Some new solutions for the axial shear of a circular cylindrical tube of compressible elastic material

2000 ◽  
Vol 35 (2) ◽  
pp. 361-369 ◽  
Author(s):  
X. Jiang ◽  
R.W. Ogden
Keyword(s):  
Elastic Material ◽  
Cylindrical Tube ◽  
Axial Shear ◽  
Circular Cylindrical Tube

The steady flow of closely fitting incompressible elastic spheres in a tube

1978 ◽  
Vol 87 (1) ◽  
pp. 1-16 ◽  
Author(s):  
Hüsnü Tözeren ◽  
Richard Skalak
Keyword(s):  
Shear Modulus ◽  
Steady Flow ◽  
Elastic Material ◽  
Displacement Field ◽  
Series Solution ◽  
Cylindrical Tube ◽  
Lubrication Theory ◽  
Flow Properties ◽  
Circular Cylindrical Tube ◽  
Neutrally Buoyant

The steady flow of a suspension of closely fitting, neutrally buoyant, incompressible and elastic spheres through a circular cylindrical tube is investigated under the assumption that lubrication theory is valid in the fluid region. A series solution giving the displacement field of an elastic incompressible sphere under axisymmetrically distributed surface tractions is developed. It is found that, for closely fitting particles, flow properties of the suspension are strongly dependent on the shear modulus of the elastic material and the velocity of the particle.

Rotation of a reinforced circular cylindrical tube

1968 ◽  
Vol 64 (2) ◽  
pp. 565-572 ◽  
Author(s):  
H. R. Chaudhry ◽  
A. N. Chawla
Keyword(s):  
Elastic Deformation ◽  
Elastic Material ◽  
Circular Tube ◽  
Cylindrical Tube ◽  
Elastic Materials ◽  
Large Elastic Deformation ◽  
Circular Cylindrical Tube

AbstractThe theory of large elastic deformation of reinforced elastic materials is applied to discuss the rotation of a circular tube of incompressible elastic material, reinforced with inextensible cords lying along helical paths.

scholarly journals The effect of residual stress on the stability of a circular cylindrical tube

2021 ◽  
Vol 127 (1) ◽  
Author(s):  
Luis Dorfmann ◽  
Ray W. Ogden
Keyword(s):  
Residual Stress ◽  
Residual Stresses ◽  
Elastic Material ◽  
Cylindrical Tube ◽  
External Pressure ◽  
Constitutive Law ◽  
Ellipticity Condition ◽  
The Stability ◽  
Strong Ellipticity Condition ◽  
Circular Cylindrical Tube

AbstractResidual stresses in an unloaded configuration of an elastic material have a significant influence on the response of the material from that configuration, but the effect of residual stress on the stability of the material, whether loaded or unloaded, has only been addressed to a limited extent. In this paper we consider the level of residual stress that can be supported in a thick-walled circular cylindrical tube of non-linearly elastic material without loss of stability when subjected to fixed axial stretch and either internal or external pressure. In particular, we consider the tube to have radial and circumferential residual stresses, with a simple form of elastic constitutive law that accommodates the residual stress, and incremental deformations restricted to the cross section of the tube. Results are described for a tube subject to a level of (internal or external) pressure characterized by the internal azimuthal stretch. Subject to restrictions imposed by the strong ellipticity condition, the emergence of bifurcated solutions is detailed for their dependence on the level of residual stress and mode number.

Phenomenological and Structural Aspects of the Mechanical Response of Arteries

2000 ◽  
Author(s):  
Ray W. Ogden ◽  
Christian A. J. Schulze-Bauer
Keyword(s):  
Residual Stresses ◽  
Mechanical Response ◽  
Physiological State ◽  
Circumferential Stress ◽  
Morphological Structure ◽  
Cylindrical Tube ◽  
Single Layer ◽  
Theory Of Elasticity ◽  
Starting Point ◽  
Circular Cylindrical Tube

Abstract In this paper we present some new data from extension-inflation tests on a human iliac artery and then, on the basis of the nonlinear theory of elasticity, we examine a possible model to represent this data. The model considers the artery initially as a thick-walled circular cylindrical tube which may consist of two or more concentric layers. In order to take some account of the architecture (morphological structure), each layer of the material is regarded as consisting of two families of mechanically equivalent helical fibers symmetrically disposed with respect to the cylinder axis. The resulting material properties are then orthotropic in each layer. General formulas for the pressure and the axial load in the symmetric inflation of an extended tube are obtained. The starting point is the unloaded circular cylindrical configuration, but (in general unknown) residual stresses are included in the formulation. The model is illustrated by specializing firstly to the case of a single layer so that the consequences of the hypothesis of uniform circumferential stress in the physiological state can be examined theoretically. This enables the required residual stresses to be calculated explicitly. Secondly, the equations are specialized for the membrane approximation in order to show how certain important characteristics of the experimental data can be replicated using a relatively simple anisotropic membrane model.

