Effect of the elastic factor on the hydrodynamic stability of a structurally viscous medium

The effect of relaxation phenomena on the hydrodynamic stability of the plane gradient flow of a structurally viscous medium is investigated using linear theory.Notation _ij stress tensor deviator - U_i components of the velocity vector - x_i coordinates - t time - P pressure - =₀L/^*V plasticity parameter - _o limiting shear stress - andc dimensionless wave number and the perturbation frequency - Re=VL/* Reynolds number - density - F_ij deformation rate tensor Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 35, No. 5, pp. 868–871, November, 1978.     

Investigation of the gapless state in bismuth-antimony alloys

The results are presented from an experimental study of the gapless state produced in semiconducting alloysBi _1–x Sb _x by pressure-induced band inversion. The magnetoresistance properties of the alloys have been investigated both in weak magnetic fields (H « 1) and in strong fields (H75 kOe) at liquidhelium temperatures in the Sb concentration interval 0.06x0.15 and pressure interval 1 bar p<20 kbar. At pressuresp close to the pressurep _k at which the gapless state is realized a semiconductor-semimetal-semiconductor transition is detected inBi _1–x Sb _x alloys withx=0.070 and 0.071. The rates of change of the gap _gL before and after inversion are determined: –(2.5±0.5)×10^–6 eV/bar and (1.5±0.5)×10^–6 eV/bar, respectively. A reduction in the carrier effective mass as _gL 0 is observed down to values of 10^–4 m ₀. It is shown that as _gL 0 the carrier mobilities in the alloys increase abruptly, the effect being a maximum in the purest alloys, where forT=4.2 K the mobility along the binary axis attains the record-high value of 3×10⁸ cm²/V · sec.     

Nonequilibrium — filtration equations

Within the framework of the linear thermodynamics of irreversible processes, a general form is obtained for the equations of isothermal nonequilibrium filtration of an incompressible Liquid through a nondeforming porous matrix.Notation Q^(e) external heat flux - Q uncompensated heat - U interval energy - S entropy - T temperature - dA⁽ⁱ⁾ elementary work of the internal surface forces - internal degrees of freedom - B thermodynamic parameters conjugate to - dissipative function - _ij stress tensor in the liquid - v_i liquid-particle velocity - V₀ volume of the porous medium - V liquid volumes - S₀ surface of volume V₀ - S_e liquid part of S₀ - S₁ liquid contact surface with the porous matrix inside V₀ - P mean (over S_e) liquid pressure - q_i filtration velocity - s Laplace-transform parameters - t time Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 39, No. 1, pp. 77–80, July, 1980.     

Modification of the iteration algorithm for solving the inverse heat conduction problem

A modification of the iteration algorithm for solving the inverse heat conduction problem is proposed by the example of solution of the coefficient inverse heat conduction equation. In order to recover the functional dependence in the iteration algorithm of the gradient type it is proposed to determine separately the depth of descent for each of the components of the sought vector of parameters upon minimization of the meansquare error, which makes unnecessary solution of the conjugated boundary problem and computing of the derivatives of the target functional. The modification reduces the amount of computations and improves convergence of the algorithm.Notation C(T) volume heat capacity - T temperature - time - _m right boundary value of the time interval - x coordinate - b right boundary value of the space interval - (T) heat conduction coefficient - () boundary temperature - J target functional - B spline - b _k ,k=0, 1, ..., m+1 parameter of the spline approximation of the function (T) - p iteration number - J gradient of the target functional - step length in the method of steepest descent - G parameter of the method of steepest descent - (x, ) increment of the temperature field - _i ,i=1,2,... error of the recovery of the function (T) at thei-th interpolation knot - noise level All-Russian Scientific Research Institute of Experimental Physics, Arzamas, Russia. Translated for Inzhenerno-Fizicheskii Zhurnal, Vol. 68, No. 3, pp. 494–499, May–June, 1995.     

