Resonant-Based Identification of the Poisson’s Ratio of Orthotropic Materials

The resonant-based identification of the in-plane elastic properties of orthotropic materials implies the estimation of four principal elastic parameters: E ₁ , E ₂ , G ₁₂ , and ν ₁₂ . The two elastic moduli and the shear modulus can easily be derived from the resonant frequencies of the flexural and torsional vibration modes, respectively. The identification of the Poisson’s ratio, however, is much more challenging, since most frequencies are not sufficiently sensitive to it. The present work addresses this problem by determining the test specimen specifications that create the optimal conditions for the identification of the Poisson’s ratio. Two methods are suggested for the determination of the Poisson’s ratio of orthotropic materials: the first employs the resonant frequencies of a plate-shaped specimen, while the second uses the resonant frequencies of a set of beam-shaped specimens. Both methods are experimentally validated using a stainless steel sheet.     

Local mass/heat transfer from a wall-mounted block in rectangular channel flow

This investigation explores the mass/heat transfer from a wall-mounted block in a rectangular fully developed channel flow. The naphthalene sublimation scheme was used to measure the level of local mass transfer from the block’s surfaces. The heat transfer coefficient can be obtained by analogy between heat and mass transfer. The effects of the Reynolds number on the local mass transfer from the block’s surfaces have been widely discussed. Results showed that, owing to the flow complexity induced by vortices around the block, the block’s surfaces appeared four different spatial Sherwood number distributions, termed “Wave type”, “U type”, “Slant type”, and “Pit type”. A change in the Reynolds number significantly altered the spatial Sherwood number distributions on the block’s surfaces. Besides, four correlations between the Reynolds number and the surface-averaged Sherwood number were presented for the front, top, side, and rear surfaces of the block at a given block’s height, for the purpose of practical applications.     

Analytical and numerical analysis for the FGM thick sphere under combined pressure and temperature loading

Thermo-mechanical analysis of functionally graded hollow sphere subjected to mechanical loads and one-dimensional steady-state thermal stresses is carried out in this study. The material properties are assumed to vary non-linearly in the radial direction, and the Poisson’s ratio is assumed constant. The temperature distribution is assumed to be a function of radius, with general thermal and mechanical boundary conditions on the inside and outside surfaces of the sphere. In the analysis presented here, the effect of non-homogeneity in FGM thick sphere was implemented by choosing a dimensionless parameter, named β _i (i = 1, . . . , 3), which could be assigned an arbitrary value affecting the stresses in the sphere. It is observed that the solution process for β _i (i = 3) = −1 are different from those obtained for other values of β _i (i = 1, . . . , 3). Cases of pressure, temperature, and combined loadings were considered separately. It is concluded that by changing the value of β _i (i = 1 . . . 3), the properties of FGM can be so modified that the lowest stress levels are reached. The present results agree well with existing results. Using FEM simulations, the analytical findings for FGM spheres under the influence of internal pressure and temperature gradient were compared to finite element results.     

Secondary flow patterns and mixing in laminar pulsating flow through a curved pipe

Mixing by secondary flow is studied by particle image velocimetry (PIV) in a developing laminar pulsating flow through a circular curved pipe. The pipe curvature ratio is η = r ₀/r _c  = 0.09, and the curvature angle is 90°. Different secondary flow patterns are formed during an oscillation period due to competition among the centrifugal, inertial, and viscous forces. These different secondary-flow structures lead to different transverse-mixing schemes in the flow. Here, transverse mixing enhancement is investigated by imposing different pulsating conditions (Dean number, velocity ratio, and frequency parameter); favorable pulsating conditions for mixing are introduced. To obviate light-refraction effects during PIV measurements, a T-shaped structure is installed downstream of the curved pipe. Experiments are carried out for the Reynolds numbers range 420 ≤ Re_st ≤ 1,000 (Dean numbers 126.6 ≤ Dn ≤ 301.5) corresponding to non-oscillating flow, velocity component ratios 1 ≤ (β = U _max,osc/U _m,st) ≤ 4 (the ratio of velocity amplitude of oscillations to the mean velocity without oscillations), and frequency parameters 8.37 < (α = r ₀(ω/ν)^0.5) < 24.5, where α² is the ratio of viscous diffusion time over the pipe radius to the characteristic oscillation time. The variations in cross-sectional average values of absolute axial vorticity (|ζ|) and transverse strain rate (|ε|) are analyzed in order to quantify mixing. The effects of each parameter (Re_st, β, and α) on transverse mixing are discussed by comparing the dimensionless vorticities (|ζ _P |/|ζ _S |) and dimensionless transverse strain rates (|ε _P |/|ε _S |) during a complete oscillation period.     

