Modelling of rotational factor in notched bend specimen under general and local yield situation

The location of the plastic hinge axis in a three point SEN bend specimen is a highly controversial issue. An unambiguous and reliable estimation of rotational factor (r_p) is very essential for the accurate determination of CTOD data. In contrast to the numerous studies reported on the r_p determination in a cracked situation, limited information is available for a blunt notch situation, although many engineering structures do contain notchlike defects with finite root radius. An attempt is made to determine r_p for two situations, namely well below the general yield and around the general yield. The work is based on a theoretical estimation of the plastic zone size using the stress concentration factor and the elastic as well as the elastic-plastic stress distribution. A theoretical estimation of r_p in both the pseudo-elastic and the elastic-plastic situation is estimated through analytical modelling involving factors like plastic zone size, bend angle and notch opening displacement. The values of the rotational factor are found to increase from a small value to around 0.29 in a well below general yield situation to 0.53 to 0.54 in a general yield situation with continued loading. A wide discrepancy in the P/P_GY ratio separating the two situations, i.e. well below general yield and around general yield, is observed. Consideration of the elastic and the elasto-plastic stress distribution indicates a much smaller value of P/P_GY as compared to the ratio obtained from experimental load-displacement plots.     

The transient motion of a dislocation in a solid of general anisotropy

The transient motion of a dislocation starting from rest and moving in an arbitrary rectilinear motion in an anisotropic solid is analyzed by transform techniques and inversion according to the Cagniard-de Hoop technique.     

A finite strain model of stress, diffusion, plastic flow, and electrochemical reactions in a lithium-ion half-cell

We formulate the continuum field equations and constitutive equations that govern deformation, stress, and electric current flow in a Li-ion half-cell. The model considers mass transport through the system, deformation and stress in the anode and cathode, electrostatic fields, as well as the electrochemical reactions at the electrode/electrolyte interfaces. It extends existing analyses by accounting for the effects of finite strains and plastic flow in the electrodes, and by exploring in detail the role of stress in the electrochemical reactions at the electrode-electrolyte interfaces. In particular, we find that that stress directly influences the rest potential at the interface, so that a term involving stress must be added to the Nernst equation if the stress in the solid is significant. The model is used to predict the variation of stress and electric potential in a model 1-D half-cell, consisting of a thin film of Si on a rigid substrate, a fluid electrolyte layer, and a solid Li cathode. The predicted cycles of stress and potential are shown to be in good agreement with experimental observations.     

Nonequilbrium chemical reactions in a shock layer for flow of a mixture of CO2, N,and Ar past a sphere

Knowledge of the distribution of the various components in the shock wave is necessary, as an example, in determining the radiational heating of a body and also for clarification of several other processes. In the following we present results of calculations of supersonic flow of a mixture of CO₂, N, and Ar past a sphere. The kinetic of the formation of the strongly radiating CN component is examined.     

Weakly nonlinear propagation of small-wavelength,impulsive acoustic waves in a general atmosphere

Multiple-scale asymptotic analysis is applied to small-wavelength, weakly nonlinear propagation of an impulsive acoustic wave in a general (3D, in-motion and time dependent) atmosphere. In keeping with previous work on sonic booms and nonlinear acoustics in general, the result is a combination of ray tracing and a generalised Burgers equation describing evolution of the waveform carried by a ray. This is nonetheless, to our knowledge, the first derivation of such a model based on asymptotic analysis of the governing equations for a general atmosphere. Results are given, discussed and compared with measurements for the particular example of the test explosion known as Misty Picture.     

Vibrations of membranes and plates in a general nonlinear formulation

International Applied Mechanics -     

Flow of a dual-temperature plasma in the channel of a disk-magnetohydrodynamic generator,taking account of nonequilibrium ionization and recombination reactions

The establishment of a supersonic one-dimensional flow of a dual-temperature, partially ionized plasma is investigated in the channel of a disk-MHD generator, taking account of nonequilibrium ionization and recombination reactions. A detailed formulation of the problem is given in [1]; flows are considered in the absence of ionization and recombination reactions and in the case of equilibrium reactions.Moscow. Translated from Izvestiya Akademii Nauk SSSR. Mekhanika Zhidkosti i Gaza, No. 6, pp. 135–142, November–December, 1972.     

