Hostname: page-component-cd9895bd7-dk4vv Total loading time: 0 Render date: 2024-12-27T12:41:11.878Z Has data issue: false hasContentIssue false
  • English
  • Français

Time-Dependent Poiseuille Flows of an Elasto-Viscoplastic Fluid with Hypoplastic Effects

Published online by Cambridge University Press:  05 May 2011

C. Fang
C. Fang*
Affiliation:
Department of Civil Engineering, National Cheng Kung University, Tainan City, Taiwan 70101, R.O.C.
*
*Assistant Professor
Get access

Abstract

An evolution equation for the Cauchy stress tensor is proposed, taking into account the elastic, viscous and plastic characteristics of complex fluids. Hypoplasticity, in particular, is incorporated to model the plastic features. The model is applied to investigate time-dependent Poiseuille flows between two parallel plates to simulate non-Newtonian behavior of complex rheological fluids. Results show that while different degrees of elastic and viscous features can be indexed by varying the values of the model parameters, hypoplasticity is capable of simulating the plastic characteristics. The fluid tends to be divided into different parallel layers as hypoplastic effects enhance gradually. Applications of the model may be found in geomorphic fluid motions involved granular materials.

Keywords

Stress tensorHypoplasticityGranular matterTime-dependent Poiseuille flow.
Type
Articles
Information
Journal of Mechanics , Volume 25 , Issue 4 , December 2009 , pp. 421 - 431
Copyright
Copyright © The Society of Theoretical and Applied Mechanics, R.O.C. 2009

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

1.Barnes, H. A. and Hutton, J. F., Walters, FRS K., An Introduction to Rheology, Elsevier, Amsterdam (1989).Google Scholar
2.Tabor, D., Gases, Liquids and Solids and Other States of Matter, 3rd Ed., Cambridge University Press, UK (1993).Google Scholar
3.Hsiao, K. L., “Heat and Mass Transfer for Electrical Conducting Mixed Convection with Radiation Effect for Viscoelastic Fluid Past a Stretching Sheet,” Journal of Mechanics, 24, pp. N21–N27 (2008).CrossRefGoogle Scholar
4.Tanner, R. I., Engineering Rheology. Oxford University Press, Oxford New York, Toronto (1992).Google Scholar
5.Truesdell, C. and Noll, W., The Non-linear Theories of Mechanics, Handbuch der Physik, III/3, Flügge, S., Ed., Springer Verlag, Berlin Heidelberg, New York (1965).Google Scholar
6.Pudasaini, S. and Hutter, K., Avalanche Dynamics, Springer Verlag Berlin Heidelberg (2007).Google Scholar
7.Jakob, M. and Hunger, O., Eds., Debris-Flow Hazards and Related Phenomena, Springer Verlag, Berlin Heidelberg (2005).Google Scholar
8.Fang, C., Wang, Y. and Hutter, K., “A Unified Evolution Equation for the Cauchy Stress Tensor of an Isotropic Elasto-Visco-Plastic Material, I. On Thermodynamically Consistent Evolution,” Continuum Mech. Thermodyn., 19, pp. 423–440 (2008).CrossRefGoogle Scholar
9.Fang, C. and Lee, C. H., “A Unified Evolution Equation for the Cauchy Stress Tensor of an Isotropic Elasto-Visco-Plastic Material, II. Normal Stress Difference in a Viscometric Flow, and an Unsteady Flow with a Moving Boundary,” Continuum Mech. Thermodyn., 19, pp. 441–455 (2008).CrossRefGoogle Scholar
10.Fang, C. and Lee, C. H., “Unsteady Parallel Flows of an Elasto-Visco-Plastic Fluid with Oscillating Boundary,” Appl. Rheol., 18, pp. 45001–45011 (2008).Google Scholar
11.Rao, K. K. and Nott, P. R., Introduction to Granular Flows, Cambridge University Press, London, New York (2008).CrossRefGoogle Scholar
12.Takahashi, T., Debris Flows: Mechanics, Predictions and Countermeasures. Taylor and Francis, New York (2007).CrossRefGoogle Scholar
13.Das, B. M., Fundamentals of Geotechnical Engineering. 3rd Ed., CL-Engineering, New York (2007).Google Scholar
14.Tropea, C., Yarin, A. L. and Foss, J. F., Eds., Springer Handbook of Experimental Fluid Mechanics. Springer Verlag, Berlin Heidelberg, New York (2008).Google Scholar
15.Kolymbas, D., “An Outline of Hypoplasticity,” Arch. Appl.Mech., 61, pp. 143–151 (1991).CrossRefGoogle Scholar
16.Kolymbas, D., Introduction to Hypoplasticity, Balkema, Rotterdam (2000).CrossRefGoogle Scholar
17.Wu, W., “On High-Order Hypoplastic Models for Granular Materials,” J. Eng. Math., 56, pp. 23–34 (2006).CrossRefGoogle Scholar
18.Wu, W. and Kolymbas, D., Hypoplasticity Then and Now, Constitutive Modelling of Granular Materials Kolymbas, D. Ed., Springer Verlag, Berlin Heidelberg New York, pp. 57–105 (2000).CrossRefGoogle Scholar
19.Anderson, D. A., Tannehill, J. C. and Pletcher, R. H., Computational Fluid Mechanics and Heat Transfer McGraw-Hill, New York (1984).Google Scholar
20.Panton, R. L., Incompressible Flow, 2nd Ed., John Wiley and Sons Inc., New York (1996).Google Scholar
21.Liepmann, H. W. and Roshko, A., Elements of Gas Dynamics, John Wiley and Sons, Inc., New York (1957).Google Scholar