Rate equations for viscoplastic materials subjected to finite strains

The constitutive equations for plasticity proposed by Voyiadjis [1984] and Voyiadjis & Kiousis [1987] are modified here in order to introduce rate sensitivity in the plastic region. Some of the basic concepts of the theory of viscoplasticity outlined by Naghdi & Murch [1963], Perzyna & Wojno [1966], and Eisenberg & Yen [1981] are used in this work in order to obtain the proposed viscoplastic constitutive model for finite strain deformation analysis.Uniaxial loading-reverse loading tests are conducted so as to check the validity of the proposed constitutive model as well as to determine its material parameters. The model is effectively used in simulating numerically the obtained experimental results at finite strains.     

有限弹塑性变形的三维组集式本构模型

本文将文[1]中提出的三维组集式弹塑性本构模型推广应用于有限变形分析,导出了全量型和增量型本构关系在初始构形上的拉格朗日(Total Lagrange)形式和瞬时构形上的拉格朗日(Updated Lagrange)形式。文中对晶体单轴拉伸中的宏观剪切带进行了分析。预测结果与实验吻合。从而说明这种本构模型能够模拟有限变形中的几何非线性效应和晶体材料塑性变形中的宏观力学行为。     

Shear response of monodomains of flow-aligning nematic liquid crystals: TIF model comparisons and effect of pre-tilt

This work is the continuation of a previous study [Van Horn BL, Winter HH (2000) Dynamics of shear aligning nematic liquid crystal monodomains. Rheol Acta 39:294–300] on the shear dynamics of monodomains of shear aligning nematic liquid crystals [NLC]. The strain dependence of director orientation has been experimentally investigated for monodomains of a NLC with various initial orientations. Comparison of experimental results to predictions using Ericksen's transversly isotropic fluid [TIF] model supports the validity of the TIF model for systems of low molecular weight NLCs. The TIF model has been used to examine the effect of pre-tilt on the dynamics of flow-aligning NLC monodomains. It is shown that small deviations from planar alignment (no pre-tilt) have a large effect on orientation dynamics.     

Constitutive modeling of textured body-centered-cubic (bcc) polycrystals

A new latent hardening model for body-centered-cubic (bcc) single crystals motivated by the inapplicability of the Schmid law (Critical Resolved Shear Stress Criterion) is presented. This model is based on the asymmetry of shearing resistance of the {112} slip planes depending on the shearing direction in the sense of ‘twin’ and ‘anti-twin’. For the interpretation of deformation of polycrystalline aggregates depending upon initial texture, a constitutive law for bcc single crystals is developed. This law is based on a rigorous constitutive theory for crystallographic slip that accounts for the effects of strain hardening, rate-sensitivity and thermal softening. The deformation response of textured polycrystal is investigated by means of a Taylor type averaging scheme and an established numerical procedure. Results for textured tungsten polycrystals at low and high strain rates for two different textures [001] and [011] are presented and compared with experimental results. The predictions compare well with experimental observations for the [001] texture. In the [011] texture, due to the reduced symmetry of deformation, lateral tensile stresses develop even under uniaxial compression. These lateral tensile stresses are responsible for observed lack of ductility and transgranular failure in the [011] texture.     

Solution of the problem of a flow of rarefied gas of constant density around a semiinfinite plate by the integral diffusion method

Several papers [1–4] have proposed approximate diffusion models which can be used to examine the transport process in a rarefied gas where the mean free path is large and transport is not determined by the local gradient of the particular quantity.In this paper the integral diffusion model [2] is used to solve the problem of determination of the friction stress and velocity of a flow of an incompressible gas around a plane semi-infinite plate in the whole range of Knudsen numbers. The obtained solution is compared with published solutions and experimental data [9].     

A one-dimensional numerical model of heat and mass transfer in air-water droplet flow

This paper presents a one-dimensional numerical model of the heat, mass and momentum transfer between water droplets and humid air in the disperse process device. The model merges a model of the disintegration of a water sheet presented by Dombrowski et al. [1] and a one-dimensional numerical model of the transport phenomena in the air washer presented by Demird?i? et al. [10]. Numerical results are compared with the available experimental results. Numerical simulations can predict one-dimensional analysis of the geometrical and thermophysical parameters in the disperse process device.     

