A method for computing the stress fields in a deformable elastic half-space with a polysynthetic twin near the surface

The problem of computing the stress fields around a polysynthetic twin near the surface under the action of a lumped or distributed load on the boundary of an elastic half-space is solved without using the thin twin approximation. It is found that the action of external stresses leads to the stress redistribution such that the stress localization is observed not only in the region of the external load action but also far from the vertices of the twins of the polysynthetic twin.     

Dislocation Model of Polysynthetic Shear Bands in Amorphous Materials

A dislocation model for a polysynthetic shear band in an amorphous material is proposed. The stress fields near the polysynthetic shear band are calculated. The distribution of impurities in an amorphous binary Fe–B medium containing a polysynthetic shear band is determined.     

Wedge-shaped cut in three-dimensional elastic wedge

An asymptotic solution of the integro-differential equation of the problem of describing a low-angle wedge-shaped cut in a three-dimensional elastic wedge is found. On the basis of the solution, the asymptotic behavior of the contact pressures at the apex of the punch, which in horizontal projection forms one side of an elastic wedge that includes a low-angle wedge-shaped cut, is investigated. Scientific Research Institute for Mechanics and Applied Mathematics, Rostov University, Russia. Translated from Prikladnaya Mekhanika, Vol. 35, No. 3, pp. 27–32, March, 1999.     

Use of thin polyparaxylene films to study the plastic deformation bismuth single crystals

The effect of thin polyparaxylene films on the mechanical twinning of bismuth single crystals with the (111) surface subjected to local deformation. It is found that the number of twins formed near the stress concentrator increases in the presence of the film. Possible mechanisms are proposed to explain an increase in the mobility of twin dislocations in a deformable crystal whose surface is coated with a polyparaxylene film. Spalling of bismuth is found in the regions deformed by the indenter. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 47, No. 4, pp. 162–166, July–August, 2006.     

Using three-dimensional fractal dimension to analyze the complexity of fetal cortical surface from magnetic resonance images

This study aims to investigate the complexity of the developing fetal cortical surface based on the notion of fractal dimension (FD). Forty-four fetal MR images were selected at 22–36 weeks of gestational age (GA) and distributed between two groups: 32 normal fetal brains (excluding twins) and 12 abnormal fetal brains, including twins, mild ventricular dilatation, Cornelia de Lange syndrome (small brain), and cortical dysplasia (developmental delay). We adopted the commonly used box-counting (BC) method to estimate the FD of the developing fetal cortical surface. Results from normal fetal brains show that the increase of cortical complexity is highly correlated with fetal developing weeks of GA. In addition, after 28 weeks of GA, the value of FD increases more rapidly because of the faster development of convolved folds. In comparison with results from the normal fetal group, the abnormal fetal brains were examined and the results show that: (1) mild ventricular dilatation has no significant developing difference compared with normal fetal brains; (2) twins had lower FD than that of normal fetal brains, which may be a delay of 2–3 weeks; (3) the case of cortical dysplasia also had low FD, indicating that developing delay may mean less cortical complexity. The results of the normal group are in good agreement with fetal brain development and demonstrate the effectiveness of FD as a promising means for the quantification of complexity of the fetal cortical surface.     

Indentation of punches into a piezoceramic body: two-dimensional contact problem of electroelasticity

The paper establishes the relationship between the solutions of the static contact problems of elasticity (no friction) for an isotropic half-plane and problems of electroelasticity for a transversely isotropic piezoelectric half-plane with the boundary perpendicular to the polarization axis. This allows finding the contact characteristics in the electroelastic case from the known elastic solution, without the need to solve the electroelastic problem. The contact problems of electroelasticity for different types of wedge-shaped punches (flat punch with rounded one or two edges, half-parabolic punch, and a periodic system of punches) are solved as examples Translated from Prikladnaya Mekhanika, Vol. 44, No. 11, pp. 55–70, November 2008.     

