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Part of the book series: NATO ASI Series ((NSSE,volume 302))

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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.

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References

  1. Lodge, A.S. (1969) Elastic liquids, Academic Press. London

    Google Scholar 

  2. 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

    Google Scholar 

  3. Boger, D.V. and Walters, K. (1993) Rheological Phenomena in Focus, Elsevier, Amsterdam

    MATH  Google Scholar 

  4. Tanner, R.I. (1985) Engineering Rheology, Clarendon Press, Oxford

    MATH  Google Scholar 

  5. Barnes, H.A., Hutton, J.F., and Walters, K. (1989) An Introduction to Rheology, Elsevier. Amsterdam

    MATH  Google Scholar 

  6. Crochet, M.J., Davies, A.R. and Walters, K. (1984) Numerical Simulation of NonNewtonian Flows, Elsevier, Amsterdam

    Google Scholar 

  7. Crochet, M.J. (1989) Numerical Simulation of Viscoelastic Flow : a Review, Rubber Chemistry and Technology, Vol. no. 62, pp. 426–455

    Article  Google Scholar 

  8. Bird, R.B. Armstrong, R.C., and Hassager, O. (1987) Dynamics of Polymeric Liquids, Vol 1: Fluid Mechanics, 2nd ed., Wiley, New-York

    Google Scholar 

  9. 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

    Article  MATH  Google Scholar 

  10. Leonov, A. I. (1976) Nonequilibrium Thermodynamics and Rheology of Viscoelastic Polymer Media, Rheol. Acta, Vol. no. 15, pp. 85–98

    Article  MATH  Google Scholar 

  11. 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

    Article  MATH  Google Scholar 

  12. 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

    Article  MATH  Google Scholar 

  13. Larson, R.G. (1988) Constitutive Equations for Polymer Melts and Solutions, Butterworths. Boston

    Google Scholar 

  14. 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

    Google Scholar 

  15. 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

    Article  MATH  Google Scholar 

  16. 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

    Article  MATH  Google Scholar 

  17. Zienkiewicz, O.C. and Morgan, K. (1983) Finite Elements and Approximations, Wiley, New-York

    Google Scholar 

  18. Zienkiewicz, O.C. and Taylor, R.L. (1991) The Finite Element Method (4th edition), McGraw-Hill, London

    Google Scholar 

  19. Kawahara, M. and Takeuchi, N. (1977) Mixed Finite Element Method for Analysis of Viscoelastic Fluid Flow, Comp. Fluids, Vol. no. 5, pp. 33–45

    Article  ADS  MATH  Google Scholar 

  20. 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

    Article  Google Scholar 

  21. Ladyzhenskaya, O.A. (1969) The .Mfathematical Theory of Viscous Incompressible Flow. Gordon and Breach. New-York

    Google Scholar 

  22. 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

    MathSciNet  MATH  Google Scholar 

  23. 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

    Article  MATH  Google Scholar 

  24. 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

    Article  MATH  Google Scholar 

  25. 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

    Article  MathSciNet  ADS  MATH  Google Scholar 

  26. Johnson, C. (1987) Numerical Solution of Partial Differential Equations by the Finite Element Method, Cambridge Univ. Press, Cambridge

    MATH  Google Scholar 

  27. 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

    MATH  Google Scholar 

  28. 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

    Article  MATH  Google Scholar 

  29. 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

    Article  MathSciNet  MATH  Google Scholar 

  30. 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

    Article  MATH  Google Scholar 

  31. 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

    MATH  Google Scholar 

  32. 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

    Article  MATH  Google Scholar 

  33. 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

    Article  MATH  Google Scholar 

  34. 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

    Article  ADS  Google Scholar 

  35. Baaijens, F.P.T. (1992) Numerical Analysis of Unsteady Viscoelastic Flow, Comp. Meth. Appl. Mech. Engng., Vol. no. 94, pp. 285–299

    Article  ADS  MATH  Google Scholar 

  36. 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

    Article  MATH  Google Scholar 

  37. 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

    Article  MATH  Google Scholar 

  38. 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

    Article  MATH  Google Scholar 

  39. 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

    Article  ADS  Google Scholar 

  40. 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

    Article  ADS  Google Scholar 

  41. Warichet, V. and Legat, V. (1994) An Adaptive hp Finite Element Method for Calculating Viscoelastic Fluids Flow. (in preparation)

    Google Scholar 

  42. 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

    Google Scholar 

  43. Purnode, B. and Crochet, M.J. (1995) ,(in preparation)

    Google Scholar 

  44. 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

    Article  MathSciNet  ADS  MATH  Google Scholar 

  45. 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

    Google Scholar 

  46. 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

    Article  ADS  Google Scholar 

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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

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  • 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

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