Relationship between the energy supply parameters and the physicochemical l characteristics of polymer compositions during drying and thermal processing

The effect of the type of energy supply on the formation of temperature and concentration fields in the thermal processing of polymer compositions is considered.Notation T₀, T initial and current temperature of the coating - T_m temperature of the air - =(T-T_o)/(T_m-T₀) dimensionless temperature of the coating - a thermal diffusivity - A absorption power of the coating - D diffusion coefficient - thermal conductivity - c thermal capacity - density - _k convective heat transfer coefficient - i number of moles of reacting groups per unit volume of polymer - K₀ factor in front of the exponential - R gas constant - u concentration - Q thermal effect of the reaction - q_n density of the incident radiant flux - =x/ dimensionless coordinate over the thickness of the coating - Ki=Aq_n /(T_m-T₀) Kirpichev criterion characterizing the thermal effect of the reaction - Ki_p=Qi/c (T_m-T₀) analog of the Predvoditelev criterion, characterizing the rate of occurrence of a chemical excess in the system - Bu= Bouguer criterion - Lu=D/a Lykov number - Fo=a/² Fourier number - Bi= _k Biot number Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 39, No. 1, pp. 26–33, July, 1980.     

Inhomogeneous shear flows of linear polymers

Solutions of a system of equations of nonlinear viscoelastic fluid motion describing inhomogeneous shear flows of linear polymers are indicated.Notation _ij stress tensor - p pressure - F_i mass force vector - _ij Kronecker delta - coefficient of shear viscosity - relaxation time - _ij inner parameter - _ij=vi/x_j velocity gradient tensor - ₀ initial value of the shear viscosity coefficient - ₀ initial value of the relaxation time - D dimensionless first invariant of the additional stress tensor - A, B, C constants of integration - f(D) universal function characterizing the material - r, , z cylindrical coordinates - u=v_z axial component of the velocity vector - v=v circumferential component of the velocity vector - ₁, ₂ first and second differences of the normal stress - Q volume mass flow rate - R radius of a circular tube - R₁, R₂ radii of the inner and outer cylinders, respectively - M moment per unit length Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 41, No. 3, pp. 449–456, September, 1981.     

Analysis of strain localization in strain-softening hyperelastic materials,using assumed stress hybrid elements

Newly developed assumed stress finite elements, based on a mixed variational principle which includes unsymmetric stress, rotation (drilling degrees of freedom), pressure, and displacement as variables, are presented. The elements are capable of handling geometrically nonlinear as well as materially nonlinear two dimensional problems, with and without volume constraints. As an application of the elements, strain localization problems are investigated in incompressible materials which have strain softening elastic constitutive relations. It is found that the arclength method, in conjunction with the Newton Raphson procedure, plays a crucial role in dealing with problems of this kind to pass through the limit load and bifurcation points in the solution paths. The numerical examples demonstrate that the present numerical procedures capture the formation of shear bands successfully and the results are in good agreement with analytical solutions.List of Symbols u displacement - R rotation - U right stretch tensor - r^* Biot stress tensor - t first Piola Kirchhoff stress tensor - Cauchy stress tensor - I identity tensor - F deformation gradient I+(u)^T - ab a _ib_jg ⁱ g ^j =dyad - a·b a _ibⁱ=dot product - A·b A _ijb^j g ⁱ - A·B A _ikB _inf.j ^supk. g ⁱ g ^j - A:B A _ijB^ij - v velocityu - W spin tensorR - D rate of stretch r - r^* UL rate of r^* - t UL rate of t - _n Kronecker's delta - - J det F=det{I+(u)^T} - symm (A) 1/2(A+A ^T ) - skew (A) 1/2(A-A ^T ) - trace (A) A _inf.i ^supi. This research is supported by the Office of Naval Research. The first author wishes to express his appreciation to Dr. H. Murakawa, Dr. E. F. Punch, Mr. A. Cazzani, and Dr. H. Okada for fruitful discussions on the subject     

Two singular points finite elements in the analysis of kinked cracks

A formulation for incorporating two singular points (TSP) of variable orders in a single finite element is presented. Though the element does not satisfy any of the convergence criterion, its performance is found to be good, which has been demonstrated by considering number of examples on kinked cracks. In each case only one such element is incorporated in the whole discretization. These examples illustrate the usefulness of the element to analyse kinked cracks of various sizes and shapes and subjected to different loading and boundary conditions. Computed J-integrals are compared with analytical solutions, wherever possible, and the accuracy appears quite good. Effect of size of the element on, and the path independence of, J are also examined.List of symbols , conventional natural coordinate system - ₁, ₂ another elemental natural coordinate system - L _ij equation of side ij of an element - A _ij , B _ij constants - N _i shape function associated node i - ₁, ₂ constants associated with the order of singularities - , an elemental natural coordinate system - u _i , v _i displacement components in the Cartesian directions     

