Spectrum of normal oscillations of a dislocation ensemble in a viscoplastic medium

Dynamic equations of a dislocation ensemble are derived within the framework of the gauge model of an elastic body with defects. The governing relation between the defect field and the material continuum is obtained with allowance for the analogy between the equations obtained and Maxwell's electrodynamic equations. In the phenomenological theories of plasticity, this relation corresponds to the definition of a viscoplastic body. The dispersion relations and configurations of the normal oscillations of a dislocation ensemble in a viscoplastic medium are calculated. Institute of the Physics of Strength and Materials Science, Siberian Division, Russian Academy of Sciences, Tomsk 634821. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 41, No. 1. pp. 182–185, January–February, 2000.     

Forced oscillations of a gas bubble in a spherical volume of a compressible liquid

A spherically symmetric problem of oscillations of a single gas bubble at the center of a spherical flask filled with a compressible liquid under the action of pressure oscillations on the flask wall is considered. A system of differential-difference equations is obtained that extends the Rayleigh-Plesset equation to the case of a compressible liquid and takes into account the pressure-wave reflection from the bubble and the flask wall. A linear analysis of solutions of this system of equations is performed for the case of harmonic oscillations of the bubble. Nonlinear resonance oscillations and nearly resonance nonharmonic oscillations of the bubble caused by harmonic pressure oscillations on the flask wall are analyzed. Ufa Scientific Center, Russian Academy of Sciences, Ufa 450000. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 40, No. 2, pp. 111–118, March–April, 1999.     

Rheological characterization and constitutive modeling of bread dough

Bread dough (a flour–water system) has been rheologically characterized using a parallel-plate, an extensional, and a capillary rheometer at room temperature. Based on the linear and nonlinear viscoelastic and viscoplastic data, two constitutive equations have been applied, namely a viscoplastic Herschel–Bulkley model and a viscoelastoplastic K–BKZ model with a yield stress. For cases where time effects are unimportant, the viscoplastic Herschel–Bulkley model can be used. For cases where transient effects are important, it is more appropriate to use the K-BKZ model with the addition of a yield stress. Finally, the wall slip behavior of dough was studied in capillary flow, and an appropriate slip law was formulated. These models characterize the rheological behavior of bread dough and constitute the basic ingredients for flow simulation of dough processing, such as extrusion, calendering, and rolling.     

Radial oscillations of soluble vapor-gas bubbles in a liquid

Soluble vapor-gas bubbles performing small radial oscillations in a liquid are considered. The heat- and mass-transfer processes and temperature and concentration inhomogeneities in the vaporgas mixture are taken into account. Expressions for the damping rate of radial oscillations of soluble vapor-gas bubbles are obtained. In [1–3] the dynamics of vapor-gas bubble oscillations were considered for a gas insoluble in liquid.     

Accounting for the elastic properties of a non-Newtonian material under its viscosimetric flow

This paper considers the deformation and viscoplastic flow of a non-Newtonian material enclosed between coaxial rigid cylindrical surfaces, each of which performs a rotation followed by a stop and a rotation in the opposite direction. The problem is solved using the model of large elastoviscoplastic deformations, in contrast to the classical solutions obtained using the model of a rigid viscoplastic body. The parameters of the viscosimetric process are calculated in both the region of viscoplastic flow developed and the region of elastic deformation. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 49, No. 2, pp. 143–151, March–April, 2008.     

Mechanical Performance of a Recycled Carbon Fibre/PP Composite

A composite made of recycled carbon fibres in recycled polypropylene matrix is studied experimentally to describe the features of the elastic and time dependent nonlinear mechanical behaviour. The properties of the developed material have a large variability to be addressed and understood. It was found that the stress-strain curves in tension are rather nonlinear at low strain rate and the strength is sensitive to strain rate. The elastic properties’ reduction for this composite after loading to high strains is rather limited. More important is that even in the “elastic region” due to viscoelastic effects the slope of loading–unloading curve is not the same and that at higher stress large viscoplastic strains develop and creep rupture is typical. The time and stress dependence of viscoplastic strains was analysed and described theoretically. The viscoelastic response of the composite was analysed using creep compliance, which was found to be slightly nonlinear.     

Propagation of pressure waves in a gas-liquid medium with a cluster structure

Propagation of a stepwise shock wave in a liquid containing spherical gas-liquid clusters is experimentally studied. Measured results are compared with available theoretical models. It is shown that resonant interaction of gas-liquid clusters in the wave can increase the amplitude of oscillations in the shock wave. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 46, No. 3, pp. 50–60, May–June, 2005.     

