On the measurement of elastoplastic stresses

In principle, one should be able to measure elastoplastic stresses in the same manner as one does elastic stresses; i.e., measure the strains and compute the stresses from the constitutive law. In practice, this is rarely done because of the more complicated material response and the anisotropy of the plastic behavior. Further, elastoplastic stresses should be computed incrementally in the general case. This paper presents procedures for computing stresses from elastoplastic strains measured incrementally in a test under microcomputer control. The approach is evaluated for four different materials—two obeying the assumptions of classical plasticity and two showing anisotropic behavior—by computing the stresses in a smooth specimen from measured principal strains. A useful application is presented by computing the stresses at a notch root from biaxial strains measured with laser-based interferometry. The general conclusion is that even in situations where the material is clearly anisotropic, this approach can give a reasonableestimate of the largest local principal stress. Paper was presented at the 1991 SEM Spring Conference on Experimental Mechanics held in Milwaukee, WI on June 9–13.     

TWO－DIMENSIONAL DEFORMATION OF ANANISOTROPIC ELASTIC BODY WITH A PARABOLIC BOUNDARY

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Large Eddy Simulation of a Methane–Air Diffusion Flame

Large Eddy Simulation has been applied to a piloted methane/air diffusion flame—the Sandia D flame—for which detailed experimental data are available. To evaluate the reacting density, temperature and species mass fractions a conserved scalar laminar flamelet formulation is employed, utilising a single virtually unstrained flamelet. The results of two simulations are discussed, comparing the use of the standard Smagorinsky model and a dynamic variant for closure of the unknown sub-grid stress. The chosen sub-grid scale model is shown to be extremely influential on the final solution. Whilst the use of the standard model results in a relatively poor simulation the dynamic closure offers an excellent velocity field prediction throughout the flame. Although the flame does show some strain rate influence on burning, particularly close to the inlet nozzle, the relatively simple ‘unstrained’ flamelet model applied is shown to provide an accurate representation of temperature and major species distribution.     

Ballistic magnetocumulative generator

The reusable source of a pulsed magnetic field—a ballistic magnetocumulative generator (BMG)—is considered. Electrical engineering analysis of the efficiency of operation of the generator on an active-inductive load is performed. A method for calculating the two-dimensional distribution of the field in the busbars of the generator is developed. Experimental results are obtained for the operation of aBMG model on some types of load. Central Scientific-Research Institute “Burevestnik,” Nizhnii Novgorod 603603. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 39, No. 3, pp. 22–29, May–June, 1998.     

On the stress distribution in a spherical shell with an off-center curvilinear hole

A numerical analysis is made of the joint effect of two factors of asymmetry—ellipticity and eccentricity—on the stress distribution near a free hole in a spherical shell. The nature of deformation is determined by the predominant factor. Whether there are “fixed” points on the graphs of stress distribution around a small hole at which they intersect depends on how rigidly the outer edge is fixed. As the rigidity of fixation is increased, the points smear __________ Translated from Prikladnaya Mekhanika, Vol. 42, No. 1, pp. 113–118, January 2006.     

Determining equations of two-phase flows through anisotropic porous media

A new interpretation of the concept of relative phase permeability is given. Relative phase permeabilities are represented in the form of fourth-rank tensors. It is shown that in the case of anisotropic porous media functions depending not only on the saturation but also on the anisotropy parameters represented in the form of ratios of the principal values of the absolute permeability coefficient tensor correspond to the classical representation of the relative phase permeabilities. For a two-phase flow in anisotropic porous media with orthotropic and transversely-isotropic symmetry a generalized two-term Darcy’s law is analyzed. Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 2, pp. 87–94, March–April, 1998. The work was carried out with support from the Russian Foundation for Fundamental Research (project No. 96-01-00623).     

Disclinations in a homogenously deformed nematic elastomer

We consider a nematic elastomer which has been cross-linked in an isotropic state. As an application, we consider the time-independent, isochoric, homogeneous deformation of a right circular cylinder wherein each circular cross section of the specimen is deformed into an ellipse. We explore the possibility of the existence of disclinations when the molecular conformation is uniaxial. Numerical solution of the governing boundary-value problem indicates the presence of an isotropic core (the disclination core) of material surrounding the cylinder axis in which the polymeric chains are shaped as spherical coils. The isotropic core is bounded by a narrow transition layer across which the molecular conformation changes from spherical to uniaxial. The material thereby becomes anisotropic away from the disclination. The anisotropic regions show a markedly different distribution for the free energy. This distribution of energy determines the radius of the core to be on the order of 10⁻² μm. This work is a first step toward gaining an understanding of the existence of defective states in homogenous deformed nematic elastomers.     