Experimental investigation of CO vibrational deactivation in a supersonic cooling gas flow

Abstract. The vibrational relaxation time of CO molecules at collisions with H atoms was measured in shock tube experiments by means of the CARS-spectroscopy method. The measurements of the CO vibrational temperature at gas temperatures of 1800–3000 K were performed in a supersonic cooling gas flow. The gas was heated behind the incident and reflected shock wave and then flowed out of a wedge-shaped nozzle. H atoms were generated in the reflected shock wave because of dissociation of H and HO admixtures. The extremely high efficiency of H atoms in CO vibrational deactivation was confirmed. Received 1 February 2000 / Accepted 20 February 2000     

Technique for Combined Dynamic Compression–Shear Testing of PBXs

We modify the split Hopkinson pressure bar and propose a compression–shear experimental method to investigate the dynamic behavior of polymer-bonded explosives (PBXs). The main apparatuses used include an incident bar with a wedge-shaped end and two transmission bars. We employ Y-cut quartzes with a rotation angle of 17.7° to measure the shear force and an optical system for shear strain measurement. A PBX with a density of 1.7 g/cm³ is investigated using the proposed method. Experimental results show that the specimen endures both compression and shear failure. Compression failure stress rises, and shear failure stress decreases as the strain rate increases. The sequences of shear and compression failure times are various at different strain rates. Based on the maximum shear failure criterion, we conclude that these phenomena are related to the experimental loading path.     

Measurement and chemical kinetic model predictions of detonation cell size in methanol–oxygen mixtures

In this study, detonation cell sizes of methanol–oxygen mixtures are experimentally measured at different initial pressures and compositions. Good agreement is found between the experiment data and predictions based on the chemical length scales obtained from a detailed chemical kinetic model. To assess the detonation sensitivity in methanol–oxygen mixtures, the results are compared with those of hydrogen–oxygen and methane–oxygen mixtures. Based on the cell size comparison, it is shown that methanol–oxygen is more detonation sensitive than methane–oxygen but less sensitive than hydrogen–oxygen.     

The propagation mechanism of high speed turbulent deflagrations

The propagation regimes of combustion waves in a 30 cm by 30 cm square cross–sectioned tube with an obstacle array of staggered vertical cylindrical rods (with BR=0.41 and BR=0.19) are investigated. Mixtures of hydrogen, ethylene, propane, and methane with air at ambient conditions over a range of equivalence ratios are used. In contrast to the previous results obtained in circular cross–sectioned tubes, it is found that only the quasi–detonation regime and the slow turbulent deflagration regimes are observed for ethylene–air and for propane–air. The transition from the quasi–detonation regime to the slow turbulent deflagration regime occurs at (where D is the tube “diameter” and is the detonation cell size). When , the quasi–detonation velocities that are observed are similar to those in unobstructed smooth tubes. For hydrogen–air mixtures, it is found that there is a gradual transition from the quasi–detonation regime to the high speed turbulent deflagration regime. The high speed turbulent deflagration regime is also observed for methane–air mixtures near stoichiometric composition. This regime was previously interpreted as the “choking” regime in circular tubes with orifice plate obstacles. Presently, it is proposed that the propagation mechanism of these high speed turbulent deflagrations is similar to that of Chapman–Jouguet detonations and quasi-detonations. As well, it is observed that there exists unstable flame propagation at the lean limit where . The local velocity fluctuates significantly about an averaged velocity for hydrogen–air, ethylene–air, and propane–air mixtures. Unstable flame propagation is also observed for the entire range of high speed turbulent deflagrations in methane–air mixtures. It is proposed that these fluctuations are due to quenching of the combustion front due to turbulent mixing. Quenched pockets of unburned reactants are swept downstream, and the subsequent explosion serves to overdrive the combustion front. The present study indicates that the dependence on the propagation mechanisms on obstacle geometry can be exploited to elucidate the different complex mechanisms of supersonic combustion waves. Received 5 November 2001 / Accepted 12 June 2002 / Published online 4 November 2002 Correspondence to: J. Chao (e-mail: jenny.chao@mail.mcgill.ca) An abridged version of this paper was presented at the 18th Int. Colloquium on the Dynamics of Explosions and Reactive Systems at Seattle, USA, from July 29 to August 3, 2001.     

