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1.
A. G. Knyazeva 《Journal of Applied Mechanics and Technical Physics》1999,40(6):1088-1096
Several modifications of the Clausius-Clapeyron equation for deformable media, including solid-phase transformations which
depend on the change of additional parameters, are proposed. A model of the medium with tensor concentrations of the components
for which the unique Clausius-Clapeyron equation is also valid is proposed. The tensor analog of the transition heat is introduced,
and an expression for the total transition heat related to the energies of chemical bonds in the crystal lattice is obtained.
At least for slow processes, the fundamental possibility of determining the self transition heat in the experiment is shown
analytically.
Tomsk State University, Tomsk 634050. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 40, No. 6, pp. 103–111,
November–December, 1999. 相似文献
2.
The material time rate of Lagrangean strain measures, objective corotational rates of Eulerian strain measures and their defining
spin tensors are investigated from a general point of view. First, a direct and rigorous method is used to derive a simple
formula for the gradient of the tensor-valued function defining a general class of strain measures. By means of this formula
and the chain rule as well as Sylvester's formula for eigenprojections, explicit basis-free expressions for the material time
rate of an arbitrary Lagrangean strain measure can be derived in terms of the right Cauchy–Green tensor and the material time
rate of any chosen Lagrangean strain measure, e.g. Hencky's logarithmic strain measure. These results provide a new derivation
of Carlson–Hoger's general gradient formula for an arbitrary generalized strain measure and supply a new, rigorous proof for
Carlson–Hoger's conjecture concerning the n-dimensional case. Next, by virtue of the aforementioned gradient formula, a general
fact for objective corotational rates and their defining spin tensors is disclosed: Let Ω = ϒ ( B, D, W) be any spin tensor
that is continuous with respect to B, where B, D and B are the left Cauchy–Green tensor, the stretching tensor and the vorticity
tensor. Then the corotational rate of an Eulerian strain measure defined by Ω is objective iff Ω = W + υ ( B, D), where Υ
is isotropic. By means of this fact and certain necessary or reasonable requirements, it is further found that a single antisymmetric
function of two positive real variables can be introduced to characterize a general class of spin tensors defining objective
corotational rates. A general basis- free expression for all such spin tensors and accordingly a general basis-free expression
for a general class of objective corotational rates of an arbitrary Eulerian strain measure are established in terms of the
left Cauchy–Green tensor B and the stretching tensor B as well as the introduced antisymmetric function. By choosing several
particular forms of the latter, all commonly-known spin tensors and corresponding corotational rates are shown to be incorporated
into these general formulas in a natural way. In particular, with the aid of these general formulae it is proved that an objective
corotational rate of the Eulerian logarithmic strain measure ln V is identical with the stretching tensor D and moreover that
in all possible strain tensor measures only ln V enjoys this property.
This revised version was published online in August 2006 with corrections to the Cover Date. 相似文献
3.
C.G. Speziale 《Theoretical and Computational Fluid Dynamics》1999,13(3):161-166
A resent extension of the nonlinear K–ε model is critically discussed from a basic theoretical standpoint. While it was said in the paper that this model was formulated
to incorporate relaxation effects, it will be shown that the model is incapable of describing one of the most basic such turbulent
flows as is obvious but is described for clarity. It will be shown in detail that this generalized nonlinear K–ε model yields erroneous results for the Reynolds stress tensor when the mean strains are set to zero in a turbulent flow
– the return-to-isotropy problem which is one of the most elementary relaxational turbulent flows. It is clear that K–ε type models cannot describe relaxation effects. While their general formalism can describe relaxation effects, the nonlinear
K–ε model – which the paper is centered on – cannot. The deviatoric part of the Reynolds stress tensor is predicted to be zero
when it actually only gradually relaxes to zero. Since this model was formulated by using the extended thermodynamics, it
too will be critically assessed. It will be argued that there is an unsubstantial physical basis for the use of extended thermodynamics
in turbulence. The role of Material Frame-Indifference and the implications for future research in turbulence modeling are
also discussed.
Received 19 February 1998 and accepted 23 October 1998 相似文献
4.