Continuum-mechanical, Anisotropic Flow model for polar ice masses, based on an anisotropic Flow Enhancement factor

A complete theoretical presentation of the Continuum-mechanical, Anisotropic Flow model, based on an anisotropic Flow Enhancement factor (CAFFE model) is given. The CAFFE model is an application of the theory of mixtures with continuous diversity for the case of large polar ice masses in which induced anisotropy occurs. The anisotropic response of the polycrystalline ice is described by a generalization of Glen’s flow law, based on a scalar anisotropic enhancement factor. The enhancement factor depends on the orientation mass density, which is closely related to the orientation distribution function and describes the distribution of grain orientations (fabric). Fabric evolution is governed by the orientation mass balance, which depends on four distinct effects, interpreted as local rigid body rotation, grain rotation, rotation recrystallization (polygonization) and grain boundary migration (migration recrystallization), respectively. It is proven that the flow law of the CAFFE model is truly anisotropic despite the collinearity between the stress deviator and stretching tensors.     

Pore space network characterization with sub-voxel definition

Morphological measurements in 3D for pore space characterization (connectivity pore-body/throat classification, shape factors, virtual fluid intrusion) are based on computed intensive digital-thinning operations for skeletonization and medial axis extraction from 3D digital images. We present an alternative method that is measurably faster and allows sub-voxel definition of the pore space network. The method allows extracting—based on morphological considerations only—the centered and shortest stream-lines—i.e., the paths—to follow in order to go through the pore space from one given point to another and to exit. In addition the method penalizes long and narrow pore-throats in favor of short stubby/ones—i.e., it has a built-in exemplification capacity. It exploits well-established mathematical methods successfully applied in medical endoscopy.     

Explosion Dynamics in Saturated Rocks and Solids

Non-elastic pore deformations and crack propagations are the principal causes of dynamic damage in rocks and soils. In the case of downhole blasting from wellbores, these two mechanisms compete with each other. Therefore, to carry out a mechanical analysis of rock blasting, a sufficiently complete model that takes these various mechanisms into account has to be developed. To address this issue, this paper proposes the use of an elastic–plastic model, which includes a yield condition with a non-associated plastic flow rule, the effects of pore fluid saturation, and a brittle failure criterion under extension. The results presented in this paper describe underground explosions with spherical motion (cavity growth under the internal pressure of detonated gases without leakage into the formation), typical for oil or water reservoirs. The governing equations are written in a Cartesian system of coordinates for the case of spatial dynamic medium deformation. For this case, Cartesian coordinates are more convenient than spherical coordinates because they avoid numerical difficulties connected with the non-divergent terms of the non-linear form of the Biot–Frenkel equations. The numerical method uses the Wilkins approach, which has been generalized for the model described in this paper. The dilatancy of the material during plastic deformation is neglected for simplicity. The numerical results show that, when using typical parameters for relatively “soft” porous skeleton, the plastic flow overcomes the brittle failure. An extension zone only appears near the cavity. The results also show the presence of the two Biot P-waves. The second Biot wave, however, is only seen in the case of an extremely high permeability rock. Furthermore, in the case of the first Biot wave, the saturating liquid and the solid skeleton particles are moving with different velocities in a 100 darcy rock and with the same velocity in a 0.01 darcy rock. Calculated radial particle velocities as a function of the scaled radius are close to measured velocities in rigid dense media but are larger than measured ones in clays. It is suggested that the difference is due to different levels of water saturation, assumed full saturation in the calculation, partial saturation in the experiments.     

Effective and relative permeabilities of anisotropie porous media

A model composed of a three-dimensional orthogonal network of capillary tubes was used to simulate the flow behavior in an unsaturated anisotropic soil. The anisotropy in the network's permeability was introduced by randomly selecting the radii in the three mutually orthogonal directions of the network tubes from three different lognormal probability distributions, one for each direction. These three directions were assumed to be the principal directions of anisotropy. The sample was gradually drained, with only tubes smaller than a certain diameter remaining full at each degree of saturation. Computer experiments were conducted to determine the network's effective permeability as a function of saturation. The main conclusion was that the relationship between saturation and effective permeability depends on direction. Consequently the concept of relative permeability used in unsaturated flow should be limited to isotropic media and not extended to anisotropic ones.     

