Linear viscoelasticity and irreversible thermodynamics

The underlying thermodynamic aspects of linear viscoelasticity are discussed. In particular, from the Extended Irreversible Thermodynamics theory we systematically derive the Maxwell model exhibiting its compatibility with thermo-dynamics and assessing its conditions of validity. We also calculate the equilibrium transverse velocity auto-correlation function and the frequency dependent shear viscosity. Nonlinear generalizations of our model are suggested and the possible role of extended thermodynamics in selecting constitutive equations is also discussed.     

Extended irreversible thermodynamics as a framework for transport phenomena in porous media

A theoretical extended thermodynamic approach to describe transport in porous media is presented. For a particular model of the porous medium, approximate time evolution equations for the fluxes in the system are derived. The use of these equations is illustrated by considering three different transport problems. A finite velocity for the propagation of thermal disturbances within the medium is predicted in the case of heat transport in a system where the effective porosity is zero. Also, a generalization of the Darcy-Brinkman law that incorporates thermal effects, independently of the presence of external forces, arises when consideration is given to the combined mass and heat transport problem. Finally, for the isothermal transport of fluid, the thermodynamic framework provides a possible interpretation of the origin and the role played by both the Brinkman and the Forchheimer corrections to Darcy's law.Work supported by PAPIID of DGAPA-UNAM under project IN-100-289.On sabbatical leave from Area de Física, Universidad Autónoma Chapingo.     

Dissipative flow model based on dissipative surface and irreversible thermodynamics

Summary A dissipative flow model is presented to describe dissipative deformation processes in a macroscopic solid continuum. Dissipative process may consist of material plasticity, material damage and other intrinsic mechanical phenomena represented by internal variables. The concept of a dissipative surface is introduced in the paper to distinguish between conservative and dissipative processes. Conventional plastic yielding and damage initiation are expressed by a unique condition which may else include other possible intrinsic mechanical dissipations. The proposed model is based on the principles of irreversible thermodynamics and the minimum free energy theorem. A modified material stability postulate, modified Drucker's postulate, in thermodynamic stress space is also used to obtain the same results. Received 1 July 1998; accepted for publication 13 January 1999     

Nonlinear evolution of probability vectors of interest in discrete kinetic theory

In the framework of the discrete Boltzmann equation, a suitable space-time discretization of the one-dimensional fourteen discrete velocity model by Cabannes, leads in a bounded domain to the nonlinear Markovian evolution of a probability vector, whose moments represent the macroscopic quantities of the gas. Convergence of the probability vector towards the equilibrium steady state is proven when the walls are at a temperature compatible with the equilibrium itself. A physical application is subsequently dealt with. The classical problem of heat transfer between two parallel plates at different temperatures is formulated and solved, and the properties of the final steady state are discussed.     

基于Cosserat理论的广义协调元法

首次将广义协调元理论与Cosserat理论相结合,构造了一个基于Cosserat理论的平面四节点广义协调等参元。依据常应力与线性应力下的广义协调条件,推导了广义协调位移,进而得到有限元列式。利用广义协调元,一方面克服了协调元过于刚硬的缺点,另一方面消除了非协调元不一定收敛的弱点。分析了带有圆孔的应力集中问题,可以看出,...     

Solutions of the kinetic theory for bounded collisional granular flows

We consider collisional granular flows of nearly elastic spheres featuring a single constituent or binary mixtures in various bounded geometries. We review the equations of the kinetic theory for the conservation of mass, momentum, fluctuation energy and species concentration. We illustrate their solutions for shear flows in rectilinear or axisymmetric rectangular channels with or without a body force. We show that proper boundary conditions yield numerical solutions in good agreement with molecular dynamical simulations and with data from physical experiments carried out in microgravity.Received: 3 December 2002, Accepted: 3 February 2003, Published online: 27 June 2003PACS: 45.70.Mg, 45.70.-n, 05.20.Dd, 83.10.Rs     

Internal viscosity in polymer kinetic theory: shear flows

The Gaussian closure method and Brownian dynamics simulations have been used to calculate the shear material properties of a dilute solution of Hookean dumbbells with internal viscosity. Results for the zero-shear-rate material properties and small amplitude oscillatory shear material properties have been found analytically, and numerical results for the steady state shear material properties are also presented. Two interpretations of the stress tensor are investigated and results are compared. Brownian dynamics simulations are used to obtain material properties of the Hookean dumbbell with internal viscosity without approximations. These simulation results are compared with the perturbation solution of Booij and van Wiechen as well as with a new Gaussian closure solution. Also presented are the contracted distribution functions as derived from the Gaussian closure method and from Brownian dynamics simulations.     

