Abstract
It is well known that the behaviour of all materials cannot be predicted by the classical Hookean elastic solids or Newtonian viscous liquids. Viscoelasticcoelastic effects, i.e. phenomena that cannot be explained on the basis of nonlinear purely-viscous or purely-elastic behaviour, can be important in polymer processing applications [1] [2] [3] [4]. Rheological non-linearities and geometrical singularities render analytical investigations difficult and lead to the numerical simulation of viscoelastic effects in complex geometries where simplifying assumptions cannot be made.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Lodge, A.S. (1969) Elastic liquids, Academic Press. London
Keunings, R. (1989) Simulation of Viscoelastic Fluid Flow Fundamentals of Computer Modeling for Polymer Processing, Ed. Tucker III, C.L., Carl Hanser Verlag, Munich, pp. 403–470
Boger, D.V. and Walters, K. (1993) Rheological Phenomena in Focus, Elsevier, Amsterdam
Tanner, R.I. (1985) Engineering Rheology, Clarendon Press, Oxford
Barnes, H.A., Hutton, J.F., and Walters, K. (1989) An Introduction to Rheology, Elsevier. Amsterdam
Crochet, M.J., Davies, A.R. and Walters, K. (1984) Numerical Simulation of NonNewtonian Flows, Elsevier, Amsterdam
Crochet, M.J. (1989) Numerical Simulation of Viscoelastic Flow : a Review, Rubber Chemistry and Technology, Vol. no. 62, pp. 426–455
Bird, R.B. Armstrong, R.C., and Hassager, O. (1987) Dynamics of Polymeric Liquids, Vol 1: Fluid Mechanics, 2nd ed., Wiley, New-York
Giesekus, H. (1982) A Simple Constitutive Equation for Polymer Fluids Based on the concept. of Deformation Dependent Tensorial Mobility, J. Non-Newtonian Fluid Mech., Vol. no. 11, pp. 69–109
Leonov, A. I. (1976) Nonequilibrium Thermodynamics and Rheology of Viscoelastic Polymer Media, Rheol. Acta, Vol. no. 15, pp. 85–98
Phan Thien, N. and Tanner, R.I. (1977) A New Constitutive Equation derived from Network Theory, J. Non-Newtonian Fluid Mech., Vol. no. 2, pp. 353–365
Apelian, I.R., Armstrong, R.C., and Brown, R.A. (1988) Impact of the Constitutive Equation and Singularity on the Calculation of stick-slip Flow : the Modified upper convected Maxwell Model, J. Non-Newtonian Fluid Mech., Vol. no. 27, pp. 299–321
Larson, R.G. (1988) Constitutive Equations for Polymer Melts and Solutions, Butterworths. Boston
Bird, R.B., Curtiss, C.F., Amstrong, R.C., and Hassager, O. (1987) Dynamics of Polymeric Liquids, Vol 2: Kinetic Theory, 2nd ed., Wiley, New-York
Chilcott, M. D. and Rallison, J. N.(1988) Creeping Flow of Dilute Polymer Solutions past Cylinders and Spheres, J. Non-Newtonian Fluid Mech., Vol. no. 29, pp. 381–432
Bernstein, B., Kearsley, E.A and Zapas, L. (1963) A Study of Stress Relaxation with Finite Strain, Trans. Soc. Rheol., Vol. no. 7, pp. 391–410
Zienkiewicz, O.C. and Morgan, K. (1983) Finite Elements and Approximations, Wiley, New-York
Zienkiewicz, O.C. and Taylor, R.L. (1991) The Finite Element Method (4th edition), McGraw-Hill, London
Kawahara, M. and Takeuchi, N. (1977) Mixed Finite Element Method for Analysis of Viscoelastic Fluid Flow, Comp. Fluids, Vol. no. 5, pp. 33–45
Crochet, M.J. and Keunings, R. (1980) Die Swell of a Maxwell Fluid : Numerical Prediction, J. Non-Newtonian Fluid ,ech., Vol. no. 7, pp. 199–212
Ladyzhenskaya, O.A. (1969) The .Mfathematical Theory of Viscous Incompressible Flow. Gordon and Breach. New-York
Brezzi F. (1974) On the Existence. Uniqueness and Approximation of Saddle-point Problem Arising from Lagrange Multipliers, Revue Française d’Automatique Inform. Rech. Opér., Série Rouge Anal. Nurnér. 8, Vol. no. R-2, pp. 129–151
Marchal, J.M. and Crochet, M.J. (1986) Hermitian Finite Element for Calculating Viscoelastic Flow, J. Non-Newtonian Fluid Mech., Vol. no. 20, pp. 187–207
Marchal, J.M. and Crochet, M.J. (1987) A New Mixed Finite Element for Calculating Viscoelastic Flow, J. Non-Newtonian Fluid Mech., Vol. no. 26, pp. 77–114
Brooks, A.N., and Hughes, T.J.R. (1982) Streamline Upwind/Petrov-Galerkin Formulation for Convection Dominated Flows with Particular Emphasis on the Incompressible Navier-Stokes Equations, Comp. Meth. Appl. Mech. Engng., Vol. no. 32, pp. 199–259