The general derivation of Ritz method and Trefftz method in elastomechanics

This paper derives the Ritz method and Trefftz method in linear elastomechanis with the help of general mathematical expressions. Thus it is proved that Ritz method gives the upper bound of the corresponding functional extremurn, while Trefftz method gives its lower bound. At the same time it has been found that the eigenvalue problem (e.g. thenatural frequency problem) concerning the functional variational method in Trefftz method is in concord with the lower bound method of the loosened boundary condition which seeks for the eigenvalue. Of course, the results of this derivation are also applicable to the sort of functional variational method of which Euler’s equation is linear positive definite.     

The numerical solution of the flow in a general bifurcating channel at moderately high Reynolds number using boundary-fitted co-ordinates,primitive variables and Newton iteration

A numerical code has been implemented for the numerical solution of the steady, incompressible Navier–Stokes equations using primitive variables in a bifurcating channel. A boundary-fitted, numerically generated grid is placed onto the domain of the channel which is transformed into either a rectilinear C- or T-shaped region. The differenced equations are solved using Newton's iteration which makes upwinding at high Reynolds number unnecessary. Practical implications of inverting the huge Jacobian matrix of Newton's method are discussed. The results have relative error of 2–3 × 10^?3 at Reynolds number 100, with T-geometry being marginally but significantly more accurate than C-geometry. Results have been obtained for Reynolds numbers up to 1000 for three bifurcations one of which models the carotid arterial bifurcation in the human head. For this latter bifurcation the wall shear stress is calculated in connection with the onset of atherosclerosis. Finally, the results of flows having different daughter tube end pressures are presented.     

The general solution of second order effects in elastic half-space acted upon by a non-uniform shear load

I.IntroductionInfiniteelasticitytheorythemathematicalequationsgoverningthedeformationofanisotropiccompressibleelasticmaterialarehighlynonlinear.Asaresult,theexactsolutionsoftheboundaryvalueproblemshavebeenpossibleonlyinsomerestrictedcasesand,oftenapproxim…     

Dynamics of a single bubble in a liquid in the presence of chemical reactions and interphase heat and mass exchange

The influence of inert and chemically reactive additives in the form of microdrops on the dynamics of a single bubble filled with an active gas mixture and collapsing under the action of a shock wave is considered. The development of a reaction during formation of the mixture is analyzed for instantaneous and dynamic evaporation of drops with allowance for various phases of their injection t _inj . It is shown that in instantaneous evaporation, an increase in the fraction of gaseous argon in the H₂+O₂ system raises the final temperature of the system under cryogenic conditions, lowers it under ordinary conditions, and causes appreciable oscillations of the values of γ, heat release, and molecular weight. It is noted that there are values of t _inj and D₀ at which the final temperature of the mixture decreases practically to the initial temperature. Lavrent’ev Institute of Hydrodynamics, Siberian Division, Russian Academy of Sciences, Novosibirsk 630090. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 40, No. 2, pp. 119–127, March–April. 1999.     

Atomistically determined phase-field modeling of dislocation dissociation,stacking fault formation,dislocation slip,and reactions in fcc systems

