A theory of anisotropic fluids

1962 ◽  
Vol 13 (1) ◽  
pp. 33-46 ◽  
Author(s):  
George L. Hand
Keyword(s):  
Stress Tensor ◽  
Symmetric Tensor ◽  
Deformation Tensor ◽  
Anisotropic Fluid ◽  
Stress Components ◽  
Fluid Theory ◽  
Anisotropic Fluids ◽  
Special Case ◽  
Theory And Experiment ◽  
Good Agreement

A theory is proposed in which the stress tensor is a function of the components of the rate of deformation tensor and a symmetric tensor describing the microscopic structure of a fluid. The expression for the stress tensor can be written in closed form using results from the Hamilton-Cayley theorem. This theory is shown to contain Prager's theory of dumbbell suspensions as a special case. By limiting the type of terms in the constitutive equations, various stress components can be evaluated for simple shear. These exhibit non-Newtonian behaviour typical of certain higher polymer solutions.Some of the results of the anisotropic fluid theory are compared with experimental measurements of normal stress and apparent viscosity. Certain high polymers in solution show good agreement between theory and experiment, at least for low enough values of the rate of shear.

Flow Characteristics of a Powder Lubricant in a Slider Bearing

2001 ◽  
Author(s):  
Manjunath Pappur ◽  
M. M. Khonsari
Keyword(s):  
Slip Velocity ◽  
Thrust Bearing ◽  
Volume Fraction ◽  
Flow Characteristics ◽  
Slider Bearing ◽  
Systematic Development ◽  
Powder Lubrication ◽  
Insight Into ◽  
Theory And Experiment ◽  
Good Agreement

Abstract This paper deals with a systematic development of theory of powder lubrication with the appropriate formalism based on the fundamentals of fluid mechanics. The theory is capable of predicting flow velocity, fluctuation (pseudo-temperature), powder volume fraction, and slip velocity at the boundaries. An extensive set of parametric simulations covering particle size, surface roughness, volumetric flow, load and speed are performed to gain insight into the performance of a powder lubricated thrust bearing. The results of simulations are compared to the published experimental results. Good agreement between the theory and experiment attests to the capability of the model and its potential for design of powder lubricated bearings.

Morphology of Voltage-Triggered Ordered Wrinkles of a Dielectric Elastomer Sheet

2017 ◽  
Vol 84 (11) ◽  
Author(s):  
Guoyong Mao ◽  
Lei Wu ◽  
Xueya Liang ◽  
Shaoxing Qu
Keyword(s):  
High Voltage ◽  
Optical Sensor ◽  
Material Science ◽  
Dielectric Elastomer ◽  
Theoretical Studies ◽  
Science And Engineering ◽  
Future Design ◽  
Experimental And Theoretical Studies ◽  
Theory And Experiment ◽  
Good Agreement

Wrinkles widely existing in sheets and membranes have attracted a lot of attention in the fields of material science and engineering applications. In this paper, we present a new method to generate ordered (striplike) and steady wrinkles of a constrained dielectric elastomer (DE) sheet coated with soft electrodes on both sides subjected to high voltage. When the voltage reaches a certain value, wrinkles will nucleate and grow. We conduct both experimental and theoretical studies to investigate the wavelength and amplitude of the wrinkle. The results show a good agreement between theory and experiment. Moreover, the amplitude and wavelength of ordered wrinkles can be tuned by varying the prestretch and geometry of the DE sheet, as well as the applying voltage. This study can help future design of DE transducers such as diffraction grating and optical sensor.