scholarly journals Effects of Rheological Parameters of a Viscoplastic Fluid on Peristaltic Pumping in a Cylindrical Tube

2019 ◽  
Vol 286 ◽  
pp. 09003
Author(s):  
H. Rachid ◽  
M. Ouazzani Touhami
Keyword(s):  
Fluid Model ◽  
Pressure Rise ◽  
Cylindrical Tube ◽  
Mechanical Efficiency ◽  
Viscoplastic Fluid ◽  
Rheological Parameters ◽  
Rheological Characterization ◽  
Peristaltic Pumping ◽  
Fluid Foods ◽  
Circular Cylindrical Tube

In this paper, we study theoretically the peristaltic transport of a generalized four-parameter plastic fluid in a circular cylindrical tube. The present fluid model is presented for the rheological characterization of inelastic fluid foods. Long wavelength and low Reynolds number approximations are taken into account to get solution. The effects of embedded parameters on pressure rise, frictional force and especially on the mechanical efficiency have been numerically displayed and physically discussed.

UNSTEADY MODEL OF TRANSPORTATION OF JEFFREY-FLUID BY PERISTALSIS

2010 ◽  
Vol 03 (04) ◽  
pp. 473-491 ◽  
Author(s):  
S. K. PANDEY ◽  
DHARMENDRA TRIPATHI
Keyword(s):  
Relaxation Time ◽  
Flow Rate ◽  
Volume Flow Rate ◽  
Cylindrical Tube ◽  
Maximum Flow ◽  
Mechanical Efficiency ◽  
Volume Flow ◽  
Jeffrey Fluid ◽  
Retardation Time ◽  
Circular Cylindrical Tube

The investigation is to explore the transportation of a viscoelastic fluid by peristalsis in a channel as well as in a circular cylindrical tube by considering Jeffrey-model. In order to apply the model to the swallowing of food-bolus through the oesophagus, the wave equation assumed to propagate along the walls is such that the walls contract in the transverse/radial direction and relax but do not expand further. Solutions have been presented in the closed form by using small Reynolds number and long wavelength approximations. The expressions of pressure gradient, volume flow rate and average volume flow rate have been derived. It is revealed on the basis of computational investigation that for a fixed flow rate, pressure decreases when the ratio of relaxation time to retardation time is increased. In both the channel and tubular flows, the pressure decreases on increasing the ratio of relaxation time to retardation time if the averaged flow rate is less than the maximum flow rate. It is also revealed that the maximum tubular flow rate is higher than that of the channel-flow. It is further found through the theoretical analysis that mechanical efficiency, reflux and local wall shear stress remain unaffected by viscoelastic property of the fluid modelled as Jeffrey-fluid.

PERISTALTIC TRANSPORT OF A THIRD-ORDER FLUID IN A CIRCULAR CYLINDRICAL TUBE

2002 ◽  
Vol 12 (12) ◽  
pp. 1691-1706 ◽  
Author(s):  
T. HAYAT ◽  
Y. WANG ◽  
A. M. SIDDIQUI ◽  
K. HUTTER ◽  
S. ASGHAR
Keyword(s):  
Numerical Solutions ◽  
Cylindrical Tube ◽  
Deborah Number ◽  
Peristaltic Transport ◽  
Average Radius ◽  
Third Order ◽  
Living Body ◽  
Analytic Perturbation ◽  
Circular Cylindrical Tube ◽  
Problem Comparison

The effect of a third-order fluid on the peristaltic transport is analysed in a circular cylindrical tube, such as some organs in the living body. The third-order flow of an incompressible fluid in a circular cylindrical tube, on which an axisymmetric travelling sinusoidal wave is imposed, is considered. The wavelength of the peristaltic waves is assumed to be large compared to the tube average radius, whereas the amplitude of the wave need not be small compared to the average radius. Both analytic (perturbation) and numerical solutions are given. For the perturbation solution, a systematic approach based on an asymptotic expansion of the solution in terms of a small Deborah number is used and solutions up to the first order are presented in closed forms. The numerical solution, valid for any Deborah number, represents a new approach to peristaltic flows, and its features illuminate the physical behaviour much more than the analytical research on this problem. Comparison is made between the analytic (perturbation) and numerical results. Furthermore, the obtained results could also have applications to a range of peristaltic flows for a variety of non-Newtonian fluids such as aqueous solutions of high-molecular weight polyethylene oxide and polyacrylamide.

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