W. D. Thacker S. Sarkar T. B. Gatski 《Theoretical and Computational Fluid Dynamics》2007,21(3):171-199
The influence of compressibility on the rapid pressure–strain rate tensor is investigated using the Green’s function for the
wave equation governing pressure fluctuations in compressible homogeneous shear flow. The solution for the Green’s function
is obtained as a combination of parabolic cylinder functions; it is oscillatory with monotonically increasing frequency and
decreasing amplitude at large times, and anisotropic in wave-vector space. The Green’s function depends explicitly on the
turbulent Mach number M
t
, given by the root mean square turbulent velocity fluctuations divided by the speed of sound, and the gradient Mach number
M
g
, which is the mean shear rate times the transverse integral scale of the turbulence divided by the speed of sound. Assuming
a form for the temporal decorrelation of velocity fluctuations brought about by the turbulence, the rapid pressure–strain
rate tensor is expressed exactly in terms of the energy (or Reynolds stress) spectrum tensor and the time integral of the
Green’s function times a decaying exponential. A model for the energy spectrum tensor linear in Reynolds stress anisotropies
and in mean shear is assumed for closure. The expression for the rapid pressure–strain correlation is evaluated using parameters
applicable to a mixing layer and a boundary layer. It is found that for the same range of M
t
there is a large reduction of the pressure–strain correlation in the mixing layer but not in the boundary layer. Implications
for compressible turbulence modeling are also explored.
相似文献
5.
Chung Fang 《Archive of Applied Mechanics (Ingenieur Archiv)》2009,79(2):169-173
In the present study, the constitutive relations derived in the revised Goodman–Cowin theory for granular matter are shown
to imply a generalized Mohr–Coulomb criterion for impending flows. Due to the concept of microcontinuum and the incorporation
of the internal friction into the expression of the Cauchy stress tensor, a constrained equilibrium stress state characterized
by the Mohr–Coulomb criterion is yet obtained under uniform distributions of the grains. 相似文献
6.
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
7.
We consider the symmetry of discrete and continuous crystal structures which are compatible with a given choice of dislocation
density tensor. By introducing the notion of a ‘defective point group’ (determined by the dislocation density tensor), we
generalize the notion of Ericksen–Pitteri neighborhoods to this context. 相似文献
8.
David Harris 《Meccanica》2006,41(3):351-362
Some properties of a new continuum model for the bulk flow of a dense granular material in which neighbouring grains are in
contact for a finite duration of time and in which the contact force is non-impulsive – the so called slow flow regime – are
presented. The model generalises both the plastic potential and double-shearing models and contains an additional kinematic
quantity – the intrinsic spin. The stress tensor is, in general, non-symmetric and separate yield conditions govern translational
and rotational yield. We consider homogeneous, quasi-static loadings for the symmetric part of the stress and dynamic loading
for the anti-symmetric part of the stress. A solution for the stress state in terms of a single parameter, namely the major
principal direction of the symmetric part of the stress, is presented. This direction itself is determined by a consideration
of the flow equations in the context both dilatant and isochoric simple shear flows. These simple flows are used to complete
the characterisation of the relationship between the anti-symmetric part of the stress and the intrinsic spin. 相似文献
9.
V. P. Bushlanov 《Journal of Applied Mechanics and Technical Physics》2000,41(4):722-724
An expression for the surface force in a medium with developed boundary surface that is convenient for practice is obtained
by an additional space averaging of the known expression for the bulk density of this force in the form of surface-energy
doubled density tensor divergence.
Tomsk Branch of the Institute of Structural Macrokinetics, Tomsk 634021. Translated from Prikladnaya Mekhanika i Tekhnicheskaya
Fizika, Vol. 41, No. 4, pp. 165–167, July–August, 2000. 相似文献
10.
Manish K. Tiwari Alexander V. Bazilevsky Alexander L. Yarin Constantine M. Megaridis 《Rheologica Acta》2009,48(6):597-609
Rheological behavior of concentrated suspensions of chemical vapor deposition carbon nanotubes in uniaxial elongation and
simple shear is studied experimentally and theoretically. Nanotubes are suspended in viscous host liquids—castor oil or its
blends with n-decane. The elongational measurements are performed by analyzing self-thinning (due to surface tension effect) liquid threads
of nanotube suspensions. A quasi-one-dimensional model is used to describe the self-thinning process, whereas corrections
accounting for thread nonuniformity and necking are introduced a posteriori. The effects of nanotube concentration and aspect
ratio, viscosity of the suspending liquid, and initial diameter of the self-thinning thread in uniaxial elongation are elucidated.
