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1.
A thermodynamically consistent continuum theory for single-phase, single-constituent cohesionless granular materials is presented. The theory is motivated by dimensional inconsistencies of the original Goodman-Cowin theory [1–3]; it is constructed by removing these inconsistencies through the introduction of an internal length ℓ. Four constitutive models are proposed and discussed in which ℓ is (i) a material constant (Model I), (ii) an independent constitutive variable (Model II), (iii) an independent dynamic field quantity (Model III) and (iv) an independent kinematic field quantity (Model IV). Expressions of the constitutive variables emerging in the systems of the balance equations in these four models in thermodynamic equilibrium are deduced by use of a thermodynamic analysis based on the Müller-Liu entropy principle. Comments on the validity of these four models are given and discussed; the results presented in the current study show a more general formulation for the constitutive quantities and can be used as a basis for further continuum-based theoretical investigations on the behaviour of flowing granular materials. Numerical results regarding simple plane shear flows will be discussed and compared in Part II of this work. 相似文献
2.
We develop a continuum-mechanical formulation and generalization of the Navier–Stokes-α equation based on a recently developed framework for fluid-dynamical theories involving higher-order gradient dependencies.
Our flow equation involves two length scales α and β. The first of these enters the theory through the specific free-energy α
2|D|2, where D is the symmetric part of the gradient of the filtered velocity, and contributes a dispersive term to the flow equation. The
remaining scale is associated with a dissipative hyperstress which depends linearly on the gradient of the filtered vorticity
and which contributes a viscous term, with coefficient proportional to β
2, to the flow equation. In contrast to Lagrangian averaging, our formulation delivers boundary conditions and a complete structure
based on thermodynamics applied to an isothermal system. For a fixed surface without slip, the standard no-slip condition
is augmented by a wall-eddy condition involving another length scale ℓ characteristic of eddies shed at the boundary and referred to as the wall-eddy length. As an application, we consider the
classical problem of turbulent flow in a plane, rectangular channel of gap 2h with fixed, impermeable, slip-free walls and make comparisons with results obtained from direct numerical simulations. We
find that α/β ~ Re
0.470 and ℓ/h ~ Re
−0.772, where Re is the Reynolds number. The first result, which arises as a consequence of identifying the specific free-energy with the
specific turbulent kinetic energy, indicates that the choice β = α required to reduce our flow equation to the Navier–Stokes-α equation is likely to be problematic. The second result evinces the classical scaling relation η/L ~ Re
−3/4 for the ratio of the Kolmogorov microscale η to the integral length scale L.
相似文献
3.
Ju Min Kim Song Geun Lee Chongyoup Kim 《ournal of non Newtonian Fluid Mechanics》2008,150(2-3):162-176
The objective of this work is to investigate what mechanisms should be employed to qualitatively/quantitatively predict particle migration in a suspension flow. Based on the diffusive flux model originally proposed by Phillips et al. [R.J. Phillips, R.C. Armstrong, R.A. Brown, A.L. Graham, A constitutive equation for concentrated suspensions that account for shear-induced particle migration, Phys. Fluids A 4 (1992) 30–40], we survey the accuracy of three models including original Phillips model (Model I), modified Phillips model with curvature-induced migration mechanism (Model II), and finally the modified Model II with volume-fraction-dependent parameters (Model III). The empirical parameters which appear in the three models are determined by fitting to independent concentric Couette experiments. The accuracy of three models in concentric Couette problem is comparable except that Model III shows more improved predictions near the inner cylinder. However, the predictions of the three models are entirely different on a qualitative level for parallel plate problems and the existence and direction of particle migration are severely model-dependent. Models II and III predict no migration or very slight migration at high volume fraction, which is in good agreement with the previous experiments, whereas Model I predicts inward migration. We show that Model III accurately predicts a solid-free region near the center at low volume fraction, which was experimentally observed.In addition to a survey of migration mechanisms, we developed a frame-invariant curvature-induced migration model applicable to multi-dimensional flows. A transient 2D mixed-order finite element method (FEM) code was implemented to compare the predictions of the three models in a 2D problem. In this work, we considered the eccentric Couette problem, which is often used as a benchmarking problem. Though there is not much difference among the three models, Model III predicts that the particle migration is slightly retarded at high shear rate regions. 相似文献
4.