The purpose of the current work is the development of a phase field model for dislocation dissociation, slip and stacking fault formation in single crystals amenable to determination via atomistic or ab initio methods in the spirit of computational material design. The current approach is based in particular on periodic microelasticity (Wang and Jin, 2001, Bulatov and Cai, 2006, Wang and Li, 2010) to model the strongly non-local elastic interaction of dislocation lines via their (residual) strain fields. These strain fields depend in turn on phase fields which are used to parameterize the energy stored in dislocation lines and stacking faults. This energy storage is modeled here with the help of the ”interface” energy concept and model of Cahn and Hilliard (1958) (see also Allen and Cahn, 1979, Wang and Li, 2010). In particular, the “homogeneous” part of this energy is related to the “rigid” (i.e., purely translational) part of the displacement of atoms across the slip plane, while the “gradient” part accounts for energy storage in those regions near the slip plane where atomic displacements deviate from being rigid, e.g., in the dislocation core. Via the attendant global energy scaling, the interface energy model facilitates an atomistic determination of the entire phase field energy as an optimal approximation of the (exact) atomistic energy; no adjustable parameters remain. For simplicity, an interatomic potential and molecular statics are employed for this purpose here; alternatively, ab initio (i.e., DFT-based) methods can be used. To illustrate the current approach, it is applied to determine the phase field free energy for fcc aluminum and copper. The identified models are then applied to modeling of dislocation dissociation, stacking fault formation, glide and dislocation reactions in these materials. As well, the tensile loading of a dislocation loop is considered. In the process, the current thermodynamic picture is compared with the classical mechanical one as based on the Peach-Köhler force.     

Movement of gas bubbles in a liquid layer in the presence of diffusion and chemical reactions

The problem of a bubbling reactor, in which gas and liquid are mixed by the passage of bubbles of gas through a liquid layer, is discussed. We give the results of a numerical solution of the system of equations describing the processes occurring in the reactor in the case where there are no chemical reactions, and also in the case where chemical reactions take place at constant temperature.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 1, pp. 131–135, January–February, 1971.The authors thank L. A. Chudov for advice and interest in the work.     

Conjugated heat and mass transfer between a reactive solid and a gas in the presence of nonequilibrium chemical reactions

An investigation of a multicomponent boundary layer taking account of nonequilibrium chemical reactions has been made in a number of publications [1–3]; here, the temperature of the solid was assumed to be known or was determined from the condition of the conservation of energy at the interface between the gas and the solid, taking account of the solution of the equation of thermal conductivity in the solid phase. At the same time, heating of the material of a coating is an unavoidable step in any mechanism of thermokinetic decomposition and, in view of this, it is necessary to take account of the lag of the heat-transfer process inside the solid. Therefore, it is necessary to solve the equation of the energy balance in the solid phase simultaneously with the system of the equations of the boundary layer, i.e., the conjugate problem. The present article discusses the problem of flow around a solid in the vicinity of a frontal critical point, taking account of the dependence of the processes taking place in the solid body on the time, in the presence of two heterogeneous and one homogeneous reactions. The distributions of the velocity, the temperature, and the concentrations in the boundary layer are obtained, as well as the mass rate of entrainment of the material at different moments of time. The time of the change between kinetic and diffusion conditions of the course of the heterogeneous chemical reactions (the ignition time) is determined. It is established that, in the presence of a homogeneous chemical reaction, the mass rate of entrainment is less than with a frozen flow.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 121–128, March–April, 1974.     

Screening for C283Y gamma-sarcoglycan mutation in a high-risk group of Bulgarian Gypsies: evidence for a geographical localization and a non-random distribution among Gypsy subgroups

Limb-girdle muscular dystrophy type 2C (LGMD2C) is an autosomal recessive disorder caused by mutations in the gamma-sarcoglycan gene. A 'private' Gypsy C283Y mutation was detected in this gene. Recently, a number of LGMD2C-affected families belonging to a Xoroxane Gypsy group have been detected in eastern Bulgaria and all of these cases were due to the same mutation. We have screened 300 unrelated individuals of reproductive age from this high-risk Xoroxane Gypsy group, settled in Sliven. The genetic test by PCR-SSCP analysis for the C283Y mutation revealed a carrier frequency of 7.7%. The screened sample was ethnically not homogeneous. It was divided in ethnonym groups on the basis of social and economic status, language characteristics and trades. We found that the C283Y was not randomly distributed among the Gypsy subgroups. The disease seemed to be limited to the Xoroxane Gypsy group and geographically localized in eastern Bulgaria.