The results for uniaxial elongation are compared with those for simple shear. The correspondence in the results of the shear
and elongational measurements is addressed and interpreted. The results conform to the Herschel–Bulkley rheological constitutive
equation (i.e., power law fluids with yield stress). However, the yield stress in elongation is about 40% higher than in simple
shear flow, which suggests that the original Herschel–Bulkley model need modification with the yield stress being a function
of the second invariant of the deviatoric stress tensor. The present effort is the first to study capillary self-thinning
of Herschel–Bulkley liquids, which are exemplified here by suspensions of carbon nanotubes. 相似文献
11.
N. M. Borodachev 《International Applied Mechanics》2006,42(8):849-878
New representations of the stress tensor in the linear theory of elasticity and thermoelasticity are proposed. These representations
satisfy the equilibrium equations and the strain compatibility equation. The stress tensor is expressed in terms of a harmonic
tensor or a harmonic vector. The second boundary-value problem for an elastic half-space and an elastic layer is solved as
an example
__________
Translated from Prikladnaya Mekhanika, Vol. 42, No. 8, pp. 3–35, August 2006. 相似文献
12.
A new general constitutive model in terms of the principal stretches is proposed to reflect limiting chain extensibility resulting
in severe strain-stiffening for incompressible, isotropic, homogeneous elastic materials. The strain-energy density involves
the logarithm function and has the general Valanis–Landel form. For specific functions in the Valanis–Landel representation,
we obtain particular strain-energies, some of which have been proposed in the recent literature. The stress–stretch response
in some basic homogeneous deformations is described for these particular strain-energy densities. It is shown that the stress
response in these deformations is similar to that predicted by the Gent model involving the first invariant of the Cauchy–Green
tensor. The models discussed here depend on both the first and second invariants.
相似文献
13.
Holm Altenbach Victor A. Eremeyev Leonid P. Lebedev Leonardo A. Rendón 《Archive of Applied Mechanics (Ingenieur Archiv)》2010,80(3):217-227
Acceleration waves in nonlinear thermoelastic micropolar media are considered. We establish the kinematic and dynamic compatibility
relations for a singular surface of order 2 in the media. An analogy to the Fresnel–Hadamard–Duhem theorem and an expression
for the acoustic tensor are derived. The condition for acceleration wave’s propagation is formulated as an algebraic spectral
problem. It is shown that the condition coincides with the strong ellipticity of equilibrium equations. As an example, a quadratic
form for the specific free energy is considered and the solutions of the corresponding spectral problem are presented. 相似文献
14.
L. A. Pal’tsev 《Fluid Dynamics》1997,32(1):131-139
On the basis of the linearized kinetic Choh-Uhlenbeck equation the stress tensor and energy flux are found in the gasdynamic
approximation for steady states of a monatomic gas with allowance for the first virial correction to the transport coefficients.
Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, pp. 155–164, January–February,
1997. 相似文献
15.
I. Yu. Tsvelodub 《Journal of Applied Mechanics and Technical Physics》2008,49(1):129-135
A variant of the multimodulus elasticity theory for isotropic materials is proposed under the assumption that the shear modulus
in Hooke’s law is a constant and the volume modulus depends on the sign of the first invariant of the stress tensor. Plane
problems (plane strain and generalized plane stressed state) and problems of plate bending are considered. Some examples are
given.
__________
Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 49, No. 1, pp. 157–164, January–February, 2008. 相似文献
16.
V. D. Bondar’ 《Journal of Applied Mechanics and Technical Physics》1999,40(2):360-366
The relations of the nonlinear model of the theory of elasticity are considered. The Cauchy and the strain gradient tensors
are taken to be the characteristics of the stress-strain state of a body. Sufficient conditions under which the static equations
of elasticity are of elliptic type are established. These conditions are expressed in the form of constraints imposed on the
derivatives of the elastic potential with respect to the strain-measure characteristics. The cases of anisotropic and isotropic
bodies are treated, including the case where the Almansi tensor is taken to be the strain measure. The plane strain of a body
is investigated using actual-state variables.