Jaume Llibre Paulo R. da Silva Marco A. Teixeira 《Journal of Dynamics and Differential Equations》2012,24(1):1-12
In this article we establish an interaction between non-smooth systems, geometric singular perturbation theory and synchronization
phenomena. We find conditions for a non-smooth vector fields be locally synchronized. Moreover its regularization provide
a singular perturbation problem with attracting critical manifold. We also state a result about the synchronization which
occurs in the regularization of the fold-fold case. We restrict ourselves to the 3-dimensional systems (ℓ = 3) and consider the case known as a T-singularity. 相似文献
5.
The goal of this paper is to present a flexible multibody formulation for Euler-Bernoulli beams involving large displacements. This method is based on a discretisation of internal and kinetic energies. The beam is represented by its line of centroids and each section is oriented by a frame defined by three Euler angles. We apply a finite element formulation to describe the evolution of these angles along the neutral fibre and describe the internal energy. The kinetic energy is approximated as the one of two rigid bars tangent to the neutral fibre at the ends of the beam. We derive the equations of motion from a Lagrange formulation. These equations are solved using the Newmark method or/and the Newton-Raphson technique. We solve some very classic problems taken from the literature as the curved beam presented by Simo [Simo, J. C., ‘A three-dimensional finite-strain rod model. the three-dimensional dynamic problem. Part I’, Comput. Meths. Appl. Mech. Engrg.
49, 1985, 55–70; Simo, J. C. and Vu-Quoc, L., ‘A three-dimensional finite-strain rod model, Part II: Computationals aspects’, Comput. Meths. Appl. Mech. Engrg.
58, 1988, 79–116] and Lee [Lee, Kisu, ‘Analysis of large displacements and large rotations of three-dimensional beams by using small strains and unit vectors’, Commun. Numer. Meth. Engrg.
13, 1997, 987–997] or the rotational rod presented by Avello [Avello, A., Garcia de Jalon, J., and Bayo, E., ‘Dynamics of flexible multibody systems using cartesian co-ordinates and large displacement theory’, Int. J. Num. Methods in Engineering
32, 1991, 1543–1563] and Simo [Simo, J. C. and Vu-Quoc, L., ‘On the dynamics of flexible beams under large overall motions – the planar case. Part I’ Jour. of Appl. Mech.
53, 1986, 849–854; Simo, J. C. and Vu-Quoc, L., ‘On the dynamics of flexible beams under large overall motions – the planar case. Part II’, Jour. of Appl. Mech.
53, 1986, 855–863]. 相似文献
6.
Turbulence Modeling Effects on the Prediction of Equilibrium States of Buoyant Shear Flows 总被引:1,自引:0,他引:1
The effects of turbulence modeling on the prediction of equilibrium states of turbulent buoyant shear flows were investigated.
The velocity field models used include a two-equation closure, a Reynolds-stress closure assuming two different pressure-strain
models and three different dissipation rate tensor models. As for the thermal field closure models, two different pressure-scrambling
models and nine different temperature variance dissipation rate ɛτ) equations were considered. The emphasis of this paper is focused on the effects of the ɛτ-equation, of the dissipation rate models, of the pressure-strain models and of the pressure-scrambling models on the prediction
of the approach to equilibrium turbulence. Equilibrium turbulence is defined by the time rate of change of the scaled Reynolds
stress anisotropic tensor and heat flux vector becoming zero. These conditions lead to the equilibrium state parameters, given
by /ɛ,
τ/ɛτ, , Sk/ɛ and G/ɛ, becoming constant. Here, and
τ are the production of turbulent kinetic energy k and temperature variance , respectively, ɛ and ɛτ are their respective dissipation rates, R is the mixed time scale ratio, G is the buoyant production of k and S is the mean shear gradient. Calculations show that the ɛτ-equation has a significant effect on the prediction of the approach to equilibrium turbulence. For a particular ɛτ-equation, all velocity closure models considered give an equilibrium state if anisotropic dissipation is accounted for in
one form or another in the dissipation rate tensor or in the ɛ-equation. It is further found that the models considered for
the pressure-strain tensor and the pressure-scrambling vector have little or no effect on the prediction of the approach to
equilibrium turbulence.