Asymptotic computation of the inhomogeneity energy in a body in an external stress field

We consider a problem on an ellipsoidal inhomogeneity in an infinitely extended homogeneous isotropic elastic medium. The inhomogeneity differs from the ambient body in the elastic moduli (Poisson’s ratio ν and shear modulus μ) and in that it has intrinsic strains. We use the equivalent inclusion method to write out expressions for the Helmholtz and Gibbs free energy of the inhomogeneity as quadratic forms in the intrinsic strains and strains at infinity. The general expressions for the coefficients of these quadratic forms are written out as three rank four tensors characterizing the contribution to the energy by the plastic strain (ɛ _p ²), by the strain at infinity (ɛ ₀²), and (only for the Gibbs energy) by the cross term ɛ ⁰ ɛ _p .     

Rosetta Stone Experiments

Dynamic failure events such as armor penetration and explosive fragmentation are too complex to be treated by classical single-crack continuum fracture mechanics. In such cases deformation and fracture result from multiple cracks, voids, and shear bands acting simultaneously and influencing one another’s evolution. An alternative “meso” fracture mechanics is needed that treats microfailure activity while permitting fast and inexpensive predictive computations. This paper discusses the approach and experiments that elucidate and quantify failure physics on the micron level. “Rosetta Stone” experiments that isolate a damage mode, produce statistical distributions of damage features, and “freeze in” damage at various stages of development are described and illustrated. The observations and data lead to equations describing nucleation and growth of cracks, voids, and shear bands. The resulting mesomechanical material failure models link the microworld with the macroworld and can be used in continuum hydrocodes for fast, efficient simulations of dynamic fracture scenarios.

Stress analysis of functionally graded rotating discs: analytical and numerical solutions

This study deals with stress analysis of annular rotating discs made of functionally graded materials(FGMs).Elasticity modulus and density of the discs are assumed to vary radially according to a power law function,but the material is of constant Poisson’s ratio.A gradient parameter n is chosen between 0 and 1.0.When n = 0,the disc becomes a homogeneous isotropic material.Tangential and radial stress distributions and displacements on the disc are investigated for various gradient parameters n by means of the diverse elasticity modulus and density by using analytical and numerical solutions.Finally,a homogenous tangential stress distribution and the lowest radial stresses along the radius of a rotating disc are approximately obtained for the gradient parameter n = 1.0 compared with the homogeneous,isotropic case n = 0.This means that a disc made of FGMs has the capability of higher angular rotations compared with the homogeneous isotropic disc.     

Stability, Instability, and Error of the Force-based Quasicontinuum Approximation

Due to their algorithmic simplicity and high accuracy, force-based model coupling techniques are popular tools in computational physics. For example, the force-based quasicontinuum (QCF) approximation is the only known pointwise consistent quasicontinuum approximation for coupling a general atomistic model with a finite element continuum model. In this paper, we present a detailed stability and error analysis of this method. Our optimal order error estimates provide a theoretical justification for the high accuracy of the QCF approximation: they clearly demonstrate that the computational efficiency of continuum modeling can be utilized without a significant loss of accuracy if defects are captured in the atomistic region. The main challenge we need to overcome is the fact that the linearized QCF operator is typically not positive definite. Moreover, we prove that no uniform inf-sup stability condition holds for discrete versions of the W ^1,p -W ^1,q “duality pairing” with 1/p + 1/q = 1, if 1 ≤ p < ∞. However, we were able to establish an inf-sup stability condition for a discrete version of the W ^1,∞-W ^1,1 “duality pairing” which leads to optimal order error estimates in a discrete W ^1,∞-norm.     

On Poisson’s Ratio in Linearly Viscoelastic Solids

Poisson’s ratio in viscoelastic solids is in general a time dependent (in the time domain) or a complex frequency dependent quantity (in the frequency domain). We show that the viscoelastic Poisson’s ratio has a different time dependence depending on the test modality chosen; interrelations are developed between Poisson’s ratios in creep and relaxation. The difference, for a moderate degree of viscoelasticity, is minor. Correspondence principles are derived for the Poisson’s ratio in transient and dynamic contexts. The viscoelastic Poisson’s ratio need not increase with time, and it need not be monotonic with time. Examples are given of material microstructures which give rise to designed time dependent Poisson’s ratios.     

