A constitutive model for the deformation induced anisotropic plastic flow of metals

A mathematical framework is established for the equations governing inelastic deformation under multi-dimensional stress states and for the associated evolution equations of the internal state variables. The formulation is based on a generalization of the Prandtl-Reuss flow law. In the evolution equations for the inelastic state variables that control plastic flow, it is assumed that part of the rate of change is isotropic and the remaining part varies according to the sign and orientation of the current rate of deformation vector. This leads to a minimum of twelve components of the internal state tensor which represents resistance to inelastic deformation. In this manner, both initial and load history induced plastic anisotropy can be modeled. A specific set of equations for anisotropic plastic flow is developed consistent with the inelastic state variables.     

功能梯度圆板的三维瞬态热弹性分析

基于线性热弹性理论的基本方程,采用两个位移分量,两个应力分量,温度变量和一个热流分量作为状态变量,应用状态空间理论,建立了功能梯度材料轴对称圆板结构在动态热载荷作用下的状态方程,考虑了运动惯性项以及热传导过程中的耦合效应,根据微分求积法,将状态方程沿径向进行离散.采用Laplace变换和打靶法,数值求解了材料常数按幂率变化的周边固支圆板在热冲击下的热响应.为求解功能梯度结构三维热弹性瞬态响应提供了一种方法.分析了组分材料分布对功能梯度圆板的热响应行为,包括板内温度变化,横向挠度以及板内应力分量的影响规律.     

Compressive splitting failure of composites using modified shear lag theory

The shear lag model has been used in conjunction with the 3D elasticity equations to determine the stress state in a fiber/matrix system containing an interface crack. The use of a shear lag model to capture the stress state at the crack tip and the modelling of the region away from the crack tip by the elasticity equations leads to a simple analytical expression which can be used to determine the compliance changes for both unsteady crack growth as well as steady state crack propagation under compressive loading. Certain modifications to the assumptions used in the classical shear lag model have been made to increase the accuracy of the predictions for the rate of change of compliance with respect to crack length, dc/dl. The present approach leads to closed form expressions for the compressive strength of unidirectional fiber reinforced composites.     

炸药爆轰热力学数据非线性拟合方法研究

利用最小二乘法拟合得到炸药爆轰产物热力学数据的非线性拟合方程。为了验证此方程的准确性,分别采用Kast平均热容法和非线性拟合法计算物质的焓变（H^T－H²⁹⁸）,并与理论值比较。结果显示:非线性拟合法计算值最大误差为0.5%;Kast平均热容法的计算最小误差为3.1%,最大误差为12.5%。为实现爆轰参数的编程计算和验证非线性拟合法计算爆轰参数的可行性,根据前期研究成果,选取BKW状态方程作为爆轰产物的状态方程,利用最小自由能原理和Hugoniot关系,建立求解数学模型,分别结合Kast平均热容法和非线性拟合法,计算密度为1.80 g/cm³的RDX和密度为1.14 g/cm³的硝基甲烷的爆轰参数和爆轰产物组成,计算过程由自编程序完成。计算结果显示,非线性拟合法比Kast平均热容法计算的爆轰参数值更接近实验值;非线性拟合法计算RDX的爆温、爆压和爆速与实验值的误差分别为3.3%、0.4%和0.3%。     

Lyapunov stability of columns, pipes and rotating shafts under time-dependent excitation

Structural or mechanical systems governed by non-autonomous partial differential equations are considered. The systems are such that they would be conservative in the absence of dissipation and time variation of the loading parameter. They possess an equilibrium state, and sufficient conditions for its stability are obtained with the use of Lyapunov's direct method. Three problems are treated: a column with a time-varying axial load, a pipe conveying fluid with time-varying velocity, and a rotating shaft with time-varying angular velocity. These excitations appear in coefficients of the equations of motion, and the stability conditions involve the excitations and their time rates of change     

Breakdown of symmetry in an exemplary turing system

Based on the well-established Rashevsky-Turing theory of morphogenesis, a two- compartment reaction-diffusion model consisting of cross-inhibitoriiy coupled, potentially oscillating two-variable subsystems (4-dimensionai flow) is reported, the dynamics of which can be described by a few coupled nonlinear ordinary differential equations. We focus on the evocation of symmetry-breaking instabilities developing from an originally symmetrical stationary state under parametric change of the diffusive coupling. The spatio-temporal correlation behaviour of the evocated system flow is analysed on the way from stable steady state towards irregularly recurring differentiation. The model ingredients are finally projected onto the dynamical possibilities of a non-equilibrium semiconductor experiment     

Wide-range semiempirical equations of state of matter for numerical simulation on high-energy processes

An equation of state is a fundamental characteristic of a substance. It is necessary in numerous studies and practically important problems of high energy density physics. In this review, we consider the modern requirements to equations of state, theoretical and experimental methods used to study the thermodynamic properties of a substance, different aspects of constructing wide-range equations of state, and examples of application of wide-range equations of state in simulation of high-energy processes.     