Interfacial phenomena of plasma arc welding of mild steel and aluminium

The interfacial microstructures and intermetallic compounds produced by plasma arc butt fusion welding of aluminium to mild steel have been investigated. An intermetallic compound alloy layer formed at the interface region between mild steel and aluminium was determined using quantitative metallography and the mechanism of the intermetallic layer formation and growth was elucidated. The melt width and the alloy layer thickness decrease with increasing transfer-speed of the plasma torch. The intermetallic layers formed at the interface region between mild steel and aluminium are predominantly-phase (Fe₂Al₅) and-phase (FeAl₃). The-phase layer with columnar crystal grows rapidly as tongue-like structures in the direction of the mild steel substrate and the-phase layer with granular crystals projects slowly to the aluminium side in the course of solidification. As a result, many vacancies are produced in the-phase layer. The structures of the melted zone and the fusion boundary of the mild steel change into grain refinement, whereas the melted zone of the aluminium has a eutectic structure of aluminium and-phase.     

Prediction of material damping of laminated polymer matrix composites

In this study the material damping of laminated composites is derived analytically. The derivation is based on the classical lamination theory in which there are eighteen material constants in the constitutive equations of laminated composites. Six of them are the extensional stiffnesses designated by [A] six of them are the coupling stiffnesses designated by [B] and the remaining six are the flexural stiffnesses designated by [D]. The derivation of damping of [A], [B] and [D] is achieved by first expressing [A], [B] and [D] in terms of the stiffness matrix [Q]^(k) andh _k of each lamina and then using the relations ofQ _ij ^(k) in terms of the four basic engineering constantsE _L,E _T, G_LT andv _LT. Next we apply elastic and viscoelastic correspondence principle by replacingE _L,E _T...by the corresponding complex modulusE _L ^*,E _T ^*,..., and [A] by [A]^*, [B] by [B]^* and [D] by [D]^* and then equate the real parts and the imaginary parts respectively. Thus we have expressedA _ij ,A _y ,B _ij ,B _ij , andD _ij in terms of the material damping _L ^(k) and _T ^(k)...of each lamina. The damping _L ^(k), _T ^(k)...have been derived analytically by the authors in their earlier publications. Numerical results of extensional damping l _ij =A _ij /A _ij coupling dampingc _ij =B _ij /B _ij and flexural damping F _ij =D _ij /D _ij are presented as functions of a number of parameters such as fibre aspect ratiol/d, fibre orientation , and stacking sequence of the laminate.     

Effect of resonant impurity scattering on collective mode peaks in the ultrasound attenuation of heavy fermion superconductors

We have calculated the attenuation of longitudinal ultrasound due to real order parameter fluctuations in impure polar and planarp-wave superconductors. The quasiparticle self-energy and the corresponding vertex corrections have been included in thet-matrix approximation for arbitrary scattering rate =1/2_N and all scattering phase shifts _N (0 _N/2). We obtain sound attenuation peaks belowT _c whose heights, positions, and shapes depend on ₀ (sound frequency), (₀), _N, and (coupling strength due to particle-hole asymmetry). The peaks become much more distinct and sharper for _N =/2 (resonant scattering by impurities) than for _N=0 (Born approximation). By choosing , _N, and suitably, qualitative agreement between calculated and observed peaks in UBe₁₃ and UPt₃ can be achieved.     

Effect of magnesium content on the stress exponent and effective stress in the steady state creep of Al-Mg alloys

The stress exponent of steady state creep,n, and the internal ( _i) and effective stresses ( _e) have been determined using the strain transient dip test for a series of polycrystalline Al-Mg alloys creep tested at 300° C and compared with previously published data. The internal or dislocation back stress, _i, varied with applied stress,, but was insensitive to magnesium content of the alloy, being represented by the empirical equation _i=1.084 ^1.802. Such an applied stress dependence of _i can be explained by using an equation for _i of the form _i (dislocation density)^1/2 and published values for the stress dependence of dislocation density. Values of the friction stress, _f, derived using the equation _e/=(1–c) (1– _f/), indicate that _f is not dependent on the magnesium content. A constant value of _f can best be rationalized by postulating that the creep dislocation structure is relatively insensitive to the magnesium content of the alloy.On leave from Engineering Materials Department, University of Windsor, Windsor, Ontario N9B 3P4, Canada.     