Thermal stresses in two- and three-component anisotropic materials

This paper deals with an analytical model of thermal stresses which originate during a cooling process of an anisotropic solid continuum with uniaxial or triaxial anisotropy. The anisotropic solid continuum consists of anisotropic spherical particles periodically distributed in an anisotropic infinite matrix. The particles are or are not embedded in an anisotropic spherical envelope, and the infinite matrix is imaginarily divided into identical cubic cells with central particles. The thermal stresses are thus investigated within the cubic cell. This mulfi-particle-（envelope）-matrix system based on the cell model is applicable to two- and three-component materials of precipitate-matrix and precipitate-envelope-matrix types, respectively. Finally, an analysis of the determination of the thermal stresses in the multi-par- ticle-（envelope）-matrix system which consists of isotropic as well as uniaxial- and/or triaxial-anisotropic components is presented. Additionally, the thermal-stress induced elastic energy density for the anisotropic components is also derived. These analytical models which are valid for isotropic, anisotropic and isotropic-anisotropic multi-particle- （envelope）-matrix systems represent the determination of important material characteristics. This analytical determination includes： （1） the determination of a critical particle radius which defines a limit state regarding the crack initiation in an elastic, elastic-plastic and plastic components; （2） the determination of dimensions and a shape of a crack propagated in a ceramic components; （3） the determination of an energy barrier and micro-/macro-strengthening in a component; and （4） analytical-（experimental）-computational methods of the lifetime prediction. The determination of the thermal stresses in the anisotropic components presented in this paper can be used to determine these material characteristics of real two- and three-component materials with anisotropic components or with anisotropic and isotropic components.     

The Sorption Behavior of Wood Studied by Means of an Improved Cup Method

In transport models for wood, sorption is an essential parameter. Sorption is the balancing process between the two phases of water present in wood below the fiber saturation point, namely water vapor in the lumens and bound water in the cell walls. To gain better insight into the physical background of transport processes, a special experimental test setup—the improved cup method—is presented. It allows for separation of sorption from other processes. In this test, a diffusion cup contains a thin specimen of wood, with one side facing outwards to a climate chamber and the opposite side facing inwards the cup. In contrast to the common cup method, the herein presented method uses a data logger for relative humidity and temperature placed inside the cup. The use of thin cross-cut specimens allows for explicit separation of the different processes occurring during transient moisture transport. Mass changes were determined and relative humidity inside the cups was measured for eight specimens of Norway spruce with different specimen thicknesses. Relative humidity was increased in three uniform steps in the test chamber from 4.0 up to 76.5%. The results obtained with this special test setup indicate that the sorption process is different than assumed in previous publications. This emphasizes the need of improved modeling approaches.     

Determination of density and concentration from fluorescent images of a gas flow

A fluorescence image analysis procedure to determine the distribution of species concentration and density in a gas flow is proposed. The fluorescent emission is due to the excitation of atoms/molecules of a gas that is intercepted by an electron sheet. The intensity of the fluorescent light is proportional to the local number density of the gas. When the gas flow is a mixture of different species, this proportionality can be used to extract the contribution associated with the species from the spectral superposition acquired by a digital camera. In particular, the fact is exploited such that the ratio between a pair of color intensities takes different values for different gases and that different linear superpositions of different color intensities yield a ratio that varies with the species concentration. This leads to a method that simultaneously reveals species concentrations and mass density of the mixture. For the proper working of a continuous electron gun in a gas, the procedure can be applied to gas flow where the pressure is below the thresholds of 200∼300 Pa and the number density is no greater than 10²³ m⁻³. To maintain the constancy of the emission coefficients, the temperature variation in the flow should be inside the range 75–900 K (above the temperature where the probability to meet disequilibrium phenomena due to rarefaction is low, below the temperature where visible thermal emission is present). The overall accuracy of the measurement method is approximately 10%. The uncertainty can vary locally in the range from 5 to 15% for the concentration and from 5 to 20% for the density depending on the local signal-to-noise ratio. The procedure is applied to two under-expanded sonic jets discharged into a different gas ambient—Helium into Argon and Argon into Helium—to measure the concentration and density distribution along the jet axis and across it. A comparison with experimental and numerical results obtained by other authors when observing under-expanded jets at different Mach numbers is made with the density distribution along the axis of the jet. This density distribution appears to be self-similar.     