An Equation of State for the Hard-Sphere Chain Fluid Based on the Thermodynamic Perturbation Theory of Sequential Polymerization

New equations of state for freely jointed hard-sphere chain fluids are developed. The equations of state are based on the thermodynamic perturbation theory. The new equations of state use the contact values of the radial distribution function (RDF) for monomer–dimer mixtures, which is derived from the multidensity Ornstein–Zernike theory. These RDFs are composed of a monomer reference term, the Carnahan–Starling or the Percus–Yevick expression, and an additional bond contribution. These equations of state are then extended to real fluids. To calculate the phase equilibrium properties of nonassociating chain fluids, a dispersion contribution is added to the repulsive hard-chain reference term. With the new equations of state of chain fluids supplemented with the dispersion term, the vapor pressures and the coexisting densities of several real fluids are calculated.     

Phase State of a Mixture during Recondensation in a Flat Gap Filled with Inert Gas

The phase state of a mixture is analyzed with respect to the temperatures of evaporation and condensation surfaces by the example of a stationary problem on carbon recondensation in a flat gap filled with inert gas. Mass and energy transfers are described by continuum equations on the assumption of local thermodynamic equilibrium. It is shown that regions with different phase states can exist in the gap; the mixture parameters may change stepwise when passing through the interfaces of these regions.     

On the extrapolation behavior of empirical equations of state

Generally, the extrapolation behavior of empirical equations of state is regarded as poor, but it can be shown that state-of-the-art equations of state yield reliable results well beyond the range where they were fitted to experimental data. During the past years a new generation of highly accurate equations of state which yield reasonable results even up to the limits of chemical stability of the considered substances has been developed. In this paper, the positive influence of recent methods for the development of equations of state on their extrapolation behavior is discussed. The influence of the mathematical structure on the extrapolation characteristics is analyzed and requirements for a reasonable behavior up to extreme temperatures and pressures are formulated. As possible ways for assessment of the extrapolation behavior of an equation of state, comparisons with experimental data at very high pressures and temperatures and with theoretically predicted features of the so-called “ideal curves” of a fluid are discussed. Finally, the current status of our knowledge of the extrapolation behavior of empirical equations of state is summarized and its shortcomings are pointed out.     

Healing and relaxation in flows of helium II—I: Generalization of landau's equations

The Landau 2-fluid equations for the motion of helium II are often criticised on two grounds: they ignore healing of the wave function, and they require the superfluid percentage to change instantaneously when the thermodynamic state is altered. In 1970 Khalatnikov[4] proposed a way of incorporating relaxation effects associated with conversion between superfluid and normal fluid. Using this as our starting point and employing the techniques of modern continuum mechanics, we develop a thermodynamically acceptable generalization that incorporates both healing and relaxation phenomena.     

Potentials and Equations of State for Two Special Reference Configurations

On the basis of the mathematical formulation of the principle of reference invariance of the functions of state of deformed bodies, we consider two special representations of the potential of state in which the reference configuration is variable and related to the current state of the body. The first of these representations (natural) follows from the general representation of the potential of state if a current state of the basis is regarded as the reference state and the corresponding stress-free configuration is taken as the reference configuration. The second (strain-free) representation is obtained if the role of the reference configuration is played by the current configuration. For both representations, we deduce the equations of state in the form of expressions for stresses and the parameters of state connected with the basis parameters. As a constructive proof of the unconditional existence of the elastic potential, we deduce the expression for the elastic potential via the potential of state by using the natural potential of state. It is proved that the general system of equations of state consists of four independent systems of equations, namely, of the equations of elasticity, piezoeffects, stress-free distortion, and stress-free state.     

Hall Coefficient of Equilibrium Supercurrents Flowing inside Superconductors

We study augmented quasiclassical equations of superconductivity with the Lorentz force, which is missing from the standard Ginzburg–Landau and Eilenberger equations. It is shown that the magnetic Lorentz force on equilibrium supercurrents induces a finite charge distribution and the resulting electric field to balance the Lorentz force. An analytic expression is obtained for the corresponding Hall coefficient of clean type-II superconductors with simultaneously incorporating the Fermi-surface and gap anisotropies. It has the same sign and magnitude at zero temperature as the normal state for an arbitrary pairing, having no temperature dependence specifically for s-wave pairing. The gap anisotropy may bring about a considerable temperature dependence in the Hall coefficient and can lead to its sign change as a function of temperature, as exemplified for a model d-wave pairing with a two-dimensional Fermi surface. The sign change may be observed in some high-T _c superconductors.     