Near wake properties of axisymmetric bluff body flows

Experiments have been made to measure some of the near wake properties of axisymmetric bluff body flows with fixed points of separation, including the detention or residence time of fluid borne scalar entities, base pressure coefficient, wake bubble length parameter and shape parameter. Measurements were made in smooth and turbulent air flow for Reynolds number in the range 2×10³<Re<4×10⁴. The results for a given bluff body were found to be uniquely controlled by a free-stream turbulence parameter. The data for all the shapes of bluff body in the class under consideration were found to collapse into unique inter-relationships by the introduction of the face pressure coefficient as a quantitative measure of “bluffness”. This paper was originally presented at the 14th International Congress of Theoretical and Applied Mechanics, Delft (August–September, 1976).     

Further Comments on “Combined Forced and Free Convective Flow in a Vertical Porous Channel: The Effects of Viscous Dissipation and Pressure Work”

This note is concerned with the assertion of Barletta and Nield (2009a) that “a fluid with a thermal expansion coefficient greater than that of a perfect gas (β > β _perfect gas) is of marginal or no interest in the framework of convection in porous media”, and that for a remark of Magyari (Transp. Porous Media, 2009) about the forced convection eigenflow solutions, the circumstance β > β _perfect gas does not represent “a sound physical basis”. Here, it is shown, however, that these assertions are in contradiction with the experimentally measured values of β for important technical fluids as e.g., air, nitrogen, carbon dioxide, and ammonia where, in the temperature range between −20 and +100°C, just the inequality β > β _perfect gas holds.     

Dual leading-edge vortex structure for flow over a simplified butterfly model

The dye visualization experiments show that a dual leading-edge vortex (LEV) structure exists on the suction side of a simplified butterfly model of Papilio ulysses at α = 8°−12°. Furthermore, the results of particle image velocimetry (PIV) measurement indicate that the axial velocity of the primary (outer) vortex core reaches the lower extreme value while a transition from a “wake-like” to a “jet-like” axial velocity profile occurs. The work reveals for the first time the existence of dual LEV structure on the butterfly-like forward-sweep wing configuration.     

Very high Reynolds number boundary layers over 3D sparse roughness and obstacles: the mean flow

Hot-wire and oil-film interferometry measurements are taken for 3D rough wall boundary layers at very high Reynolds numbers (61,000 < Re θ < 120,000) with low blockage ratios, 10 < δ/H < 135, and high roughness, 100 < H ⁺ < 4,900. The results cover flows over both rough walls and over obstacles and are compared with and provide extension to recent lower Reynolds number results. The validity of the Townsend ‘wall similarity hypothesis’ in relation to consistently increasing 3D roughness is interrogated. In agreement with recent work, Schultz and Flack (J Fluid Mech 580:381–405, 2007) and Castro (J Fluid Mech 585:469–485, 2007) found that, for relatively low roughness, Townsend’s hypothesis holds for the mean velocity field. With increasing roughness, the equilibrium layer diminishes and gradually vanishes. The viscous component of the wall shear stress decreases, while the turbulent component increases as the roughness effects extend across the boundary layer.     

Experiments on the lift of a spinning sphere in a range of intermediate Reynolds numbers

 The lift force experienced by a spinning sphere moving in a viscous fluid, with constant linear and angular velocities, is measured by means of a trajectographic technique. Measurements are performed in the range of dimensionless angular velocities γ=aω/V lying between 1 and 6, and in the range of Reynolds numbers Re=2aV/ν lying between 10 and 140 (a sphere radius, ω angular velocity, V relative velocity of the sphere centre, ν fluid kinematic viscosity). A notable departure from the theoretical relationship at low Reynolds number, C _L =2γ, is obtained, the ratio C _L /γ being found to significantly decrease with increasing γ and increasing Re. The following correlation is finally proposed to estimate the lift coefficient in the range 10<Re<140: C _L ≅0.45+(2γ−0.45) exp (−0.075γ^0.4 Re ^0.7) Received: 20 May 1996/Accepted: 9 November 1997     

The flip side of buckling

Buckling of slender structures under compressive loading is a failure of infinitesimal stability due to a confluence of two factors: the energy density non-convexity and the smallness of Korn’s constant. The problem has been well understood only for bodies with simple geometries when the slenderness parameter is well defined. In this paper, we present the first rigorous analysis of buckling for bodies with complex geometry. By limiting our analysis to the “near-flip” instability, we address the universal features of the buckling phenomenon that depend on neither the shape of the domain nor the degree of constitutive nonlinearity of the elastic material.      