Cavitation bubble collapse in nonlinear viscous and viscoplastic media

The problem of the collapse of a bubble in nonlinear viscous and viscoplastic media under the influence of pressure at infinity is solved numerically. The pressure at which the radius of the bubble begins to decrease, the limiting radius of the bubble in the viscoplastic case and the critical collapse pressure where there is no plastic component are found. The critical pressure is found to be an order smaller than the corresponding value for a Newtonian viscous fluid. Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No.2, pp. 181–184, March–April, 1994.     

Natural oscillations of a liquid of finite electrical conduction in the presence of an external magnetic field

The effect of the finite electrical conduction (finiteness of the magnetic Reynolds number), which is considered a dissipative factor, on small natural oscillations of an ideal heavy liquid of finite depth whose free surface borders on vacuum is studied. A constant external horizontal magnetic field is applied to the liquid. The energy-balance equation is derived, and the theorem of wave attenuation with time is proved. Numerical calculations and the resulting asymptotic formulas give a complete pattern of the spectrum, including its continuous part. The amplitude-frequency characteristics of the wave modes are presented. Rostov State University, Rostov-on-Don 344007. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 41, No. 2, pp. 3–10, March–April, 2000.     

Optimization of shock-wave action on a spherical bubble in an ideal incompressible liquid

The possibility of controlling the oscillations of a spherical gas bubble in an ideal incompressible liquid is subjected to theoretical analysis. Liquid surface tension forces are not taken into account. The optimization process realizing a maximum of the radius amplitude and a maximum of the gas pressure in the bubble for a given impulsive change of pressure at infinity is considered. A shock-resonance bubble oscillation procedure giving stepwise pressure changes at the extrema of the radius is constructed. This problem is of interest in connection with the investigation of cavitation erosion [1] and processes in biological tissues [2–4]. Moscow. Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 175–178, September–October, 1988.     

Acoustic properties of TiNi-based alloys

The specific features of the change in the acoustic properties of TiNi-based alloys are studied in a broad temperature internal. It is shown that in the temperature range of loading-induced martensite transformations, there is a region of long-term and small-amplitude low-frequency sound oscillations. The method of Fourier analysis is used to determine the frequency-amplitude characteristics of quasipcriodic oscillatory processes in TiNi-based alloys. In the temperature interval considered, the free low-frequency oscillations of the TiNi-based sample are characterized by a low level of damping. Institute of Medical Materials and Implants with Form Memory, Tonsk 634034. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 41, No. 4, pp. 185–189, July–August, 2000.     

Influence of the boundary of a column of incompressible liquid in investigating axisymmetric oscillations of a solid sphere in a cavity

Axisymmetric oscillations of a rigid spherical body in a column of ideal incompressible liquid with a plane boundary in the form of a free liquid surface or a rigid wall within a round cylindrical cavity are considered. The potential and pressure fields are plotted; expressions are obtained for the kinetic energy of the system and the hydrodynamic forces acting on the body. The resistance of the liquid to accelerated movement of the body is determined as a function of the distance to the boundary, for various parameter values. For specified oscillations of the body, the results obtained for axisymmetric conditions in a halfspace are compared with those obtained in an infinite cylindrical cavity. Translated from Prikladnaya Mekhanika, Vol. 35, No. 12, pp. 11–18, December, 1999.     

Construction of solutions of the problem of free oscillations of viscous fluid in a half-filled spherical tank

We study free oscillations of a viscous incompressible fluid with free boundary in a hemispherical tank. We determine four systems of coordinate functions that satisfy the equations of the problem inside the domain and possess the properties of the required solution. Then, using these systems, we construct a coordinate system that satisfies all but one boundary condition of the problem. This system is used for the solution of the problem by a projection method. We compute the eigenfrequencies and logarithmic decrements of oscillations of the fluid. The results obtained are compared with asymptotic and empirical formulas. Translated from Neliniini Kolyvannya, Vol. 11, No. 4, pp. 439–461, October–December, 2008.     

Three-dimensional flows of thin layers of viscoplastic media in deformable channels and cavities

The problem of the three-dimensional flow of a viscoplastic medium in a thin layer bounded by two deformable material surfaces whose points are displaced transversely across the layer is formulated and solved. Expressions for the velocity components and the flow-rate and equations for calculating the pressure and the boundary of the shear flow region are obtained. Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 4, pp. 201–205, July–August, 1998.     