Characteristics of liquid sheets formed by splash plate nozzles

An experimental study was conducted to identify the effect of viscosity on the characteristics of liquid sheets formed by a splash plate nozzle. Various mixtures of corn syrup and water are used to obtain viscosities in the range 1–170 mPa.s. Four different splash plates with nozzle diameters of 0.5, 0.75, 1, and 2 mm, with a constant plate angle of 55° were tested. Liquid sheets formed under various operating conditions were directly visualized. The sheet atomization process for the range of parameters studied here is governed by two different mechanisms: Rayleigh–Plateau (R–P) and Rayleigh–Taylor (R–T) instabilities. R–P occurs at the rim and R–T occurs on the thin sheet. The rim instability can be laminar or turbulent, depending on the jet Reynolds number. The R–T instability of the sheet is observed at the outer edges of the radially spreading sheet, where the sheet is the thinnest. It can also occur inside the sheet, due to formation of holes and ruptures.     

Deformation and short-term damage of physically nonlinear stochastic composites

The studies on the deformation and short-term damage of physically nonlinear homogeneous and composite materials are systemized. A single microdamage is modeled by an empty quasispherical pore in place of a microvolume damaged in accordance with the Huber–von Mises failure criterion. The ultimate microstrength is assumed to be a random function of coordinates. The porosity balance equation is derived. Together with the macrostress–macrostrain relationship, it constitutes a closed-form system of equations. The damage–macrostrain relationship and macrostress–macrostrain curves for homogeneous and composite materials are analyzed     

Vibration of beams with general boundary conditions due to a moving random load

Summary  The transverse vibrations of elastic homogeneous isotropic beams with general boundary conditions due to a moving random force with constant mean value are analyzed. The boundary conditions considered are: pinned–pinned, fixed–fixed, pinned–fixed, and fixed–free. Based on the Bernoulli beam theory, the problem is described by means of a partial differential equation. Closed-form solutions for the variance and the coefficient of variation of the beam deflection are obtained and compared for three types of force motion: accelerated, decelerated and uniform. The effects of beam damping and speed of the moving force on the dynamic response of beams are studied in detail. Received 3 December 2001; accepted for publication 30 April 2002     

A double-front structure of detonation wave as the result of phase transitions

Using thermochemical code calculations, we show that the nanographite–nanodiamond phase transition, which may occur in the detonation products of a number of carbon containing explosives, can affect the detonation properties and can cause a specific detonation regime with some unusual peculiarities. Among them, we first note the failure of the Chapman–Jouguet condition and the presence of the sonic plane, where the Mach number is equal to unity, in a detonation product expansion wave at a lower pressure than that at the Chapman–Jouguet point. The peculiarities of this detonation regime are demonstrated by the example of TNT, HNS, and RDX. The computed detonation velocities are in excellent agreement with experiments over a wide range of initial charge densities for all of the investigated explosives. The results of this work allow one to explain, e.g., contradictory experimental data on the detonation pressure and on the length of the reaction zone for TNT. We believe that some other solid–solid, solid–liquid, and liquid–liquid phase transformations in the detonation products may also cause a detonation regime with the same features as shown here for the nanographite–nanodiamond transition. We suggest a computational study that should facilitate proposing detonation experiments strongly arguing in favor of the model presented. PACS 47.40.-x; 47.40.Rs; 64.70.-p; 64.70.Kb; 05.70.-a; 05.70-.CeThis paper was based on the work that was presented at the 19th International Colloquium on the Dynamics of Explosions and Reactive Systems, Hakone, Japan, July 27–August 1, 2003.     

Domain decomposition method with hybrid approximations applied to solve problems of elasticity

To solve two-dimensional boundary-value problems of elasticity, two iteration algorithms of the domain decomposition method are proposed: parallel Neumann–Neumann and sequential Dirichlet–Neumann. They are based on the hybrid boundary–finite-element approximations. The algorithms are proved to converge. The optimal parameters are selected using the minimum-residual and steepest-descent methods. Some plane problems of elasticity are solved as examples, and stationary and nonstationary iteration algorithms in these examples are analyzed for efficiency Translated from Prikladnaya Mekhanika, Vol. 44, No. 11, pp. 18–29, November 2008.     

