An accurate time integration scheme for arbitrary rotation motion: application to metal forming simulation

详细信息    查看全文

• 作者：Koffi Kpodzo ; Lionel Fourment ; Patrice Lasne…
• 关键词：Time integration scheme ; Large rotations ; Implicit formulation ; Velocity formulation ; Finite elements ; Metal forming ; Torsion test ; Cross ; wedge rolling
• 刊名：International Journal of Material Forming
• 出版年：2016
• 出版时间：January 2016
• 年：2016
• 卷：9
• 期：1
• 页码：71-84
• 全文大小：2,764 KB
• 参考文献：1.Atluri SN, Cazzani A (1995) Rotations in computational solid mechanics. Arch Comput Methods Eng 2(1):49–138CrossRef MathSciNet
  2.Buss SR (2000) Accurate and efficient simulation of rigid-body rotations. J Comput Phys 164(2):377–406CrossRef MathSciNet MATH
  3.Ghosh S, Roy D (2010) An accurate numerical integration scheme for finite rotations using rotation vector parametrization. J Frankl Inst 347(8):1550–1565CrossRef MathSciNet MATH
  4.Rubin MB (2007) A simplified implicit Newmark integration scheme for finite rotations. Comput Math Appl 53(2):219–231CrossRef MathSciNet MATH
  5.Ibrahimbegovic A (1997) On the choice of finite rotation parameters. Comput Methods Appl Mech Eng 149(1–4):49–71CrossRef MathSciNet MATH
  6.Ibrahimbegovic A, Taylor RL (2002) On the role of frame-invariance in structural mechanics models at finite rotations. Comput Methods Appl Mech Eng 191(45):5159–5176CrossRef MathSciNet MATH
  7.Betsch P, Menzel A, Stein E (1998) On the parametrization of finite rotations in computational mechanics. Comput Methods Appl Mech Eng 155(3–4):273–305CrossRef MathSciNet MATH
  8.Pimenta PM, Campello EMB, Wriggers P (2008) An exact conserving algorithm for nonlinear dynamics with rotational DOFs and general hyperelasticity. Part 1: Rods. Comput Mech 42(5):715–732CrossRef MathSciNet MATH
  9.Cardona A, Geradin M (1988) A beam finite element non-linear theory with finite rotations. Int J Numer Methods Eng 26(11):2403–2438CrossRef MathSciNet MATH
  10.Bottasso CL, Borri M (1998) Integrating finite rotations. Comput Methods Appl Mech Eng 164(3–4):307–331CrossRef MathSciNet MATH
  11.Borri M, Trainelli L, Bottasso CL (2000) On representations and parameterizations of motion. Multibody Syst Dyn 4(2–3):129–193CrossRef MathSciNet MATH
  12.Brank B, Mamouri S, Ibrahimbegovic A (2005) Constrained finite rotations in dynamics of shells and Newmark implicit time-stepping schemes. Eng Comput 22(5/6):505–535CrossRef MATH
  13.Argyris J (1982) An excursion into large rotations. Comput Methods Appl Mech Eng 32(1–3):85–155CrossRef MathSciNet MATH
  14.Zupan E, Saje M (2011) Integrating rotation from angular velocity. Adv Eng Softw 42(9):723–733CrossRef MATH
  15.K. Traore, R. Forestier, K. Mocellin, P. Montmitonnet, and M. Souchet, Three dimensional finite element simulation of ring rolling. 2001
  16.Dialami N, Chiumenti M, Cervera M, de Saracibar C A, and Ponthot J P (Dec. 2013) “Material flow visualization in Friction Stir Welding via particle tracing”. Int. J. Mater. Form., pp. 1–15
  17.Chiumenti M, Cervera M, Agelet de Saracibar C, Dialami N (2013) Numerical modeling of friction stir welding processes. Comput Methods Appl Mech Eng 254:353–369CrossRef MathSciNet MATH
  18.Gines Losilla, Montmitonnet Pierre, and Bouziane M., “Modélisation du laminage circulaire par éléments finis. Calculs thermomécaniques et calcul microstructuraux,” presented at the Matériaux 2002, Tours, France, 2002.
  19.Soyris N, Fourment L, Coupez T, Cescutti JP, Brachotte G, Chenot JL (1992) Forging of a connecting rod: 3D finite element calculations. Eng Comput 9(1):63–80CrossRef
  20.Gay C, Montmitonnet P, Coupez T, Chenot JL (1994) Test of an element suitable for fully automatic remeshing in 3D elastoplastic simulation of cold forging. J Mater Process Technol 45(1–4):683–688CrossRef
  21.Wagoner RH, Chenot J-L (2001) Metal Forming Analysis, 1st edn. Cambridge University Press, CambridgeCrossRef
  22.Coupez T, Soyris N, Chenot J-L (1991) 3-D finite element modelling of the forging process with automatic remeshing. J Mater Process Technol 27(1–3):119–133CrossRef
  23.Mocellin K, Fourment L, Coupez T, Chenot JL (2001) Toward large scale F.E. computation of hot forging process using iterative solvers, parallel computation and multigrid algorithms. Int J Numer Methods Eng 52(5–6):473–488CrossRef MATH
  24.Fourment L, Chenot JL, Mocellin K (1999) Numerical formulations and algorithms for solving contact problems in metal forming simulation. Int J Numer Methods Eng 46(9):1435–1462CrossRef MATH
  25.Jelenić G, Saje M (1995) A kinematicsally exact space finite strain beam model — finite element formulation by generalized virtual work principle. Comput Methods Appl Mech Eng 120(1–2):131–161CrossRef MATH
  
• 作者单位：Koffi Kpodzo (1)
  Lionel Fourment (1)
  Patrice Lasne (2)
  Pierre Montmitonnet (1)
  
  1. Mines ParisTech, CEMEF -Centre for Material Forming, CNRS UMR 7635, CS 10 207, 06904, Sophia Antipolis Cedex, France
  2. Transvalor, 694 Avenue Maurice Donat Parc de Haute Technologie, 06250, Mougins, France
  
• 刊物类别：Engineering
• 刊物主题：Operating Procedures and Materials Treatment
  Materials Science
  Manufacturing, Machines and Tools
  Mechanical Engineering
  Numerical and Computational Methods in Engineering
  Computer-Aided Engineering and Design
  
• 出版者：Springer Paris
• ISSN：1960-6214

文摘

Within the frame of implicit velocity based formulations with solid elements, usual time integration schemes often turn out unsatisfactory when the movement has large rotations, especially in metal forming applications such as ring rolling or cross-wedge rolling. These rotations generally require using a much higher order integration scheme with inherent difficulties in implementing such schemes. For pure rotation motions, it is possible to use a low order integration scheme by rewriting the motion equations in the cylindrical frame that is supported by the rotation axis. Accordingly, a first order scheme is sufficient to accurately integrate the movement but it is restricted to specific problems. In the more general case, it is possible to derive parts of the domain where rotations are predominant along with the governing rotation axis from the velocity field gradient. The motion equations are then rewritten in the resulting local cylindrical frame. Performances of this first order scheme are first evaluated and highlighted over simple analytical problems, before being applied to the finite element simulation of the torsion test, and then to more complex metal forming problems involving large rotations. The accuracy and efficiency of this scheme is so numerically demonstrated. Keywords Time integration scheme Large rotations Implicit formulation Velocity formulation Finite elements Metal forming Torsion test Cross-wedge rolling