A systematic derivation of a consistent set of “Boussinesq equations”

The often used “Boussinesq equations” for the determination of the coupled flow and temperature field in natural convection are systematically deduced by an asymptotic approach. With the nondimensional temperature difference that drives the flow, ?, as a perturbation parameter the leading order equations are identified as the appropriate equations, named “asymptotic Boussinesq equations”. These equations appear as the distinguished limit $\varepsilon\rightarrow0The often used “Boussinesq equations” for the determination of the coupled flow and temperature field in natural convection are systematically deduced by an asymptotic approach. With the nondimensional temperature difference that drives the flow, ɛ, as a perturbation parameter the leading order equations are identified as the appropriate equations, named “asymptotic Boussinesq equations”. These equations appear as the distinguished limit e?0\varepsilon\rightarrow0 and Ec? 0{Ec}\rightarrow 0 with Ec/e = const.{Ec}/\varepsilon =const. The equations are compared to “Boussinesq equations” of other studies and used to calculate Nusselt numbers in laminar and turbulent flows in infinite vertical channels as an example and for the justification of the asymptotic approach.     

Rheological analysis of highly concentrated w/o emulsions

A series of highly concentrated lipophilic cosmetic emulsions were analysed, in order to determine their rheological and textural properties, as a function of their microstructure. The originality of this study lies in the methodology used, especially the shear-stress scanning analysis. The results of a very powerful and comprehensive dynamic rheological analysis suggest the existence of two critical volume fraction values: besides the “close-packed” value φ _c , a “slack-packed” value φ₀, close to 0.60 could be demonstrated. It has been shown that the close-packed structure is stable under shear; in constrast, the slack-packed configuration, defined as φ₀<φ<φ _c is unstable under shear. A comparison with theoretical models, especially that of Princen, showed good agreement and allowed the close-packed value φ _c to be defined more precisely as 0.67. The gap between 0.67 and 0.74 is probably indicative of a highly polydisperse distribution, as confirmed by microscopic analysis. Flow experiments confirmed the validity of Princen‘s model. Received: 20 February 1997 Accepted: 20 January 1998     

Single Fiber Transport in a Fracture Slit: Influence of the Wall Roughness and of the Fiber Flexibility

The transport of fibers by a fluid flow is investigated in transparent channels modeling rock fractures: the experiments use flexible polyester thread (mean diameter 280 μm) and water or a water–polymer solution. For a channel with smooth parallel walls and a mean aperture ā = 0.65 mm, both fiber segments of length ℓ = 20–150 mm and “continuous” fibers longer than the channel length have been used: in both the cases, the velocity of the fibers and its variation with distance could be accounted for while neglecting friction with the walls. For rough self-affine walls and a continuous gradient of the local mean aperture transverse to the flow, transport of the fibers by a water flow is only possible in the region of larger aperture (ā ≲ 1.1 mm) and is of “stop and go” type at low velocities. With the polymer solution, the fibers move faster and more continuously in high aperture regions and their interaction with the walls is reduced; fiber transport becomes also possible in narrower regions where irreversible pinning occurred for water. In a third rough model with parallel walls and a low mean aperture ā = 0.65 mm, fiber transport is only possible with the water–polymer solution. The dynamics of fiber deformations and entanglement during pinning–depinning events and permanent pinning is analyzed.     

Turbulence beneath finite amplitude water waves

Babanin and Haus (J Phys Oceanogr 39:2675–2679, 2009) recently presented evidence of near-surface turbulence generated below steep non-breaking deep-water waves. They proposed a threshold wave parameter a ²ω/ν = 3,000 for the spontaneous occurrence of turbulence beneath surface waves. This is in contrast to conventional understanding that irrotational wave theories provide a good approximation of non-wind-forced wave behaviour as validated by classical experiments. Many laboratory wave experiments were carried out in the early 1960s (e.g. Wiegel 1964). In those experiments, no evidence of turbulence was reported, and steep waves behaved as predicted by the high-order irrotational wave theories within the accuracy of the theories and experimental techniques at the time. This contribution describes flow visualisation experiments for steep non-breaking waves using conventional dye techniques in the wave boundary layer extending above the wave trough level. The measurements showed no evidence of turbulent mixing up to a value of a ²ω/ν = 7,000 at which breaking commenced in these experiments. These present findings are in accord with the conventional understandings of wave behaviour.