Abstract
The numerical analysis of problems in forming can be accomplished by a variety of techniques; one has finite differences, finite elements, boundary elements, and other methods. Each method has some advantage over the others in certain classes of problems, and here we review the use of boundary-element methods in some slow Newtonian and non-Newtonian (or rheological) forming problems. The term non-Newtonian fluid means a material not described by the Navier-Stokes equations. The simplest non-Newtonian fluid class includes materials where the viscosity depends on the scalar invariants of the rate-of-deformation tensor D. In some cases metal deformation can be so modelled (Karabin and Smelser 1989). A much greater challenge is posed by fluids with memory (or viscoelasticity) and part of this chapter is devoted to this category of materials; molten plastics are perhaps the most important examples of viscoelastic fluids.
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References
Banerjee PK, Butterfield R (1981) Boundary element methods in engineering science. McGraw-Hill, London
Batchelor GK (1967) An introduction to fluid dynamics. Cambridge University Press, Cambridge
Bézine G, Bonneau D (1981) Integral equation method for the study of two dimensional stokes flows. Acta Mech 41:197–209
Bird RB, Armstrong RC, Hassager O. (1987) Dynamics of polymeric liquids, vol. I. Fluid Mechanics, 2nd edn. John Wiley, New York
Brebbia CA (1980) The boundary element method for engineers. Pentech Press, London
Bush MB (1987) Boundary element simulation of polymer extrusion processes. Engng Analysis 4:7–14
Bush MB, Phan-Thien N (1985) Three dimensional viscous flows with a free surface: flow out of a long square die. J Non-Newt Fluid Mech 18:211–218
Bush MB, Tanner RI (1983) Numerical solution of viscous flows using integral equation methods. Int J Num Meth Fluids 3:71–92
Bush MB, Milthorpe JF, Tanner RI (1984) Finite element and boundary element methods for extrusion computations. J Non-Newt Fluid Mech 16:37–51
Bush MB, Tanner RI, Phan-Thien N (1985) A boundary element investigation of extrudate swell. J Non-Newt Fluid Mech 18:143–162
Coleman CJ (1981) A contour integral formulation of plane creeping Newtonian flow. Q J Mech Appl Math 34:453–464
Coleman CJ (1984) On the use of boundary integral methods in the analysis of non-Newtonian fluid flow. J Non-Newt Fluid Mech 16:347–355
Crochet MJ, Keunings R (1982) J Non-Newt Fluid Mech 10:339–356
Cruse TA (1969) Numerical solution in three-dimensional elastostatics. Int J Solids Struct 5:1265–1274
Cruse TA, Snow DW, Wilson RB (1974) Numerical solutions in axisymmetric elasticity. Com put Struct 7:445–451
Danson DJ (1981) Boundary element methods, Brebbia CA (ed), Springer-Verlag, Berlin
Ferry JD (1980) Viscoelastic properties of polymers, 3rd edn. John Wiley, New York
Karabin ME, Smelser RE (1989) The boundary element in three-dimensional forging. In: Thompson EG, Wood RD, Zienkiewicz OC, Samuelsson A, (eds) Numiform 89. Balkema, Rotterdam, pp 555–562
Kelmanson MA (1983) An integral equation method for the solution of singular slow flow problems. J Comput Phys 51:307–324
Kermanidis T (1975) A numerical solution for axially symmetrical elasticity problems. Int J Solids Struct 11:493–500
Ladyzhenskaya OA (1963) The mathematical theory of viscous incompressible flow. Gordon and Breach, New York
Larson RG (1988) Constitutive equations for polymer melts and solutions. Butterworths, Boston
Laun HM, Munstedt H (1978) Elongational behaviour of a low density polyethylene melt. Rheol Acta 17:415–425
Leonov AI (1976) Nonequilibrium thermodynamics and rheology of viscoelastic polymer media. Rheol Acta 15:85–98
Luo X-L, Tanner RI (1986) A streamline element scheme for solving viscoelastic flow problems. Part II: integral constitutive models. J Non-Newt Fluid Mech 22:61–89
Luo X-L, Tanner RI (1988) Finite element simulation of long and short circular die extrusion experiments using integral models, Int J Num Meth Engng 25:9–22
Meissner J (1975) Basic parameters, melt rheology, processing and end use properties of three similar low density polyethylene samples. Pure Appl Chern 42:553–612
Michaeli W (1984) Extrusion die design. Hanser, Munich
Onishi K, Kuroki T, Tanaka M (1984) An application of boundary element method to incompressible laminar viscous flows. Engng Analysis 1: 122–127
Onishi K, Kuroki T, Tanaka M (1985) Topics in boundary element research, vol. 2. Brebbia CA (ed), Springer-Verlag, Berlin
Ph an-Thien N (1988) Influence of wall slip on extrudate swell: a boundary element investigation. J Non-Newt Fluid Mech 26:327–340
Phan-Thien N, Tanner RI (1977) A new constitutive equation derived from network theory. J Non-Newt Fluid Mech 2:353–365
Phuoc HB, Tanner RI (1980) Thermally induced extrudate swell. J Fluid Mech 98:253–271
Rizzo FJ (1967) An integral equation approach to boundary value problems in classical elastostatics, QJ Appl Math 25:83–95
Skerget P, Alujevic A (1985) The solution of the Navier-Stokes equations in terms of vorticity-velocity variables by the boundary element method. Z Angew Math Mech 65:T245–T248
Sugeng F, Phan-Thien N, Tanner RI (1987) A study of non-isothermal non-Newtonian extrudate swell by a mixed boundary element and finite element method. J Rheol 31:37–58
Sugeng F, Phan-Thien N, Tanner RI (1988) A boundary element investigation of the pressure-hole effect. J Rheol 32:215–234
Tanner RI (1988) Engineering rheology, revised ed. Oxford University Press
Tasaka N, Onishi K (1985) Boundary integral equation formulations for steady Navier-Stokes equations using the Stokes fundamental solutions. Engng Analysis 2: 128–132
Tran-Cong T, Phan-Thien N (1988a) Three dimensional study of extrusion processes by boundary element method. Part I. An implementation of high order elements and some Newtonian results. Rheol Acta 27:21–30
Tran-Cong T, Phan-Thien N (1988b) Three dimensional study of extrusion processes by boundary element method. Part II. Some non-Newtonian results. Rheol Acta 27:639–648
Walters K (1975) Rheometry. Chapman and Hall, London
Wu JC, Rizk YM (1979) Lecture notes in physics 90. Springer-Verlag, Berlin Heidelberg New York
Youngren GK, Acrivos A (1975) Stokes flow past a particle of arbitrary shape: a numerical method of solution. J Fluid Mech 69:377–403
Zheng R, Tanner RI (1988) A numerical analysis of calendering. J Non-Newt Fluid Mech 28:149–170
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Phan-Thien, N., Tanner, R.I. (1992). Boundary-Element Analysis of Forming Processes. In: Hartley, P., Pillinger, I., Sturgess, C. (eds) Numerical Modelling of Material Deformation Processes. Springer, London. https://doi.org/10.1007/978-1-4471-1745-2_6
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DOI: https://doi.org/10.1007/978-1-4471-1745-2_6
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