ON THE MECHANISM OF TURBULENT COHERENT STRUCTURE (III)──A STATISTICAL AND DYNAMICALMODEL OF COHERENT STRUCTURE AND ITSHEAT TRANSFER MECHANISM

I.IntroductionItisaveryinlportulltdiscoveryofcoherentstrLICturcinshetlrturbulellt11owsbyexperimentinthelate1950s,whichleadsustoseekthenaturall,ropertiesofturbulcllcefromthenewideaandilladifferentway.ThestudyofthecoherclltstrLlcttlrcisofgreatimportallcetounderstandthegeneration,developmentanddecayof'tLlrbulellce,allditlsoconstructsInorerealisticturbulencemodeltheory.Meanwhile,itwillbeor11elpIYomengineerillgpoint,suchaslllassandheattrallslbr,dl'agI.eductiolland11oisecontrolproblems.Soinlnlel…     

Nonequilibrium thermodynamics of pseudoelasticity

Solid-solid phase transitions often exhibit hystereses, and a hysteresis indicates energy dissipation. Pseudoelasticity refers to a hysteretic loadingunloading characteristic observed in the stress-induced martensitic transformation of shape memory alloys.This paper describes the thermodynamic model ofideal pseudoelasticity, a largely schematized adaptation of the experimental observations, and it reviews the works of other authors on thermodynamics of pseudoelasticity. Different approaches vary widely and we have chosen to put them into perspective by contrasting their assumptions and predictions against those of ideal pseudoelasticity.Ideal pseudoelasticity receives support from the experimental results of Fu [1] and its thermodynamic properties have been exploited by Huo [2]. The model makes use of an analytical ansatz proposed by Müller [3] in which the hysteresis is assumed to be due to the presence of a coherency energy in solid phase mixtures. This model permits the study of stability of the equilibrium states and the calculation of the energy dissipation or entropy production during the phase transition: The equilibrium states of a phase mixture are found to be unstable in load-controlled processes and the dissipated energy is related to the coherency coefficient.We also discuss some open problems concerning the states inside the hysteresis loop and the formation of interfaces.     

Interaction of an external disturbance with turbulent flow

Previous calculations [1] and a critical analysis of the interpretation of some experimental data [2, 3] are verified and refined. A model is proposed that directly takes into account in the motion equations terms describing the interaction of the disturbance with turbulent oscillations. The advantages of such an approach in comparison with the use of turbulent viscosity models are demonstrated.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 1, pp. 61–66, January–February, 1976.The authors wish to express their appreciation to V. N. Shtern for discussion of the study.     

Tensor Darcy law for tissue screens of dense type

The use of screens as wicks for heat pipes in the capillary phase-splitting [1] and conditioning [2] systems creates an interest in their hydraulic characteristics. In order to optimize the structure of the screen, the values are required of its hydraulic characteristics as functions of the direction and geometrical parameters. The experimental determination of these functions is difficult and has not been achieved fully up to the present time. This paper gives a theoretical derivation of equations required to calculate the hydraulic drag of tissue screens of the dense type in an arbitrary direction in a region where Darcy's law holds, i.e., where the pressure drop depends linearly on the velocity of the free stream. The derivation is based on the application to the screens of what is called Happel's cellular porous medium flow model [3]. It should be noted that the cellular model makes it possible to obtain good agreement with experiment for a number of porous materials, in particular for fillings of spheres [3, 4] and for fibrous materials [5].Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 77–85, July–August, 1985.     