Hierarchical three dimensional curved beam element based on p-version

This paper presents a three node curved three dimensional beam element for linear static analysis where the element displacement approximation in the axial () and transverse directions ( and ) can be of arbitrary polynomial orders p , p and p . This is accomplished by, first constructing one dimensional hierarchical approximation functions and the corresponding nodal variable operators in , and directions using Lagrange interpolating polynomials and then taking the products (also called tensor product) of these hierarchical one dimensional approximation functions and the corresponding nodal variable operators. The resulting approximation functions and the corresponding nodal variables for the three dimensional beam element were hierarchical. The formulation guarantees C ⁰ continuity. The element properties are established using the principle of virtual work. In formulating the properties of the element all six components of the stress and strain tensor are ratained. The geometry of the beam element is defined by the coordinates of the nodes located at the axis of the beam and node point vectors representing the nodal cross-sections. The results obtained from the present formulation are compared with analytical solutions (when available) and the h-models using isoparametric three dimensional solid elements. The formulation is equally effective for very slender as well as deep beams since no assumptions are made regarding such conditions during the formulation.     

Nonlinear bending and vibration of symmetrically laminated orthotropic elliptical plate with simply supported edge

Summary This paper deals with the static large deflection and the large amplitude free flexural vibration of a symmetrically laminated orthotropic elliptical plate with a simply supported immovable edge. A unified approximate solution of the dynamic von Karman-type equations of the plate in terms of the deflection and two inplane displacements is presented by use of a modified Galerkin procedure. Two inplane equations of equilibrium and the associated inplane boundary conditions are satisfied exactly. Numerical computations are performed for static and dynamic responses of homogeneous and symmetric cross-ply elliptical plates with different axes ratios, numbers of layers and high-modulus material properties. In the static and dynamic linear cases, present results are compared with available data.Notations A nondimensional amplitude (=w ₀/h) - A _i, B_i constants in Eq. 912) - A _ij, D_ij plate stiffnesses defined in Eqs. (4) - a, b, h semi-major axis, semi-minor axis and thickness of elliptical plate - C _ij ^(k) reduced stiffnesses of thek-th layer - d _ij, e_ij plate constants defined in Eqs. (4) - E _L, E_T, G_LT principal and shear moduli of orthotropic material - F nondimensional time function - G ₁, G₂ constants in Eq. (11) - J _i() differential operator defined in Eq. (4) - l, m direction cosines - M _x, M_y, M_xy bending and twisting moments per unit length - M ,M ,M nondimensional moments defined in Eqs. (8) - N _x, N_y, N_xy membrane forces per unit length - N ,N ,N nondimensional membrane forces defined in Eqs. (9) - Q, q nondimensional and dimensional transverse load per unit area - T, T ₀ nondimensional nonlinear and linear periods respectively in Eq. (22) - t time - U, V, W nondimensional displacements defined in Eqs. (5) - u ⁰, v⁰, w midsurface displacement components alongx, y andz directions, respectively - w ₀ maximum deflection - x, y, z rectangular cartesian coordinates - _i constant coefficients in Eqs. (17) and (18) - coefficient of nonlinear term in Eq. (21) - , nondimensional coordinates defined in Eqs. (5) - normalization factor in Eq. (19) - axis ratio,a/b - v, v _LT Poisson's ratios of isotropic and orthotropic materials - , ₀ mass per unit area and volume, respectively - nondimensional time defined in Eqs. (5) - ₀ nondimensional fundamental linear frequency in Eq. (21) With 5 Figures     