Received 21 April 2000 and accepted 21 February 2001 相似文献
7.
Bernd Schmidt 《Archive for Rational Mechanics and Analysis》2008,190(1):1-55
We give a rigorous derivation of a continuum theory from atomic models for thin films. This scheme has been proposed by Friesecke and James in [J. Mech. Phys. Solids
48, 1519–1540 (2000)]. The resulting continuum energy expression is obtained by integrating a stored energy density which not
only depends on the deformation gradient, but also on ν-1 director fields when ν is the (fixed) number of atomic film layers. 相似文献
8.
M. Ben Slimane 《Nonlinear Oscillations》2005,8(4):431-438
The oscillation spaces
introduced by Jaffard are a variation on the definition of Besov spaces for either s ≥ 0 or s ≤ −d/p. On the contrary, the spaces
for −d/p < s < 0 cannot be sharply imbedded between Besov spaces with almost the same exponents, and, thus, they are new spaces of really
different nature. Their norms take into account correlations between the positions of large wavelet coefficients through the
scales. Several numerical studies uncovered such correlations in several settings including turbulence, image processing,
traffic, finance, etc. These spaces allow one to capture oscillatory behaviors that are left undetected by Sobolev or Besov
spaces. Unlike Sobolev spaces (respectively, Besov spaces B
p
s,q
(ℝd)), which are expressed by simple conditions on wavelet coefficients as ℓp norms (respectively, mixed ℓp − ℓq norms), oscillation spaces are written as ℓp averages of local C
s
′ norms. In this paper, we prove the completeness of oscillation spaces in spite of such a mixture of two norms of different
kinds.
Published in Neliniini Kolyvannya, Vol. 8, No. 4, pp. 435–443, October–December, 2005. 相似文献
9.
The grating objective speckle method has been applied in whole-field strain analysis of carbon-fiber-woven polyimide-composite
materials. A sequence of rosette fringe patterns was obtained from one single specklegram, indicating displacement components
along four different directions with a 45-deg interval. The spatial frequencies, which represent the sensitivities of the
fringe intervals, were 2400 ℓ/mm forU
x
,U
y
and 1697 ℓ/mm forU
45 andU
135. Normal strain components, ɛ
x
, ɛ
y
, ɛ45, and ɛ135, were trasformed to quantitative topographic representations by coupling to a digital computer system. Shear strain can be
determined by the rosette equations. 相似文献
10.
Under assumptions on smoothness of the initial velocity and the external body force, we prove that there exists T
0 > 0, ν
0 > 0 and a unique continuous family of strong solutions u
ν
(0 ≤ ν < ν
0) of the Euler or Navier–Stokes initial-boundary value problem on the time interval (0, T
0). In addition to the condition of the zero flux, the solutions of the Navier–Stokes equation satisfy certain natural boundary
conditions imposed on curl
u
ν
and curl
2
u
ν
.
相似文献
11.
IntroductionIntheframeworkofconventionalplasticity ,materialinstabilityisoneoftheprincipalfactorsthatresultinginthestrainlocalizationphenomenon .Byusingtheterminology‘homogenized’ ,itisreferredtothefactthatinitialflawsandboundaryconditionsnecessarilyinduceanon_homogeneousstressstateinaspecimenduringtesting .Inparticularintheprocessofprogressivefailure ,theflawsandlocalstressconcentrationwillcausestronglyinhomogeneousdeformationofthespecimen[1,2 ].Asthedeformation_inducedfracture/damagephenom… 相似文献
12.
In this article, we solve in closed form a system of nonlinear differential equations modelling the elastica in space of a thin, flexible, straight rod, loaded by a constant thrust at its free end. Common linearizations of strength of materials are of course not applicable any way, because we analyze great deformations, even if not so large to go off the linear elasticity range. By passing to cylindrical coordinates ρ, θ, z, we earn a more tractable differential system evaluating ρ as elliptic function of polar anomaly θ and also providing z through elliptic integrals of I and III kind. Deformed rod’s centerline is then completely described under both tensile or compressive load. Finally, the planar case comes out as a degeneracy, where the Bernoulli lemniscatic integral appears. 相似文献
13.