On an Approximate Method of Calculating Pressures on Non-lifting Head Shapes at Supersonic Speeds

1955 ◽  
Vol 6 (1) ◽  
pp. 31-45
Author(s):  
H. K. Zienkiewicz
Keyword(s):  
Method Of Characteristics ◽  
Order Theory ◽  
Stagnation Pressure ◽  
Slender Body Theory ◽  
Pressure Losses ◽  
The Method Of Characteristics ◽  
Curvature Approximation ◽  
Body Theory ◽  
Theory And Experiment ◽  
Good Agreement

SummarySlender-body theory is used to derive the ogive of curvature approximation for very slender, pointed, convex head shapes at supersonic speeds. Results of application of this approximation, together with the λ-method for circular arc ogives, to a variety of non-slender head shapes show very good agreement with the method of characteristics, van Dyke's second-order theory and experiment. Good agreement with the method of characteristics and with experiment is obtained even in cases when the stagnation pressure losses across the nose shock wave are not negligible.

Sound Propagation in Dilute Polyatomic Gases

1972 ◽  
Vol 27 (4) ◽  
pp. 583-592
Author(s):  
H. Moraal ◽  
F. Mccourt
Keyword(s):  
Pressure Range ◽  
Sound Propagation ◽  
Plane Waves ◽  
Point Of View ◽  
Perturbation Function ◽  
Sound Waves ◽  
Polyatomic Gas ◽  
Measured Pressure ◽  
Theory And Experiment ◽  
Good Agreement

Abstract Sound propagation in dilute pure gases, both monatomic and polyatomic, has been considered from the point of view of the Waldmann-Snider equation. It is shown that the commonly employed assumption that sound propagation in gases is equivalent to the propagation of plane waves is valid only in the region where collisions restore equilibrium faster than it is perturbed by the sound waves. A systematic truncation procedure for an expansion of the perturbation function in irreducible Cartesian tensors is introduced and then illustrated in solutions for three specific kinds of molecules, helium, nitrogen and rough spheres. The agreement between theory and experiment is rather good for sound absorption in the region where the ratio of the collision and sound frequencies is greater than 1.5. The agreement in the case of dispersion is good over the whole measured pressure range. One useful result obtained is to show the polyatomic gas calculations in second approximation have as good agreement with experiment as the calculations for noble gases in third approximation. This can be related to the possession by the polyatomic gas of a bulk viscosity which dominates in sound propagation.

scholarly journals Vibration of Skew Sandwich Plates With Laminated Facings

1997 ◽  
Author(s):  
C. M. Wang ◽  
K. K. Ang ◽  
C. Wang
Keyword(s):  
Ritz Method ◽  
Composite Plates ◽  
Sandwich Plates ◽  
Rectangular Plates ◽  
Vibration Frequencies ◽  
Edge Conditions ◽  
System Vibration ◽  
Special Case ◽  
Length Limitation ◽  
Good Agreement

A Rayleigh-Ritz analysis is presented for the free vibration of skew sandwich plates composed of an orthotropic core and laminated facings. By proposing a set of Ritz functions consisting of the product of mathematically complete polynomial functions and the the boundary equations raised to appropriate powers, the Rayleigh-Ritz method can be automated to handle such composite plates with any combination of edge conditions. For convenience and better accurarcy, the Ritz formulation was derived in the skew coordinate system. Vibration frequencies of rectangular plates (a special case of skew plates) obtained via this method have been found to be in good agreement with previous researchers results. Owing to length limitation, only sample vibration frequencies for skew sandwich plates are presented.

Condensation of a Downward Flowing Vapor on a Horizontal Cylinder Embedded in a Porous Medium

1991 ◽  
Vol 113 (4) ◽  
pp. 300-304 ◽  
Author(s):  
J. Orozco
Keyword(s):  
Porous Medium ◽  
Saturated Porous Medium ◽  
Horizontal Cylinder ◽  
Brinkman Model ◽  
Kutta Method ◽  
Runge Kutta Method ◽  
Condensate Layer ◽  
Theory And Experiment ◽  
Good Agreement ◽  
Liquid And Vapor Phases

This article presents the results of an investigation on condensation of a downward flowing vapor on a horizontal cylinder embedded in a vapor-saturated porous medium. The Brinkman model is used to describe theoretically the flow field in both the liquid and vapor phases. The resulting governing equation was integrated numerically with the help of the fourth-order Runge-Kutta method. The dependence of the condensate layer thickness and Nusselt number on the vapor velocity and on the permeability of the porous material is reported. Experiments were conducted to verify the theoretical findings, and good agreement was found between theory and experiment.