Johnson, C. (1987) Numerical Solution of Partial Differential Equations by the Finite Element Method, Cambridge Univ. Press, Cambridge
Crochet, M.J. and Legat, V. (1992) The consistent Streamline Petrov-Galerkin Method for Viscoelastic Flow Revisited, J. Non-Newtonian Fluid Mech., Vol. no. 42, pp. 283–299
Debbaut, B. and Hocq, B. (1992) On the Numerical Simulation of Axisymmetric Swirling Flows of Differential Viscoelastic Liquids : the Rod Climbing Effect and the Quelleffekt, J. Non-Newtonian Fluid .MMech., Vol. no. 43, pp. 103–126
Renardy, M. (1985) Existence of Slow Steady Flows of Viscoelastic Fluids with Differential Constitutive Equations. Z. Angew. Math. u. Mech., Vol. no. 65, pp. 449–451
King, R.C., Apelian, M.N., Armstrong, R.C. and Brown, R.A. (1988) Numerically Stable Finite Element Techniques for Viscoelastic Calculations in Smooth and Singular Geometries, J. Non-Newtonian Fluid Mech., Vol. no. 29, pp. 147–216
Dupret, F. and Marchal, J.M. (1986) Sur le signe des valeurs propres du tenseur des extra-contraintes dans un écoulement de fluide de Maxwell, J. Méc. Théor. Appl., Vol. no. 5, pp. 403–427
Dupret, F. and Marchal, J.M. (1986) Loss of Evolution in the Flow of Viscoelastic Fluids, J. Non-Newtonian Fluid Mech. Vol. no. 20. pp. 143–171
Rajagopalan, D., Armstrong, R.C. and Brown, R.A. (1990) Finite Element Methods for Calculation of Steady Viscoelastic Flow Using Constitutive Equations with a Newtonian Viscosity, J. Non-Newtonian Fluid Mech., Vol. no. 36, pp. 159–192
Debae, F., Legat, V. and Crochet, M.J. (1994) Practical Evaluation of Four Mixed Finite Element Methods for Viscoelastic Flow, J. of Rheology, Vol. no. 38, pp. 421–442
Baaijens, F.P.T. (1992) Numerical Analysis of Unsteady Viscoelastic Flow, Comp. Meth. Appl. Mech. Engng., Vol. no. 94, pp. 285–299
Fortin, A. and Zine, A. (1992) An Improved GMRES Method for Solving Viscoelastic Fluid Flow Problem, J. Non-Newtonian Fluid Mech., Vol. no. 42, pp. 1–18
Fortin, A., Zine, A. and Agassant, J.M. (1992) Computing Viscoelastic Fluid Flow Problems at Low Cost, J. Non-Newtonian Fluid Mech., Vol. no. 45, pp. 209–229
Beris, A.N., Armstrong, R.C. and Brown, R.A. (1987) Spectral/Finite Element Calculations of the Flow of a Maxwell Fluid between Eccentric Rotating Cylinders, J. of Non-Newtonian Fluid Mech., Vol. no. 22, pp. 129–167
Souvaliotis, A. and Beris, A.N. (1992) Application of of Domain Decomposition Spectral Collocation Methods in Viscoelastic Flows Trough Model Porous Media, J. of Rheology, Vol. no. 36, pp. 1417–1453
Talwar, K.K. and Khomami, B. (1992) Application of Higher Order Finite Element Methods for Viscoelastic Flow in Porous Media, J. of Rheology, Vol. no. 36, pp. 1377–1416
Warichet, V. and Legat, V. (1994) An Adaptive hp Finite Element Method for Calculating Viscoelastic Fluids Flow. (in preparation)
Satrape, J.V. and Crochet, M.J. (1994) Numerical Simulation of the Motion of a Sphere in a Boger Fluid, J. Non-Newtonian Fluid Mech., in press
Purnode, B. and Crochet, M.J. (1995) ,(in preparation)
Joseph D.D., Renardy, M. and Saut, J.C. (1985) Hyperbolicity and Change of Type in the Flow of Viscoelastic Fluids, Arch. Rational Mech. Anal., Vol. no. 87, pp. 213–251
Renardy, M. (1986) Inflow Boundary Conditions for Steady Flows of Viscoelastic Fluids with Differential Constitutive Laws, Mathematics Research Center Technical Summary Report2916, Univ. of Wisconsin, Madison, USA
Legat, V. and Marchai, J.M. (1992) On the Stability and the Accuracy of Fully Coupled Finite Element Techniques Used to Simulate the Flow of Differential Viscoelastic Fluids : a One-Dimensional Model, J. of Rheology, Vol. no. 36, pp. 1325–1348
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1995 Springer Science+Business Media Dordrecht
About this chapter
Cite this chapter
Legat, V. (1995). Computer Modeling of Viscoelastic Flow. In: Covas, J.A., Agassant, J.F., Diogo, A.C., Vlachopoulos, J., Walters, K. (eds) Rheological Fundamentals of Polymer Processing. NATO ASI Series, vol 302. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-8571-2_10
Download citation
DOI: https://doi.org/10.1007/978-94-015-8571-2_10
Publisher Name: Springer, Dordrecht
Print ISBN: 978-90-481-4637-6
Online ISBN: 978-94-015-8571-2
eBook Packages: Springer Book Archive