Effect of random longitudinal vibrations on the Poiseuille flow of a complex liquid

In this work, the rectilinear Poiseuille flow of a complex liquid flowing in a vibrating pipe is analyzed. The pipe wall performs oscillations of small amplitude that can be adequately represented by a weakly stochastic process, for which a quasi-static perturbation solution scheme is suggested. The flow is analyzed using the Bautista–Manero–Puig constitutive equation, consisting on the upper-convected Maxwell equation coupled to a kinetic equation to account for the breakdown and reformation of the fluid structure. A drastic enhancement of the volumetric flow is predicted in the region where the fluid experiences pronounced shear-thinning. Finally, flow enhancement is predicted using experimental data reported elsewhere for wormlike micellar solutions of cetyl trimethyl ammonium tosilate.     

Viscoplastic dynamics of isotropic plates of variable thickness under explosive loading

A problem of viscoplastic dynamic bending of isotropic plates of variable thickness is formulated. A method for integrating the initial-boundary problem is developed. Numerical results are compared with a known analytical solution obtained within a rigid-plastic model; good agreement is demonstrated. The efficiency of the method developed is verified by numerical computations. It is shown that the final flexure of plates can be reduced severalfold by applying rational design. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 48, No. 2, pp. 123–134, March–April, 2007.     

The flow of viscoplastic material between two concentric spheres

The motion of a viscoplastic medium between two concentric spheres is considered upon rotation of one sphere with constant angular velocity. This problem is solved by an heuristic iterative method. The boundary of the stagnation zones is found and its specific shape is shown. The flow characteristics versus the parameter of the medium are obtained. Voronezh State Engineering Academy, Voronezh 394017. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 40, No. 1, pp. 133–139, January–February, 1999.     

Law of flow of a viscoplastic fluid through a porous medium with allowance for inertial losses

A macroscopic law of flow of a viscoplastic Schwedoff-Bingham fluid through a porous medium is obtained on the basis of percolation theory with allowance for viscous and inertial losses. The asymptotics of the flow law are estimated and expressions for determining the limiting pressure gradient as a function of the microinhomogeneity parameters are given. Satisfactory qualitative agreement between the theoretical and known experimental data is observed. Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, pp. 68–73, January–February, 1999.     

Effect of the contact-line dynamics on the natural oscillations of a cylindrical droplet

The natural oscillations of a cylindrical droplet of an inviscid liquid surrounded by a different liquid and bounded in the axial direction by solid planes are studied. The motion of the contact line is described using an effective boundary condition. The dependence of the frequency and damping ratio on the capillary parameter is found. It is shown that the fundamental frequency of the translation mode vanishes beginning from a certain value of the capillary parameter. Depending on the ratio of the radial and axial dimensions of the droplet, the fundamental frequency of the axisymmetric mode and modes higher than the translation mode can vanish in a certain range of the capillary parameter. This dependence of the natural oscillation frequencies on the problem parameters allows one to determine the capillary parameter. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 48, No. 5, pp. 78–86, September–October, 2007.     

Buoyancy-driven motion of a two-dimensional bubble or drop through a viscous liquid in the presence of a vertical electric field

The effect of an electric field on the buoyancy-driven motion of a two-dimensional gas bubble rising through a quiescent liquid is studied computationally. The dynamics of the bubble is simulated numerically by tracking the gas–liquid interface when an electrostatic field is generated in the vertical gap of the rectangular enclosure. The two phases of the system are assumed to be perfect dielectrics with constant but different permittivities, and in the absence of impressed charges, there is no free charge in the fluid bulk regions or at the interface. Electric stresses are supported at the bubble interface but absent in the bulk and one of the objectives of our computations is to quantify the effect of these Maxwell stresses on the overall bubble dynamics. The numerical algorithm to solve the free-boundary problem relies on the level-set technique coupled with a finite-volume discretization of the Navier–Stokes equations. The sharp interface is numerically approximated by a finite-thickness transition zone over which the material properties vary smoothly, and surface tension and electric field effects are accounted for by employing a continuous surface force approach. A multi-grid solver is applied to the Poisson equation describing the pressure field and the Laplace equation governing the electric field potential. Computational results are presented that address the combined effects of viscosity, surface tension, and electric fields on the dynamics of the bubble motion as a function of the Reynolds number, gravitational Bond number, electric Bond number, density ratio, and viscosity ratio. It is established through extensive computations that the presence of the electric field can have an important effect on the dynamics. We present results that show a substantial increase in the bubble’s rise velocity in the electrified system as compared with the corresponding non-electrified one. In addition, for the electrified system, the bubble shape deformations and oscillations are smaller, and there is a reduction in the propensity of the bubble to break up through increasingly larger oscillations.