A comparison among five equations of state in predicting the inversion curve of some fluids

Five equations of state, modified Peng-Robinson by Danesh et al. (MPR1), modified SRK equation of state by Mathias and Copeman (MSRK), Vdw11, Harmens-Knapp (HK) and modified Peng-Robinson equation of state by Ruzy (MPR2) were compared in predicting of the inversion curve of some fluids. This enable us to judge the accuracy of the results obtained from different equations of state. MSRK and HK equations of state give good prediction of the low-temperatures branch of the inversion curve and are closely matched with the experimental inversion curve. As a corollary to the present study, we have perceived that the agreement of the MPR2 and Vdw11 equations of state with the inversion curve are inadequate. We also calculated maximum inversion temperature and maximum inversion pressure for every component used in this work.     

高维机电耦联系统的非线性振动

本文根据电磁场理论，用统一的方法，建立了电机瞬变过程与轴系的扭振、横振及转动相耦联的强非线性微分方程组。经过线性变换与非线性变换，得到了方程组的解。进行了数字计算，得到了启动过程的横振、扭振、转动及电流等变化规律。理论结果和实验结果吻合得较好。     

Simulating thermoelastic distortion in a body with internal degrees of freedom

Summary A system of equations has been formulated for a thermoelastic model for a body having internal degrees of freedom. The local thermodynamic state is put into correspondence with vector and tensor parameters in accordance with the extent of the structural change. A model problem of hardening in an isotropic layer is considered.Translated from Fiziko-khimicheskaya Mekhanika Materialov, Vol. 27, No. 3, pp. 79–83, May–June, 1991.     

Generalization of strain theories of plasticity based on energy concepts

For steady loading of Isotropic polycrystalline materials it is shown that based on the principle of a maximum in the increment in work of plastic strain with introduction of the work of elastic change in form functionally related to it the presence in the general case of two stages of hardening is necessary. Analytical equations for the functions of hardening very accurately describing the tensile curves of materials and equations of plastic strain in the complex stressed state bounding the areas of use of known strain theories are obtained. A modified method of variable hardening parameters is proposed for solution of applied problems within the limits of a theory taking into consideration two-stage hardening of materials.Translated from Problemy Prochnosti, No. 12, pp. 39–45, December, 1993.     

Imperfection sensitivity in the nonlinear vibration of initially stresses functionally graded plates

In this paper, the nonlinear partial differential equations of nonlinear vibration for an imperfect functionally graded plate (FGP) in a general state of arbitrary initial stresses are presented. The derived equations include the effects of initial stresses and initial imperfections size. The material properties of a FGP are graded continuously in the direction of thickness. The variation of the properties follows a simple power-law distribution in terms of the volume fractions of the constituents. Using these derived governing equations, the nonlinear vibration of initially stressed FGPs with geometric imperfection was studied. The present approach employed a perturbation technique, the Galerkin method and the Runge–Kutta method. The perturbation technique was used to derive the nonlinear governing equations. The motion of imperfect FGPs was obtained by performing the Galerkin method and then solved by the Runge–Kutta method. Numerical solutions are presented for the performances of perfect and imperfect FGPs. The nonlinear vibration of a simply supported ceramic/metal FGP was solved. It is found that the initial stress, geometric imperfection and volume fraction index greatly change the behavior of nonlinear vibration.     

An internal state variable approach to constitutive theories for granular materials with snow as an example

In this paper, a microphysical constitutive theory is developed for a class of rate dependent granular materials under finite deformation. The theory is based on non-equilibrium thermodynamics with internal state variables. The state variables may be thought of as representing the current pattern of microstructural arrangemenp and hence characterize the plastic state of the material. A significant feature of this theory is that the state variables are identified at the granular level, as opposed to the crystalline level. This allows one to develop a microdynamical theory in terms of experimentally observable quantities and is a unique feature of granular materials.The theory is used to describe the mechanical properties of snow under high rate multiaxial deformation. Snow is a highly nonlinear, rate dependent material which exhibits significant microstructural alternations under finite strain. These alternations are tracked mathematically by temporal evolution equations governing the internal state variables. The change in the state variables is directly related to the plastic strain of the material.