Particle–Nucleus Scattering at Intermediate Energies

1972 ◽  
Vol 50 (14) ◽  
pp. 1609-1613 ◽  
Author(s):  
Melvyn E. Best
Keyword(s):  
Cross Sections ◽  
Incident Neutron ◽  
Total Neutron ◽  
Intermediate Energies ◽  
Incident Pion ◽  
Glauber Theory ◽  
Nucleus Scattering ◽  
Theory And Experiment ◽  
Good Agreement

For incident neutron energies between 20 MeV and 10 GeV the total neutron–nucleus [Formula: see text] cross sections were calculated using Glauber theory. Remarkably good agreement between experiment and theory was found at energies above 250 MeV. Using the same formalism with identical nuclear parameters, the π−–C cross sections were calculated for incident pion energies near the (3, 3) resonance. In this case, however, good agreement between theory and experiment was found for pion energies above 150 MeV.

scholarly journals Damage Tensors and Tensors of Continuity in Stress Analysis

1983 ◽  
Vol 38 (12) ◽  
pp. 1383-1390 ◽  
Author(s):  
J. Betten
Keyword(s):  
Linear Operator ◽  
Coordinate System ◽  
Stress Tensor ◽  
Constitutive Equations ◽  
Symmetric Tensor ◽  
Diagonal Form ◽  
Symmetric Part ◽  
Third Order ◽  
Symmetric Property ◽  
Damage Tensor

Abstract Starting from a third order skew-symmetric tensor of continuity to represent area vectors (bivectors) of Cauchy's tetrahedron in a damaged state, a second order damage tensor is found which has the diagonal form with respect to the considered coordinate system. The second part of the paper is concerned with the stresses in a damaged continuum. Introducing a linear operator of rank four a net-stress tensor is formulated. This tensor can be decomposed into a symmetric part and into an antisymmetric one, where only the symmetric part is equal to the net-stress tensor introduced by Rabotnov [7].In view of the formulation of constitutive equations the non-symmetric property of the actual net-stress tensor is a disadvantage. Therefore, a pseudo-net-stress tensor is introduced, which is symmetric.

scholarly journals Asymmetry of the atomic-level stress tensor in homogeneous and inhomogeneous materials

2018 ◽  
Vol 474 (2217) ◽  
pp. 20180155 ◽  
Author(s):  
Ji Rigelesaiyin ◽  
Adrian Diaz ◽  
Weixuan Li ◽  
Liming Xiong ◽  
Youping Chen
Keyword(s):  
Stress Tensor ◽  
Unit Area ◽  
Symmetric Tensor ◽  
Shear Loading ◽  
Homogeneous Material ◽  
Inhomogeneous Materials ◽  
Virial Stress ◽  
Definition Of ◽  
Dynamics Simulations ◽  
Symmetric Property

The stress tensor is described as a symmetric tensor in all classical continuum mechanics theories and in most existing statistical mechanics formulations. In this work, we examine the theoretical origins of the symmetry of the stress tensor and identify the assumptions and misinterpretations that lead to its symmetric property. We then make a direct measurement of the stress tensor in molecular dynamics simulations of four different material systems using the physical definition of stress as force per unit area acting on surface elements. Simulation results demonstrate that the stress tensor is asymmetric near dislocation cores, phase boundaries, holes and even in homogeneous material under a shear loading. In addition, the atomic virial stress and Hardy stress formulae are shown to significantly underestimate the stress tensor in regions of stress concentration.

Sign in / Sign up

Export Citation Format

Share Document