Guo Zhongsan Associate Professor Xiao Fan Guo Siwen Wu Yueqing Gu Leye 《应用数学和力学(英文版)》2000,21(5):579-584
The mathematical model described in Part I was solved using “influence line method” combining analytical method and finite
element method. Many important aspects of microcirculatory dynamics were analyzed and discussed. It show that interstitial
fluid pressure changes its sign twice within one arteriolar vasomotion period and it is therefore not important that interstitial
fluid pressure is a little higher or lower than atmospheric pressure; arteriolar vasomotion can periodically result in lymph
formation and interstitial total pressure plays an important role in this procedure; local regulation of microcirculation
can meet metabolic need some extent in the form of dynamic equilibrium. The property of arteriole as a “resistant vessel”
and the efficiency of microvascular network as heat exchanger are also shown. These results show that the comprehensive mathematical
model developed in Part I is physiologically resonable.
Foundation item: the Natural Science Foundation of Sichuan Province, P R China
Biography: Guo Zhongsan (1947-) 相似文献
14.
H. Beirão da Veiga 《Journal of Mathematical Fluid Mechanics》2007,9(4):506-516
In reference [7] it is proved that the solution of the evolution Navier–Stokes equations in the whole of R
3 must be smooth if the direction of the vorticity is Lipschitz continuous with respect to the space variables. In reference
[5] the authors improve the above result by showing that Lipschitz continuity may be replaced by 1/2-H?lder continuity. A
central point in the proofs is to estimate the integral of the term (ω · ∇)u · ω, where u is the velocity and ω = ∇ × u is the vorticity. In reference [4] we extend the main estimates on the above integral term to solutions under the slip boundary
condition in the half-space R
+3. This allows an immediate extension to this problem of the 1/2-H?lder sufficient condition.
The aim of these notes is to show that under the non-slip boundary condition the above integral term may be estimated as well
in a similar, even simpler, way. Nevertheless, without further hypotheses, we are not able now to extend to the non slip (or
adherence) boundary condition the 1/2-H?lder sufficient condition. This is not due to the “nonlinear" term (ω · ∇)u · ω but to a boundary integral which is due to the combination of viscosity and adherence to the boundary. On the other hand,
by appealing to the properties of Green functions, we are able to consider here a regular, arbitrary open set Ω.
相似文献
15.
Heat fluxes close to the edge of a heated solid plate aligned parallel to the axis of an acoustic standing wave were measured
for drive ratios DR≡P
A/p
m
of 1, 2 and 3. It was found that at the highest drive ratio (3), the resulting heat flux vector at the edge of the plate
is directed into the plate, opposite to the direction of the heat flux imposed by the resistive heaters within the plate.
This observation confirms the thermoacoustic effect previously detected in the visualized temperature fields and discussed
in part I of this paper. Through the energy balance the magnitudes of the heat fluxes into the plate, caused by the thermoacoustic
effect, were determined. The measured data are in good agreement with numerical and analytical predictions.
Received on 18 August 1999 相似文献
16.
Pierre Terech Séverine Friol Neralagatta Sangeetha Yeshayahu Talmon Uday Maitra 《Rheologica Acta》2006,45(4):435-443
We present a comparative investigation of two opposite classes of self-assembled fibrillar networks. Ribbons and tubes having cross-sectional dimensions in the nanoscale can be formed in aqueous solutions of steroids derived, respectively, from deoxycholic (DC) and lithocholic (LC) acids. Rheological features distinguish energetic networks of DC ribbons rigidly fixed in cylindrical bundles and entropic transient networks of LC tubes weakly interacting in shear-sensitive suspensions. The two classes are characterized by their frequency sweep profiles, viscoelastic linear domains, scaling laws of the elastic shear modulus vs concentration, kinetics of formation of the networks, and their optical birefringence aspects. A theoretical context for networks of rigid fibers is used to account for the scaling exponents α in the G’ (and σ*) ∝C
α
laws (α=2.0 and 1.0, respectively, for DC and LC). The evolution observed in DC gels from ribbons to cylindrical fibers with monodisperse sections made up with four ribbons is an indication of an equilibrated balance between face-to-face attractions and untwisting elastic processes of the constitutive ribbons.Paper presented at the Annual Meeting of the European Society of Rheology, Grenoble, April 2005 相似文献
17.
