Equal Low-Order Finite Element Simulation of the Planar Contraction Flow for Branched Polymer Melts

REFERENCES

• McLeish , T.C.B. ; Larson , R.G. Molecular constitutive equations for a class of branched polymers: The pom-pom polymer . J. Rheol. 1998 , 42 , 81 – 110 .
   Web of Science ®Google Scholar
• Blackwell , R.J. ; McLeish , T.C.B. ; Harlen , O.G. Molecular drag-strain coupling in branched polymer melts . J. Rheol. 2000 , 44 , 121 – 136 .
   Web of Science ®Google Scholar
• Öttinger , H. Thermodynamic admissibility of the pompon model for branched polymers . Rheol. Acta 2001 , 40 , 317 – 321 .
   Google Scholar
• Verbeeten , W.M.H. ; Peters , G.W.M. ; Baaijens , F.P.T. Differential constitutive equations for polymer melts: The extended Pom–Pom model . J. Rheol. 2001 , 45 ( 4 ), 823 – 843 .
   Google Scholar
• Verbeeten , W.M.H. ; Peters , G.W.M. ; Baaijens , F.P.T. Viscoelastic analysis of complex polymer melt flows using the extended Pom-Pom model . J. Non-Newtonian Fluid Mech. 2002 , 108 , 301 – 326 .
   Google Scholar
• Verbeeten , W.M.H. ; Peters , G.W.M. ; Baaijens , F.P.T. Numerical simulations of the planar contraction flow for a polyethylene melt using the XPP model . J. Non-Newtonian Fluid Mech. 2004 , 117 , 73 – 84 .
   Google Scholar
• Clemeur , N. ; Rutgers , R.P.G. ; Debbaut , B. On the evaluation of some differential formulations for the Pom-Pom constitutive model . Rheol. Acta 2003 , 42 ( 3 ), 217 – 231 .
   Web of Science ®Google Scholar
• Inkson , N.J. ; Phillips , T.N. Unphysical phenomena associated with the extended pom-pom model in steady flow . J. Non-Newtonian Fluid Mech. 2007 , 145 , 92 – 101 .
   Google Scholar
• Brooks , A.N. ; Hughes , T.J.R. Streamline upwind/Petrov-Galerkin formulations for convection dominated flows with particular emphasis on the imcompressible Navier-Stokes equations . Comp. Methods Appl. Mech. Eng. 1982 , 32 , 199 – 259 .
   Web of Science ®Google Scholar
• Marchal , J.M. ; Crochet , M.J. A new mixed finite element for calculating viscoelastic flow . J. Non-Newtonian Fluid Mech. 1987 , 26 , 77 – 114 .
   Web of Science ®Google Scholar
• Rajagopalan , D. ; Brown , R.A. ; Armstrong , R.C. Finite element methods for calculation of steady viscoelastic flow using constitutive equations with a Newtonian viscosity . J. Non-Newtonian Fluid Mech. 1990 , 36 , 159 – 199 .
   Web of Science ®Google Scholar
• Guénette , R. ; Fortin , M. A new mixed finite element method for computing viscoelastic flows . J. Non-Newtonian Fluid Mech. 1995 , 60 , 27 – 52 .
   Web of Science ®Google Scholar
• Baaijens , F.P.T. Mixed finite element methods for viscoelastic flow analysis: A review . J. Non-Newtonian Fluid Mech. 1998 , 79 , 361 – 386 .
   Google Scholar
• Comini , G. ; Guidice , S.D. Finite element solution of incompressible Navier-Stokes equations . Num. Heat Tran. Pt. A 1972 , 5 , 463 – 478 .
   Google Scholar
• Donea , J. ; Giuliani , S. ; Laval , H. ; Quartapelle , L. Finite element solution of the unsteady Navier-Stokes equations by a fractional step method. Comput. Meth. Appl. Mech. Eng. 1982, 30, 53–73.
   Web of Science ®Google Scholar
• Aguayo , J.P. ; Tamaddon-Jahromi , H.R. ; Webster , M.F. Extensional response of the pom-pom model through planar contraction flows for branched polymer melts . J. Non-Newtonian Fluid Mech. 2006 , 134 , 105 – 126 .
   Google Scholar
• Han , X.H. ; Li , X.K. An iterative stabilized CNBS–CG scheme for incompressible non-isothermal non-Newtonian fluid flow . Int. J. Heat Mass Tran. 2007 , 50 , 847 – 856 .
   Google Scholar
• Li , X.K. ; Han , X.H. An iterative stabilized fractional step algorithm for numerical solution of incompressible N-S equations . Int. J. Numer. Meth. Fluid 2005 , 49 , 395 – 416 .
   Google Scholar
• Li , X.K. ; Duan , Q.L. ; Han , X.H. ; Sheng , D.C. Adaptive coupled arbitrary Lagrangian-Eulerian finite element and meshfree method for injection molding process . Int. J. Numer. Meth. Engrg. 2007 , 73 ( 8 ), 1153 – 1180 .
   Google Scholar
• Hassan , H. ; Regnier , N. ; Pujos , C. ; Defaye , G. Effect of viscous dissipation on the temperature of the polymer during injection molding filling . Polym. Eng. Sci. 2008 , 48 , 1199 – 1206 .
   Google Scholar
• Li , H.M. ; Chen , S.C. ; Shen , C.Y. ; Chau , S.W. ; Lin , Y.W. Numerical simulations and verifications of cyclic and transient temperature variations in injection molding process . Polym. Plast. Tech. Eng. 2009 , 48 , 1 – 9 .
   Web of Science ®Google Scholar
• Oñate , E. A stabilized finite element method for incompressible viscous flows using a finite increment calculus formulation . Comput. Meth. Appl. Mech. Eng. 2000 , 182 , 355 – 370 .
   Web of Science ®Google Scholar
• Duan , Q.L. ; Li , X.K. An ALE based iterative CBS algorithm for non-isothermal non-Newtonian flow with adaptive coupled finite element and meshfree method . Comput. Meth. Appl. Mech. Eng. 2007 , 196 ( 49–52 ), 4911 – 4933 .
   Google Scholar
• Li , X.K. ; Duan , Q.L. Meshfree iterative stabilized Taylor-Galerkin and characteristic-based split (CBS) algorithms for incompressible N-S equations . Comput. Meth. Appl. Mech. Eng. 2006 , 195 , 6125 – 6145 .
   Google Scholar
• Han , X.H. ; Li , X.K. A mixed finite element scheme for viscoelastic flows with XPP model . Acta Mech. Sin. 2008 , 24 ( 6 ), 671 – 680 .
   Google Scholar
• Bishko , G.B. ; Harlen , O.G. ; McLeish , T.C.B. ; Nicholson , T.M. Numerical simulation of the transient flow of branched polymer melts through a planar contraction using the ‘pom-pom’ model . J. Non-Newtonian Fluid Mech. 1999 , 82 , 255 – 273 .
   Web of Science ®Google Scholar
• Alves , M.A. ; Oliveira , P.J. ; Pinho , F.T. Benchmark solutions for the flow of Oldroyd-B and PTT fluids in planar contractions . J. Non-Newtonian Fluid Mech. 2003 , 110 , 45 – 75 .
   Web of Science ®Google Scholar