An investigation of the losipescu and asymmetrical four-point bend tests

The Iosipescu shear test, utilizing a notched specimen in bending and a modification—the asymmetrical four-point bend (AFPB) test—were evaluated as shear tests for composites. This paper summarizes the results of an extensive numerical and experimental investigation of the Iosipescu and AFPB test methods. Finite-element analyses were conducted to assess the influence of notch parameters and load locations on the stress state in the specimen. The shear moduli and the shear strengths were experimentally measured for a quasiisotropic graphite/epoxy laminate using both the Iosipescu and the AFPB test methods. The tests were conducted for various combinations of notch parameters and load locations. The test results indicate that changes in the notch geometry and load locations aimed at improving the stress distribution in the test section resulted in unexpected changes in the failure mode. Paper was presented at the 1985 SEM Spring Conference on Experimental Mechanics held in Las Vegas, NV on June 9–14.     

One-dimensional flow model for coal-gas outbursts and initiation criterion

This paper discribes a one-dimensional flow model to explain the basic mechanism of coal-gas outbursts. A break-start criterion of coal, as the elementary outburst criterion, is given approximately. In this ideal model, the tectonic pressure before excavation, as a load on coal body, affects the break-start and then the flow field. The flow field is decoupled with the stress field, so that the gas seepage through unbroken coal body, break-start and consequent two-phase flow, and pure gas flow can be analysed independently of the stress field. The tunnelling, an external disturbance that makes the seepage intensify relatively, is an essential factor for initiating outburst. Under steady tunnelling, seepage ought to tend to be steadily progressive. From its asymptotic solution initiation criterion is obtained. This is described by three conditions, possibility condition —tectonic pressure condition, incubation condition—tunnelling or gas condition and triggering condition —seepage velocity condition. The project supported by the National Natural Science Foundation of China     

Thermovibrational convective instability of mechanical equilibrium of an inclined fluid layer

The convective instability of mechanical equilibrium of an inclined plane layer of fluid developing under the action of a static gravity field and high-frequency vibration is studied. Configurations corresponding to four directions of the equilibrium temperature gradient — vertical, longitudinal, horizontal, and transverse — are considered for an arbitrary orientation of the vibration axis. The stability limits and the characteristics of the critical perturbations are determined. Perm’. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, pp. 8–15, January–February, 1998. This investigation was carried out with partial support form RSA-NASA (contract No. 920/18 — 5208/96).     

Thermostressed State of an Anisotropic Plate with Holes and Cracks

The thermoelastic problem for an infinite multiply connected anisotropic plate with holes and cracks in a linear heat flow is solved. The stress distribution and the stress intensity factors on heat-insulated boundaries are analyzed numerically __________ Translated from Prikladnaya Mekhanika, Vol. 41, No. 9, pp. 127–136, September 2005.     

Non-linear Model for Wood Saturation

The paper presents a non-linear model of saturation with fluid of anisotropic capillary porous bodies and the results of experimental investigations of wood saturation with methacrylate. The obtained experimental curves illustrating the distribution of methacrylate in wood samples allow the estimation of material coefficients and verification of the theoretical model. The theoretical model is developed based on the balance equations of mass, momentum, and energy, and the thermodynamics of irreversible processes. The non-linear differential equation, describing the distribution of methacrylate content in wood and its evolution during the saturation is solved numerically. The theoretical curves obtained on the basis of both linear and non-linear models are compared with the experimental data and better agreement between them for the non-linear model is stated.     

The creep behavior of simple structures with a stress range-dependent constitutive model

High temperature design remains an issue for many components in a variety of industries. Although finite element analysis for creep is now an accessible tool, most analyses outside the research domain use long standing and very simple constitutive models—in particular based on a power law representation. However, for many years, it has been known that a range of materials exhibit different behaviors at low and moderate stress levels. Recently, studies of the behavior of high temperature structures with such a stress range-dependent constitutive model have begun to emerge. The aim of this paper is to examine further the detailed behavior of simple structures with a modified power law constitutive model in order to instigate a deeper understanding of such a constitutive model’s effect on stress and deformation and the implications for high temperature design. The structures examined are elementary—a beam in bending and a pressurized thick cylinder—but have long been used to demonstrate the basic characteristics of nonlinear creep.