A systematic application of the group analysis method for modeling fluids with internal inertia is presented. The equations
studied include models such as the nonlinear one-velocity model of a bubbly fluid (with incompressible liquid phase) at small
volume concentration of gas bubbles (Iordanski Zhurnal Prikladnoj Mekhaniki i Tekhnitheskoj Fiziki 3, 102–111, 1960; Kogarko Dokl. AS USSR 137, 1331–1333, 1961; Wijngaarden J. Fluid Mech. 33, 465–474, 1968), and the dispersive shallow water model (Green and Naghdi J. Fluid Mech. 78, 237–246, 1976; Salmon 1988). These models are obtained for special types of the potential function W(r,[(r)\dot],S){W(\rho,\dot \rho,S)} (Gavrilyuk and Teshukov Continuum Mech. Thermodyn. 13, 365–382, 2001). The main feature of the present paper is the study of the potential functions with W
S
≠ 0. The group classification separates these models into 73 different classes. 相似文献
18.
Hermano Frid 《Archive for Rational Mechanics and Analysis》2006,181(1):177-199
We prove the asymptotic stability of two-state nonplanar Riemann solutions for a class of multidimensional hyperbolic systems
of conservation laws when the initial data are perturbed and viscosity is added. The class considered here is those systems
whose flux functions in different directions share a common complete system of Riemann invariants, the level surfaces of which
are hyperplanes. In particular, we obtain the uniqueness of the self-similar L∞ entropy solution of the two-state nonplanar Riemann problem. The asymptotic stability to which the main result refers is
in the sense of the convergence as t→∞ in Lloc1 of the space of directions ξ = x/t. That is, the solution u(t, x) of the perturbed problem satisfies u(t, tξ)→R(ξ) as t→∞, in Lloc1(ℝn), where R(ξ) is the self-similar entropy solution of the corresponding two-state nonplanar Riemann problem. 相似文献
19.
Shifang Han 《Acta Mechanica Sinica》2007,23(2):149-158
A continuum constitutive theory of corotational derivative type is developed for the anisotropic viscoelastic fluid–liquid
crystalline (LC) polymers. A concept of anisotropic viscoelastic simple fluid is introduced. The stress tensor instead of
the velocity gradient tensor D in the classic Leslie–Ericksen theory is described by the first Rivlin–Ericksen tensor A and a spin tensor W measured with respect to a co-rotational coordinate system. A model LCP-H on this theory is proposed and the characteristic
unsymmetric behaviour of the shear stress is predicted for LC polymer liquids. Two shear stresses thereby in shear flow of
LC polymer liquids lead to internal vortex flow and rotational flow. The conclusion could be of theoretical meaning for the
modern liquid crystalline display technology. By using the equation, extrusion–extensional flows of the fluid are studied
for fiber spinning of LC polymer melts, the elongational viscosity vs. extension rate with variation of shear rate is given
in figures. A considerable increase of elongational viscosity and bifurcation behaviour are observed when the orientational
motion of the director vector is considered. The contraction of extrudate of LC polymer melts is caused by the high elongational
viscosity. For anisotropic viscoelastic fluids, an important advance has been made in the investigation on the constitutive
equation on the basis of which a series of new anisotropic non-Newtonian fluid problems can be addressed.
The project supported by the National Natural Science Foundation of China (10372100, 19832050) (Key project). The English
text was polished by Yunming Chen. 相似文献
20.
This paper presents an experimental method for measuring the attenuation and the velocity of longitudinal ultrasonic waves
propagating through flat epoxy polymer samples. The study takes place in the first phase of epoxy polymer's polymerization,
where these materials pass slowly from liquid state to the solid state. For this purpose an experimental setup was introduced,
suitable for the accurate evaluation of the acoustic properties Δα andc
ℓ
e
, when the epoxy polymers are in their first phase of polymerization, while they are cured for 24 hours at room temperature
(20°C). The ultrasonic method used is the pulse echo-through transmission technique. From the variation ofc
ℓ
e
and Δα during the first phase of epoxy polymers curing, the three characteristic states: liquid, semi-solid and solid, are
clearly determined. It is also observed that plasticizer reduces the testability and the semi-solid state shows greater attenuation
than either the liquid or the solid state. 相似文献