A shape memory alloy model by a second order phase transition

Motivated by the experimental results of the paper [1] and unlike the general theories of shape memory alloys (SMAs), in this paper we suggest for such materials a phase field model by a second order phase transition. So that, with this new system we obtain a simulation of phase dynamics very convenient to describe the natural behavior of these materials. The differential system is governed by the motion equation, the heat equation and the Ginzburg–Landau (GL) equation and by a constitutive law between the phase field, the temperature, the strain and the stress. The use of this new model is characterized by new potentials of the GL equation and by a new dependence on the temperature in the constitutive equation. Using this new model, we obtain simulations in better agreement with experimental data and respect to previous work [2].     

油-水两相湍浮力回流双流体模型

在自然界和工程技术的许多领域,常遇到这样一类物理性质相差悬殊的两相复杂湍流,其特点是流场中包含有回流和因两相间的密度差而产生的浮力,在一定条件下,流场的密度分布会发生突变,使数学模拟和数值计算的难度大大增加。本文把研究精细的油污染预报模型作为基本目标,广泛地涉及了两相湍流精细模拟的理论和方法。用Eulerian坐标系中多流体模型统一描述油和水两相各自的运动,并分别对油和水本身的湍流输运规律以及相间相互作用规律进行模拟,建立了油-水两相湍浮力回流双流体模型及相应的数值计算方法。选定了包含有浮力和回流的两相复杂湍流作为模拟对象,对模型进行了数值验证,并与实测资料作了对比。然后,对油-水两相湍流进行了预报。结果表明,模型的模拟效果非常满意。     

Interaction of a jet exhausting from a body with an opposing supersonic stream of rarefied gas

The experimental investigation of supersonic flow past a sphere with a jet exhausting from the front point of the sphere into the flow at large [1] and moderate [2] Reynolds numbers Re has revealed an effect of shielding from the oncoming stream, this leading to a decrease in the drag coefficient of the sphere and of the energy flux to it. A numerical simulation of the flow has been made in the case of supersonic flow past a sphere with a sonic jet from a nozzle situated on the symmetry axis in the continuum regime [3]. In the present paper, this problem is investigated for flow of a rarefied gas on the basis of numerical solution of a model kinetic equation for a monatomic gas.     

Excitation ahead of shock fronts in krypton measured by single line laser absorption

The number densities of the metastable 5s[1 1/2]2 state and the 5s[1 1/2]1 state of krypton ahead of shock fronts have been determined from the measured absorption of single line laser radiation. Shocks with Mach numbers from 12 to 21 were investigated at preshock pressures from 0.7 to 2.7 kPa. An exponential rise of this excitation precursor having time constants of about 8 ws is found. The metastable concentration atM = 20 is about 10 ppm. The experimental results agree within an order of magnitude with published model predictions for argon and xenon shocks.     

Time dependence of effective properties of polycrystalline ferroelectric ceramics

In this paper, based on Merz[7] experimental results and classical nucleation theory, a micromechanics statistical model is proposed to describe the relation between the special microstructure-level evolution phenomena-domain switching and macro-response. The polycrystalline ferroelectric ceramics treated as a composition of switched domain and unswitched domain, the approaches of Eshelby's equivalent inclusion and Mori-Tanaka's mean field theory are used to analyze and predict its effective electroelastic properties. The model can incorporate the effects of time dependence of domain switching and shape of individual crystalline. To the BaTiO₃ polycrystalline ceramics, the analytical results are in good agreement with the experimental results.     

大开口复合材料层合板强度破坏研究

复合材料层合板的各向异性及非均质,使得复合材料层合板内部的破坏形式非常复杂.在复合材料结构的设计中,为满足制造及使用功能上的需求,在复合材料层合板承力结构件上不可避免地需要设计各种开口.然而,含大开口复合材料层合板的强度破坏问题变得更为复杂,使得现有的强度理论面临新的挑战.针对碳纤维增强复合材料大开口层合板受单向拉伸载荷作用下的强度破坏问题进行了数值分析和实验研究.首先,根据Hashin准则和刚度退化模型,对含不同圆形开口尺寸的[0]_(10)单向铺层、[0/90]_5和[±45]_5正交铺层的层合板,进行了单向拉伸载荷作用下渐进失效的数值模拟分析,获得了对应结构的极限载荷和破坏模式.在此基础上,采用数字图像相关方法,进行复合材料大开口层合板强度破坏的实验研究.研究结果表明,大开口复合材料层合板在单向拉伸加载下主要呈现脆性破坏形式,破坏起始位置处于应力集中区.此外,破坏强度和失效模式与复合材料铺层方式和开口尺寸大小密切相关.其中[±45]_5铺层的开口层合板承载能力最弱,分层破坏最严重.开口尺寸越大,结构的极限载荷值越低.同实验测试结果相比,数值模拟对复合材料层合板的损伤失效分析略显不足,往往很难全面分析复合材料层合板破坏失效过程中的各种因素的影响.     

