critical buckling strain with a relative error up to 20% when the inner radius downs to 0.35 nm. Therefore, the curvature effects play a significant role in axially compressed buckling problems only for DWNTs of very small radii. In addition, our results show that the effect of the vdW interaction pressure prior to buckling of DWNTs under pure axial stress is small enough and can be negligible whether the vdW interaction curvature effects are neglected or not.     

Surface electro-elastic Love waves in a layered structure with a piezoelectric substrate and a dielectric layer

The existence and behaviour of electro-elastic surface Love waves in a structure consisting of a piezoelectric substrate of crystal classe 6, 4, 6 mm, 4 mm, 622 or 422, an elastic layer and a dielectric medium is considered. The mathematical model obtained includes all the above crystal classes, i.e. the surface wave problems related to all these classes are presented in a single mathematical model. The dispersion equation for the existence of Love surface waves with respect to phase velocity is obtained. A detailed investigation of the electromechanical coupling coefficient is carried out depending on the dielectric and piezoelectric parameters of the problem. Geometrical investigation of the solutions of the dispersion equation is carried out.     

Flow of mono-dispersed particles through horizontal bend

Pipeline slurry flow of mono-dispersed particles through horizontal bend is numerically simulated by implementing Eulerian two-phase model in FLUENT software. A hexagonal shape and Cooper type non-uniform three-dimensional grid is chosen to discretize the entire computational domain, and a control volume finite difference method is used to solve the governing equations. The modeling results are compared with the experimental data collected in 53.0 mm diameter horizontal bend with radius of 148.4 mm for concentration profiles and pressure drops. Experiments are performed on narrow-sized silica sand with mean diameter of 450 μm and for flow velocity up to 3.56 m/s (namely, 1.78, 2.67 and 3.56 m/s) and four efflux concentrations up to 16.28% (namely, 0%, 3.94%, 8.82% and 16.28%) by volume for each velocity. Eulerian model gives fairly accurate predictions for both the pressure drop and concentration profiles at all efflux concentrations and flow velocities.     

Superelastic shape memory alloy cables: Part II – Subcomponent isothermal responses

This paper constitutes the second part of our experimental study of the thermo-mechanical behavior of superelastic NiTi shape memory alloy cables. Part I introduced the fundamental, room temperature, tensile responses of two cable designs (7 × 7 right regular lay, and 1 × 27 alternating lay). In Part II, each cable behavior is studied further by breaking down the response into the contributions of its hierarchical subcomponents. Selected wire strands were extracted from the two cable constructions, and their quasi-static tension responses were measured using the same experimental setup of Part I. Consistent with the shallow wire helix angles in the 7 × 7 construction, the force–elongation responses of the core wire, 1 × 7 core strand and full 7 × 7 cable were similar on a normalized basis, with only a slight decrease in transformation force plateaus and slight increase in plateau strains in this specimen sequence. By contrast, each successive 1 × 27 component (1 × 6 core strand, 1 × 15 strand, and full cable) included an additional outer layer of wires with a larger number of wires, greater helix radius, and deeper helix angle, so the normalized axial load responses became significantly more compliant. Each specimen in the sequence also exhibited progressively larger strains at failure, reaching 40% strain in the full 1 × 27 cable.Stress-induced phase transformations involved localized strain/temperature and front propagation in all of the tested 7 × 7 components but none of the 1 × 27 components aside from the 1 × 27 core wire. Stereo digital image correlation measurements revealed finer features within a global transformation front of the 1 × 7 core strand than the 7 × 7 cable, consisting of an staggered pattern of individual wire fronts that moved in lock-step during elongation. Although the 1 × 27 multi-layer strands exhibited temperature/strain localizations in a distributed pattern during transformations, the localizations did not propagate and their cause was traced back to contact indentations (stress concentrations) arising from the cable’s fabrication. The normalized axial torque responses of the multi-layer 1 × 27 components during transformation were distinctly non-monotonic and complex, due to the alternating handedness of the layers. Force and torque contributions of individual wire layers were deduced by subtracting 1 × 27 component responses, which helped to clarify the transformation kinetics within each layer and explain the unusual force and torque undulations seen in the 1 × 27 cable response of Part I.     

The high strain mechanical response of the wet Kelvin model for open-cell foams

Surface Evolver software was used to create the three-dimensional geometry of a Kelvin open-cell foam, to simulate that of polyurethane flexible foams. Finite Element Analysis (FEA) with 3D elements was used to model large compressive deformation in the [0 0 1] and [1 1 1] directions, using cyclic boundary conditions when necessary, treating the polyurethane as an elastic or elastic–plastic material. The predicted foam Young’s moduli in the [0 0 1] direction are double those of foams with uniform Plateau border cross-section edges, for the same foam density and material properties. For compression in the [1 1 1] direction, the normalized Young’s modulus increases from 0.9 to 1.1 with foam relative density, and the predicted stress–strain relationship can have a plateau, even for a linearly-elastic polymer. As the foam density increases, the predicted effects of material plasticity become larger. For foam of relative density 0.028, edge-to-edge contact is predicted to occur at a 66% strain for [1 1 1] direction compression. The foam is predicted to contract laterally when the [1 1 1] direction compressive strain exceeds 25%.     

The coefficient of normal restitution for the Hertzian contact of two rough spheres colliding in a viscous fluid

We use previous theoretical results for the added mass, history and lubrication forces between two spheres colliding in a fluid with viscosity ν to investigate the effect of viscous dissipation on the coefficient of restitution during contact. We assume that the mechanical interaction is governed by Hertzian mechanical contact of small duration τ and that the minimum approach distance between particles is approximately equal to the height σ of surface micro-asperities. A non-dimensionalization of the equation of motion indicates that the contact dynamics is governed by two parameters – the ratio ϵ of the surface roughness σ and the sphere radius a, and a contact Stokes number defined as St_c = σ²/ντ. An asymptotic solution of the equation of motion in the limit of small ϵ/St_c is used to obtain an explicit expression for the coefficient of restitution during contact and the latter is compared with estimates based on numerical solutions of the non-linear equation of motion.