A generalized Adadorov theory for anisotropic thin-walled beams

This paper presents a generalized Adadorov theory for anisotropic thin—walled beams. The theory takes account of the shear strain of the middle surface, which exerts a significant influence on the anisotropic thin-walled beams. A new approach is established to solve the governing equations, which have the same form for both open and closed section beams. The numerical examples show that the effects of the shear strain cannot be neglected for this class of beams.This work was part of research project supported by the National Natural Science Foundation of China     

Extended thermodynamics and the Jeffrey's constitutive equation

Extended irreversible thermodynamics provides an evolution equation for the viscous pressure tensor which reduces to the Jeffrey's constitutive equation in the long-wave limit. in contrast with Jeffrey's equation, the equation obtained in extended irreversible thermodynamics leads to finite speed of propagation for shear pulses. The nonlocal effects are included into the theory by allowing the entropy to depend on higher-order fluxes, instead of spatial gradients. The use of the former ones is clearly advantageous in the high-frequency domain.     

Diffusion flame analysis of twin plane jets via a kinetic theory approach

Diffusion flame solutions of twin plane jets based on a turbulent kinetic theory due to Chung and a Green function method by Hong are presented. The chemical reaction between fuel and oxidizer is assumed to be one-step, one-direction and infinitely fast. The solutions are obtained by direct integration over a constructed probability density function in velocity space. The probability density functions of reactants in transverse velocity space, species mass fraction distributions, turbulent transport of momentum and heat, temperature distributions and flame structure are also considered in this paper. The diffusion flame phenomena of the twin plane jets show that the interaction between the two jets is a dominant factor.     

基于广义非线性统一强度理论的隧道塌落拱分析

基于广义非线性统一强度的剪切破坏理论,在平面应变状态下,根据极限上限定理和隧道顶部的围岩塌落机制,在耗散能中引入了包含曲线型破裂面方程的目标函数,建立了围岩中任意断面的隧道顶部围岩的塌落机制。基于塑性位势理论,考虑塑性应变增量与塑性势函数的应力梯度成正比,由此得出了在速度间断线上任意点内能的耗散率;再运用虚功原理,建立内能耗散率和外力做功相等的关系式,从而通过变分原理得出了隧道顶部塌落面的解析表达式,由该表达式计算出隧道顶部塌落面的形状。以圆形断面隧道为例,对影响塌落拱形状的隧道半径和中间主剪应力系数等相关参数进行了讨论分析。由此得出:在平面应变状态下,隧道顶部围岩塌落体的宽度和高度随着中间主剪应力系数的不断增大而减小;塌落面的高度随着广义非线性统一强度参数的不断增大而增大,而塌落面的宽度则不断减小;塌落宽度和塌落高度随隧道半径的增大而增大。     

A dynamic slip velocity model for molten polymers based on a network kinetic theory

In this paper the slip phenomenon is considered as a stochastic process where the polymer segments (taken as Hookean springs) break off the wall due to the excessive tension imposed by the bulk fluid motion. The convection equation arising in network theories is solved for the special case of a polymer/wall interface to determine the time evolution of the configuration distribution function (Q, t). The stress tensor and the slip velocity are calculated by averaging the proper relations over a large number of polymer segments. Due to the fact that the model is probabilistic and time dependent, dynamic slip velocity calculations become possible for the first time and therefore some new insight is gained on the slip phenomenon. Finally, the model predictions are found to match macroscopic experimental data satisfactorily.Nomenclature rate of creation of polymer segments - g(Q) constant of rate of creation of polymer segments - rate of loss of polymer segments - h(Q) constant of rate of loss of polymer segments - h(Q) constant of rate of loss of polymer segments due to destruction of its B-link - H Hookean spring constant - k Boltzmann's constant - n unit vector normal to the polymer/wall interface - n ₀ number density of polymer segments - n ₀ surface number density of polymer segments - Q vector defining the size and orientation of a polymer segment - Q ^* critical length of a segment beyond which the tension may overcome the W _adh - t time - t _h howering time of broken polymer segments - T absolute temperature - W _adh work of adhesion Greek Letters _n nominal strain - strain - _n nominal shear rate - shear rate - dimensionless constant in the expressions of h(Q), g(Q) - viscosity - ^T velocity gradient tensor - ₀ time constant - standard deviation of vectors Q at equilibrium - _w wall shear stress - stress tensor - ₀ equilibrium configuration distribution function of Q - configuration distribution function of Q     