On the dispersion of gases under the action of the medium

Some general regularities of dispersion of a gas emerging from a nozzle submerged in a liquid are considered. A condition for establishment of the so-called maximum dispersion state is formulated.Notation ₀ coefficient of surface tension at the liquidgas boundary - contact angle of wetting of the nozzle material surface by the liquid - p_at atmospheric pressure - p air pressure - density of the liquid - g gravitational acceleration - h height of the liquid column - ₁, and _g dynamic viscosity coefficients of the liquid and gas, respectively - R and r radii of the bubble and nozzle, respectively - Q and F dimensionless criteria - , , , , and undetermined coefficients - ratio of the circumference of a circle to its diameter     

Dependence of Hertzian fracture angle on Poissons ratio and indentation techniques

Sub-parallel concentric conic fractures can be produced consecutively in Perspex by liquid indentation. There is a linear relationshp between the conic angle, , of Hertzian fracture and the Poisson's ratio, , of the material. This angle is about 10 higher than the calculated path of the principal stress trajectory for a given . decreases with the increase of stress application rate. This dependence of is very marked in materials with high Poisson's ratios.     

Flux motion in anisotropic type-II superconductors nearH c 2 with arbitrary vortex orientation

Flux motion in anisotropic type-II superconductors near H_{c 2} is studied in the framework of the time-dependent Ginzburg-Landau (TDGL) theory for the case that the average flux densityB is oriented in an arbitrary direction relative to the principal axes of the sample. The linearized TDGL equation for a uniformly translating order parameter is solved and expressions for all elements of the flux-flow resistivity tensor _ij (including the off-diagonal Hall elements) are obtained. The diagonal elements _ii show the angular scaling property that _ii(B) = _ii(B/H_{c 2}(, ø)), whereas the Hall elements _ij (i j) have additional angular dependences that are not contained in H_c2. For the case that the normal state Hall elements _ij ⁽ⁿ⁾ B _k with i j k, the ratios _ij/ _ij ⁽ⁿ⁾ are functions of B/H_c2 (, ) only.     

Mixing displacement of viscoplastic fluids feom a channel with a rectangular cavity

Different mixing displacement regimes for viscoplastic fluids are investigated theoretically and experimentally.Notation x and y Cartesian coordinates - h half-width of the gap - H, L dimensionless depth and length of the cavity - v_x, v_y velocity components - density - _ik components of the viscous stress tensor - e_ik components of the deformation rate tensor - dynamic viscosity - dynamic viscosity for infinitely high displacement velocity - ₀ analog of the limiting shear stress in Bingham's fluid - W parameter in Williamson's model - =/gh dimensionless viscosity - stream function - vorticity - ₀, ₀ distributions of and at the inlet - r,a, b, and c auxiliary constants - C concentration of the displacing fluid - D diffusion coefficient - Pe Peclet's number Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 40, No. 3, pp. 432–439, March, 1981.     

Transient heat conduction in hollow spheres with a moving inner boundary

The finite integral transform method is used to obtain the solution of unsteady heat conduction problems for a hollow sphere with a moving internal boundary and various boundary conditions at the outer surface. For the solution of the problems of interest integral transform formulas are presented with kernels (16), (20), and (24) and the corresponding inversion formulas (18), (22), (26), (29) and characteristic equations (17), (21), (25), (28), (31), (33).Nomenclature a, thermal diffusivity and conductivity - t temperature of phase transformation - density - heat transfer coefficient - Q total quantity of heat passing through inner boundary - F latent heat of phase transformation - Fo(1,)=a/R ₁ ² , Fo(i,)=/r _i ² , Fo(i, _i)=a _i/r _i ² Fourier numbers - Bi₂=R₂/ Biot number     

Coupling of order parameter collective modes to spin density in3He-B

We derive a general expression for the dynamic spin susceptibility of³He-B which is valid for all magnetic fields. The coupling of real and imaginary modes by particle-hole asymmetry is taken into account. Then we calculate the contribution of the mode at frequency =2 – 1/4 ( is the effective Larmor frequency) to the transverse susceptibility. The spectral weight of this mode in magnetic resonance absorption is proportional to (/)^1/2 (–)², where and are particle-hole asymmetry parameters. From the experimental coupling strength of the real squashing mode to sound we estimate (–)²10^–4. The dynamic susceptibility satisfies the sum rules of Leggett. Finally we point out the difficulties in calculating the transverse NMR frequency of³He-B. These difficulties arise from theS _z =0 Cooper pairs and from the coupling ofJ _z =±1 modes forJ=1 andJ=2.