Novosibirsk State University, Novosibirsk 630090. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 40,
No. 2, pp. 196–203, March–April, 1999. 相似文献
17.
A procedure of deriving nonlinear wave equations that describe the propagation and interaction of hyperelastic cylindrical
waves in composite materials modeled by a mixture with two elastic constituents is outlined. Nonlinearity is introduced by
metric coefficients, Cauchy-Green strain tensor, and Murnaghan potential. It is the quadratic nonlinearity of all governing
relations. For a configuration (state) dependent on the radial coordinate and independent of the angular and axial coordinates,
quadratically nonlinear wave equations for stresses are derived and a relationship between the components of the stress tensor
and partial strain gradient is established. Four combinations of physical and geometrical nonlinearities in systems of wave
equations are examined. Nonlinear wave equations are explicitly written for three of the combinations
__________
Translated from Prikladnaya Mekhanika, Vol. 43, No. 6, pp. 63–72, June 2007. 相似文献
18.
The intensity of Rayleigh and Raman scattered light from molecular structural units is proportional to the quadratic polarizability
tensor and the derived polarizability tensor, respectively. The orientation of the polymer skeletal backbone is directly related
to the orientation of the scattering structural units comprising it. The mathematical structure of the quadratic scattering
tensors for a single Kuhn bond are deduced in terms of the unit vector along a Kuhn bond from symmetry considerations alone
(Boehler 1987). Subsequent application of the Kuhn–Grün conditional probability analysis (Kuhn and Grün, Kolloid Z 101:248–271, 1942), which uses a freely jointed chain model, yields a general expression for the quadratic Raman and polarizability tensors
for a single chain segment with five independent terms. Each term is multiplied by a spectroscopic parameter that is a complex
function of the intrinsic spectroscopic tensors and the orientation distribution of monomers within an elementary Kuhn bond.
A small stretch analysis of the Kuhn–Grün representation of the quadratic polarizability reveals that independent fourth moments
of the segmental orientation distribution function can only be determined experimentally when the deformation or stretch of
the flexible polymer is large and finite, thus severely restricting a primary advantage of the Raman and Rayleigh scattering
methods. A general segmental additivity theorem is rigorously proven which demonstrates that polarized scattering experiments
physically reflect the average orientation and stretch of flexible polymer skeletal backbone segments, or sub-segments, independent
of chain architecture or molecular weight. Constitutive equations are fundamentally constructed to determine Kuhn bond orientation
and are intrinsically related to the Kuhn–Grün analysis. The decoupling approximation, which is always invoked in Doi–Edwards
type models of entangled polymeric liquids, is examined in light of the Kuhn–Grün analysis. 相似文献
19.
D. L. Blackmore N. K. Prykarpats’ka V. H. Samoilenko E. Wachnicki M. Pytel-Kudela 《Nonlinear Oscillations》2007,10(1):22-31
We develop the Cartan-Monge geometric approach to the characteristic method for nonlinear partial differential equations of
the first and higher orders. The Hamiltonian structure of characteristic vector fields related with nonlinear partial differential
equations of the first order is analyzed, and tensor fields of special structure are constructed for defining characteristic
vector fields naturally related with nonlinear partial differential equations of higher orders.
Published in Neliniini Kolyvannya, Vol. 10, No. 1, pp. 26–36, January–March, 2007. 相似文献
20.
Didier Bresch El Hassan Essoufi Mamadou Sy 《Journal of Mathematical Fluid Mechanics》2007,9(3):377-397
In this paper, we look at the influence of the choice of the Reynolds tensor on the derivation of some multiphasic incompressible
fluid models, called Kazhikhov–Smagulov type models. We show that a compatibility condition between the viscous tensor and
the diffusive term allows us to obtain similar models without assuming a small diffusive term as it was done for instance
by A. Kazhikhov and Sh. Smagulov. We begin with two examples: The first one concerning pollution and the last one concerning
a model of combustion at low Mach number. We give the compatibility condition that provides a class of models of the Kazhikhov–Smagulov
type. We prove that these models are globally well posed without assumptions between the density and the diffusion terms. 相似文献