The setting up of the equations for two-phase flows by the kinetic theory method

The fundamental equations for two-phase flows are deduced from the Boltzmann's equation. The collision terms are treated with a method similar to what is used in the classical kinetic theory for handling the transport properties of dense gases. It is shown that collision pressure and collision thermal flux exist in gas-particle flows in addition to the general partial pressure and partial thermal flux. Their physical natures are quite different from those of the general partial pressure and partial thermal flux. The applicability of the binary collision assumption and the molecular chaos assumption to gas-particle flows is also discussed. Finally, the equations for two-phase flows obtained by the method of the kinetic theory are compared with those obtained by average continuum models and by the model of particle clouds. The results from the kinetic theory show clearly the physical significance of various parameters and clarify some confusing concepts. Institute of Mechanics, Academia Sinica     

On the modeling of granular traffic flow by the kinetic theory for active particles trend to equilibrium and macroscopic behavior

The modeling of vehicular traffic flow is developed by methods of the discrete mathematical kinetic theory for active particles. The discretization refers to the velocity variable in the case of spatially homogeneity. The discretization overcomes, at least in part, some technical difficulties related to the selection of the correct representation scale. Moreover, the modeling approach includes in the state equation of the vehicle an activity variable suitable to model the quality (low or high) of the vehicle-driver system. This paper aims to be the first of a project concerning traffic flow by active particles methods.     

基于一种广义梁理论的弹性地基FGM简支梁自由振动解析解

基于一种扩展的n阶广义剪切变形梁理论(n-GBT),应用Hamilton原理,建立了以轴向位移、横向位移及转角为未知函数的Winkler-Pasternak弹性地基功能梯度材料(FGM)梁的自由振动方程,采用Navier法获得了弹性地基FGM简支梁自由振动的精确解。与多种梁理论预测结果进行比较,讨论并给出了GBT阶次n的理想取值;分析了梯度指标、跨厚比及地基刚度对FGM梁频率的影响。结果表明:本文方法有效且适用范围广,若采用高阶剪切梁理论模型,宜取n≥3的奇数;FGM梁的自振频率随材料梯度指标的增大而减小;随跨厚比的增加而增大,但当跨厚比大于20,跨厚比增加对频率的影响很小;随地基刚度的增加而增大,地基刚度足够大时,频率趋于收敛。     

Region-wise variational principles and generalized variational principles on large strain for consolidation theory

Introduction Thedeformationofsaturatedsoftclayisoneofimportantquestionsingeotechnical engineering.Thenotablecharacteristicisthatthedegreeofitsstrainisgenerallylargerthan10percent.Oneofthecauses[1],Whichleadtoaquantitativedifferencebetweenthe numericalsimu…     

Linear rheology of diluted linear, star and model long chain branched polymer melts

We present experiments and theory on the diluted melt dynamics of monodisperse entangled polymers of linear, star and H-shaped architecture. Frequency-dependent rheological data on a series of progressively diluted linear, star and H-polymers are in good agreement with a refined tube-model theory that, for H-polymers, combines star polymer melt behaviour at high frequency, with linear polymer reptation behaviour at low frequencies. Taking into account the effect of dilution via some simple scaling relations, mild polydispersity and by incorporating the high frequency Rouse modes, we are able to model quantitatively the entire frequency range. This work suggests a novel rheological route to analysing long chain branching in polymer melts. Received: 6 April 2000/Accepted: 21 December 2000     

A unified constitutive theory for polymeric liquids I. Basic considerations and a simplified model

By combining a continuum mechanical approach with considerations of network theory and thermodynamics of irreversible processes, a set of differentialtype constitutive equations for polymeric liquids are obtained which provide expressions for the stress tensor, evolution equations of the effective Finger strain and Cauchy strain for the network deformation, and a first order differential equation governing the rigidity modulus. Unlike Giesekus' recent unified approach that starts from the bead-spring model, the theory lends itself more readily to a better understanding of most of the current theories based on continuum mechanics and molecular network concepts. Different recent models such as those due to Leonov, Dashner—Van Arsdale, Phan Thien—Tanner, and Acierno et al. (or Marrucci) can be unambiguously interpreted as resulting from specific approximations or additional assumptions.