The Basic Features of Viscoplasticity

  • Raja R. HuilgolEmail author


Consider an incompressible Bingham fluid at rest between two parallel walls. Assume that the domain \(\varOmega \) of the fluid can be described through a region symmetrical about the \(x\)-axis


Pressure Drop Variational Inequality Wall Shear Stress Yield Surface Obstacle Problem 
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  1. 1.
    Nouar C, Frigaard IA (2001) Nonlinear stability of Poiseuille flow of a Bingham fluid: theoretical results and comparison with phenomenological criteria. J Non-Newt Fluid Mech 100:127–149Google Scholar
  2. 2.
    Stakgold I (1968) Boundary value problems of mathematical physics, vol II. Macmillan, New YorkGoogle Scholar
  3. 3.
    Duvaut G (1973) Résolution d’un problème de Stéfan (Fusion d’un bloc de glace à zéro degré). C R Acad Sci Paris 276:1461–1463zbMATHMathSciNetGoogle Scholar
  4. 4.
    Baiocchi C (1978) Free boundary problems and variational inequalities. Technical Summary Report 1883, Mathematics Research Center, University of Wisconsin-MadisonGoogle Scholar
  5. 5.
    Kinderlehrer D (1978) Variational principles and free boundary problems. Bull Am Math Soc 84:7–26CrossRefzbMATHMathSciNetGoogle Scholar
  6. 6.
    Baiocchi C, Capelo A (1984) Variational and quasivariational inequalities: applications to free-boundary problems. Wiley, New YorkzbMATHGoogle Scholar
  7. 7.
    Duvaut G, Lions JL (1972) Les inéquations on mécanique et en physique. Dunod, ParisGoogle Scholar
  8. 8.
    Duvaut G, Lions JL (1976) Inequalities in mechanics and physics. Springer, New YorkCrossRefzbMATHGoogle Scholar
  9. 9.
    Glowinski R (1974) Sur l’ecoulement d’un fluide de Bingham dans une conduite cylindrique. J de Méc. 13:601–621MathSciNetGoogle Scholar
  10. 10.
    Fortin A, Côté D, Tanguy PA (1991) On the imposition of friction boundary conditions for the numerical simulation of Bingham fluid flows. Comput Methods Appl Mech Eng 88:97–109CrossRefzbMATHGoogle Scholar
  11. 11.
    Ramamurthy AV (1986) Wall slip in viscous fluids and influence of materials of construction. J Rheol 30:337–357CrossRefGoogle Scholar
  12. 12.
    Damianou Y, Philippou M, Kaoullas G, Georgiou GC (2014) Cessation of viscoplastic Poiseuille flow with wall slip. J Non-Newt Fluid Mech 203:24–37CrossRefGoogle Scholar
  13. 13.
    Doraiswamy D (2002) The origins of Rheology: a short historical excursion. Rheol Bull 71(1):7–9, 11, 13–17Google Scholar
  14. 14.
    Bingham EC (1922) Fluidity and plasticity. McGraw-Hill, New YorkGoogle Scholar
  15. 15.
    Barnes HA (2007) The ‘The yield stress myth?’ paper - 21 years on. Appl Rheol 17:43110-1–43110-5Google Scholar
  16. 16.
    Nguyen QD, Boger DV (1992) Measuring the flow properties of yield stress fluids. Ann Rev Fluid Mech 24:47–88CrossRefGoogle Scholar
  17. 17.
    Barnes HA, Walters K (1985) The yield stress myth? Rheol Acta 24:323–326CrossRefGoogle Scholar
  18. 18.
    Rivlin RS (1960) Some topics in finite elasticity. In: Goodier JN, Hoff NJ (eds) Structural mechanics: proceedings of the first symposium on naval structural mechanics. Pergamon, Oxford, pp 169–198Google Scholar
  19. 19.
    Rajagopal KR (2011) Modeling a class of geological materials. Int J Adv Eng Sci Appl Math 3:2–13CrossRefMathSciNetGoogle Scholar
  20. 20.
    Astarita G (1990) Letter to the editor: the engineering reality of the yield stress. J Rheol 34:275–277CrossRefGoogle Scholar
  21. 21.
    Tabuteau H, Coussot P, de Bruyn JR (2007) Drag force on a sphere in steady motion through a yield-stress fluid. J Rheol 51:125–137CrossRefGoogle Scholar
  22. 22.
    Beris AN, Tsamopoulos JA, Armstrong RC, Brown RA (1985) Creeping motion of a sphere through a Bingham plastic. J Fluid Mech 158:219–244CrossRefzbMATHMathSciNetGoogle Scholar
  23. 23.
    Beaulne M, Mitsoulis E (1997) Creeping motion of a sphere in tubes filled with Herschel-Bulkley fluids. J Non-Newt Fluid Mech 72:55–71CrossRefGoogle Scholar
  24. 24.
    Papanastasiou TC (1987) Flow of materials with yield. J Rheol 31:385–404CrossRefzbMATHGoogle Scholar

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© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  1. 1.Flinders Mathematical Sciences Laboratory, School of Computer Science, Engineering and MathematicsFlinders University of South AustraliaAdelaideAustralia

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