Prediction of separation flows around a 6：1 prolate spheroid using RANS/LES hybrid approaches

This paper presents hybrid Reynolds-averaged Navier–Stokes (RANS) and large-eddy-simulation (LES) methods for the separated flows at high angles of attack around a 6:1 prolate spheroid. The RANS/LES hybrid methods studied in this work include the detached eddy simulation (DES) based on Spalart–Allmaras (S–A), Menter’s k–ω shear-stress-transport (SST) and k–ω with weakly nonlinear eddy viscosity formulation (Wilcox–Durbin+, WD+) models and the zonal-RANS/LES methods based on the SST and WD+ models. The switch from RANS near the wall to LES in the core flow region is smooth through the implementation of a flow-dependent blending function for the zonal hybrid method. All the hybrid methods are designed to have a RANS mode for the attached flows and have a LES behavior for the separated flows. The main objective of this paper is to apply the hybrid methods for the high Reynolds number separated flows around prolate spheroid at high-incidences. A fourth-order central scheme with fourth-order artificial viscosity is applied for spatial differencing. The fully implicit lower–upper symmetric-Gauss–Seidel with pseudo time sub-iteration is taken as the temporal differentiation. Comparisons with available measurements are carried out for pressure distribution, skin friction, and profiles of velocity, etc. Reasonable agreement with the experiments, accounting for the effect on grids and fundamental turbulence models, is obtained for the separation flows. The project supported by the National Natural Science Foundation of China (10502030 and 90505005).     

In situ force-balance tensiometry

 Although a fundamental physical parameter, surface tension is difficult to measure. Common tensiometry inaccuracy comes from failure to control air–liquid–solid contact conditions, or account for liquid meniscus geometry and buoyancy corrections. This paper describes an in situ tensiometry technique, based on withdrawal of a thin-walled tube from the liquid interface, that enforces a known air–liquid–solid contact condition. This technique can be pursued at any level of experimental hygiene. Experimental results for filtered tap water, an alcohol–water solution, and a surfactant–water solution show that results repeatable to three significant digits are obtained with modest effort for a variety of geometrical parameters. Received: 7 October 1997/Accepted: 23 April 1998     

Estimation of Chaotic and Regular (Stick–Slip and Slip–Slip) Oscillations Exhibited by Coupled Oscillators with Dry Friction

In this paper, we present a novel approach to quantify regular or chaotic dynamics of either smooth or non-smooth dynamical systems. The introduced method is applied to trace regular and chaotic stick–slip and slip–slip dynamics. Stick–slip and slip–slip periodic and chaotic trajectories are analyzed (for the investigated parameters, a stick–slip dynamics dominates). Advantages of the proposed numerical technique are given.     

Possibilities and Limitations of Computer Simulations of Industrial Turbulent Dispersed Multiphase Flows

We give an overview on the usage of computer simulations in industrial turbulent dispersed multiphase flows. We present a few examples of industrial flows: bubble columns and bubbly pipe flows, stirred tanks, cyclones, and a fluid catalytic cracking unit. The fluid catalytic cracking unit is used to illustrate the complexity of the physical phenomena involved, and the possibilities and limitations of the different approaches used: Eulerian–Lagrangian (particle-tracking) and Eulerian–Eulerian (two-fluid). In the first approach, the continuous phase is solved using either RANS simulations (Reynolds-Averaged Navier–Stokes simulations) or DNS/LES (Direct Numerical Simulations/Large-Eddy Simulations), and the individual particles are tracked. In the second approach, the dispersed phase is averaged, leading to two sets equations, which are quite similar to the RANS equations of single-phase flows. The Eulerian–Eulerian approach is the most commonly used in industrial applications, however, it requires a significant amount of modelling. Eulerian–Lagrangian RANS can be simpler to use; in particular in situations involving complex boundary conditions, polydisperse flows and agglomeration/breakup. The key issue for the success of the simulations is to have good models for the complex physics involved. A major weakness is the lack of good models for: the turbulence modification promoted by the particles, the inter-particle interactions, and the near-wall effects. Eulerian–Lagrangian DNS/LES can play an important role as a research tool, in order to get a better physical understanding, and to improve the models used in the RANS simulations (either Eulerian–Eulerian or Eulerian–Lagrangian).     

Dust acoustic shock waves in coupled dusty plasmas with nonthermal ions

Dust acoustic shock waves of the Korteweg-de Vries–Burgers (KdV–Burgers) equation and the modified Korteweg-de Vries–Burgers (MKdV–Burgers) equation are studied in strongly coupled dusty plasmas containing nonthermal ions and Boltzmann-distributed electrons. The effects of important parameters, such as nonthermal parameter, relative temperature, relative density and dust particles viscosity, on the properties of shock waves are discussed.