Propagation of one-dimensional elastoviscoplastic waves in composite materials

We consider the problems of propagation of elastic and elastoviscoplastic waves in laminated and fiber composites on the basis of the two-velocity model proposed in [1]. We study plane waves propagating parallel to the fibers and waves propagating in the perpendicular direction. We compare our solutions with the experimental results presented in the literature [2, 3] for several specific composites (carbon-filled plastics, boron plastics, and wolfram fibers in aluminum matrix). The coincidence between the theoretical results and experimental data is shown to be good. To understand the typical features of propagation of nonstationary waves in composites, we solved several one-dimensional problems about the propagation of both elastic and elastoviscoplastic waves in laminated and fiber composites. We compare the solutions obtained using the one-velocity and two-velocity models [1, 4] with the results of experiments and the results obtained in the literature using different models, which permits estimating the accuracy of both models and the numerical method in question. We use the numerical method of characteristics to improve the accuracy of calculations in the solution of the resulting systems of hyperbolic equations.     

Multi-axial behavior of shape-memory alloys undergoing martensitic reorientation and detwinning

Recently, a rate-independent, finite-deformation-based crystal mechanics constitutive model for martensitic reorientation and detwinning in shape-memory alloys has been developed by Thamburaja [Thamburaja, P., 2005. Constitutive equations for martensitic reorientation and detwinning in shape-memory alloys. Journal of the Mechanics and Physics of Solids 53, 825–856] and implemented in the ABAQUS/Explicit [Abaqus reference manuals. 2005. Providence, RI] finite-element program. In this work, we show that the aforementioned model is able to quantitatively predict the experimental response of an initially textured and martensitic polycrystalline Ti–Ni rod under a variety of uniaxial and multi-axial stress states. By fitting the material parameters in the model to the stress–strain response in simple tension, the constitutive model predicts the stress–strain curves for experiments conducted under simple compression, torsion, proportional-loading tension–torsion, and path-change tension–torsion loading conditions to good accord. Furthermore the constitutive model also reproduces the force–displacement response for an indentation experiment to reasonable accuracy.     

Analytical solution to the problem of heat interaction of fluid flow and solid filling

The results of analytical solution to the problem of thermal interaction of a fluid stream with a media of solid particles found on the basis of the ODTPM model [1] are presented. A non-stationary behaviour of the volume-averaged temperature of solid filling, being a measure of the efficiency from heat transfer between fluid and solid phases, and of the heat-carrier temperature at the exit of the layer is studied. Time dependences computed according to the obtained relationships are in good agreement with the results of numerical calculations [1] for different sets of the problem parameters. The found solution expands the possibilities to analyze the efficiency of the “fluid-solid phase” systems and can be a basis to develop methods of experimental evaluation of different parameters of the system.     

Dynamics of shear aligning of nematic liquid crystal monodomains

The equations of linear and angular momentum for nematic liquid crystals have been described with Ericksen's transversely isotropic fluid [TIF] model and solved for start-up of shear flow at constant rate and varying initial alignment conditions. An analytical solution for the rotation provides predictions of the nematic director which closely agree with experimental results of Boudreau et al. (1999), supporting the validity of Ericksen's TIF model. The solution is limited to flows where the effects of director gradients are negligible. Received: 13 September 1999/Accepted: 24 January 2000