Advances in stabilized finite element and particle methods for bulk forming processes

Computer Methods in Applied Mechanics and Engineering

Volumn 195, Issue 48-49, 2006, Pages 6750-6777

  Onate E ^a   Rojek, J ^a   Chiumenti, M ^a   Idelsohn, S R ^a   Del Pin, F ^a   Aubry, R ^a  

^a INTERNATIONAL CENTER FOR NUMERICAL METHODS IN ENGINEERING CIMNE   (Spain)

Author keywords

Bulk forming processes; Mixing processes; Particle finite element method; Particle method; Stabilized finite element method

Indexed keywords

DIFFERENTIATION (CALCULUS); FINITE ELEMENT METHOD; METAL CASTING; MIXING;

BULK FORMING PROCESSES; BULK METAL FORMING; FINITE CALCULUS; MIXING PROCESSES; PARTICLE FINITE ELEMENT METHOD; STABILIZED FINITE ELEMENT METHOD;

METAL FORMING;

DIFFERENTIATION (CALCULUS); FINITE ELEMENT METHOD; METAL CASTING; METAL FORMING; MIXING;

EID: 33746656802     PISSN: 00457825     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cma.2004.10.018     Document Type: Article

References (58)

1. In: Chenot J.L., and Oñate E. (Eds). Modelling of Metal Forming Processes (1988), Kluwer Academic, Dordrecht
2. In: Pittman J.F.T., Zienkiewicz O.C., Wood R.D., and Alexander J.M. (Eds). Numerical Analysis of Forming Processes (1984), Wiley, Chichester
3. In: Huetnik J., and Baaijens F.P.T. (Eds). Simulation of Materials Processing: Theory, Methods and Applications, NUMIFORM 98, Enschede, Países Bajos, 22-5 June (1998), A.A. Balkema, Rotterdam
4. In: Pietrzyk M., Kusiak J., Majta J., Hartley P., and Pillinger I. (Eds). Metal Forming 2000 (2000), A.A. Balkema, Rotterdam
5. Mori K. Simulation of Material Processing: Theory, Methods and Applications (2001), A.A. Balkema, Lisse
6. In: Owen D.R.J., Oñate E., and Suarez B. (Eds). Computational Plasticity VII. Fundamentals and Applications (2003), CIMNE, Barcelona
7. Ghosh S., Castro J.C., and Lee J.K. Material Processing and Design: Simulation and Applications, NUMIFORM 2004 (2004), American Institute of Physics
8. Zienkiewicz O.C., Taylor R.C., and Nithiarasu A. The Finite Element Method vol. 3, 6th ed. (2005), Elsevier
9. Hirsch C. Numerical Computation of Internal and External Flow vol. 1 (1988), J. Wiley, London vol. 2, 1990
10. Peraire J., Morgan K., and Peiro J. The simulation of 3D incompressible flows using unstructured grids. In: Caughey D.A., and Hafez M.M. (Eds) (1994), J. Wiley, London (Chapter 16)
11. Storti M., Nigro N., and Idelsohn S.R. Steady state incompressible flows using explicit schemes with an optimal local preconditioning. Comput. Methods Appl. Mech. Engrg. 124 (1995) 231-252
12. Heinrich J.C., Hayakorn P.S., and Zienkiewicz O.C. An upwind finite element scheme for two dimensional convective transport equations. Int. J. Numer. Methods Engrg. 11 (1977) 131-143
13. Brooks A., and Hughes T.J.R. Streamline upwind/Petrov-Galerkin formulation for convection dominated flows with particular emphasis on the incompressible Navier-Stokes equations. Comput. Methods Appl. Mech. Engrg. 32 (1982) 199-259
14. Hughes T.J.R., and Mallet M. A new finite element formulations for computational fluid dynamics: III. The generalized streamline operator for multidimensional advective-diffusive systems. Comput. Methods Appl. Mech. Engrg. 58 (1986) 305-328
15. Cruchaga M.A., and Oñate E. A finite element formulation for incompressible flow problems using a generalized streamline operator. Comput. Methods Appl. Mech. Engrg. 143 (1997) 49-67
16. Cruchaga M.A., and Oñate E. A generalized streamline finite element approach for the analysis of incompressible flow problems including moving surfaces. Comput. Methods Appl. Mech. Engrg. 173 (1999) 241-255
17. Hughes T.J.R., Franca L.P., and Hulbert G.M. A new finite element formulation for computational fluid dynamics: VIII. The Galerkin/least-squares method for advective-diffusive equations. Comput. Methods Appl. Mech. Engrg. 73 (1989) 173-189
18. Donea J. A Taylor-Galerkin method for convective transport problems. Int. J. Numer. Methods Engrg. 20 (1984) 101-119
19. Löhner R., Morgan K., and Zienkiewicz O.C. The solution of non-linear hyperbolic equation systems by the finite element method. Int. J. Numer. Methods Fluids 4 (1984) 1043
20. Codina R., Vazquez M., and Zienkiewicz O.C. A general algorithm for compressible and incompressible flow-Part III. The semi-implicit form. Int. J. Numer. Methods Fluids 27 (1998) 13-32
21. Codina R., and Zienkiewicz O.C. CBS versus GLS stabilization of the incompressible Navier-Stokes equations and the role of the time step as stabilization parameter. Commun. Numer. Methods Engrg. 18 2 (2002) 99-112
22. Codina R., and Soto O. A numerical model to track two-fluid interfaces based on a stabilized finite element method and the level set technique. Int. J. Numer. Methods Fluids 4 (2002) 293-301
23. Codina R. Stabilized finite element approximation of transient incompressible flows using orthogonal subscales. Comput. Methods Appl. Mech. Engrg. 191 (2002) 4295-4321
24. Donea J., and Huerta A. Finite Element Method for Flow Problems (2003), J. Wiley, London
25. Zienkiewicz O.C., Rojek J., Taylor R.L., and Pastor M. Triangles and tetrahedra in explicit dynamic codes for solids. Int. J. Numer. Methods Engrg. 43 (1998) 565-583
26. Rojek J., Zienkiewicz O.C., Oñate E., and Postek E. Advances in FE explicit formulations for simulation of metal forming processes. J. Mater. Process. Technol. 119 (2001) 41-47
27. Chiumenti M., Valverde Q., Agelet de Saracibar C., and Cervera M. A stabilized formulation for incompressible elasticity using linear displacement and pressure interpolations. Comput. Methods Appl. Mech. Engrg. 191 46 (2002) 5253-5264
28. Cervera M., Chiumenti M., Valverde Q., and Agelet de Saracibar C. Mixed linear/linear simplicial elements for incompressible elasticity and plasticity. Comput. Methods Appl. Mech. Engrg. 192 49-50 (2003) 5249-5263
29. Chiumenti M., Valverde Q., Agelet de Saracibar C., and Cervera M. A stabilized formulation for incompressible plasticity using linear triangles and tetrahedra. Int. J. Plastic. 20 8-9 (2004) 1487-1504
30. Oñate E. Derivation of stabilized equations for advective-diffusive transport and fluid flow problems. Comput. Methods Appl. Mech. Engrg. 151 (1998) 233-267
31. Oñate E. Possibilities of finite calculus in computational mechanics. Int. J. Numer. Methods Engrg. 60 1 (2004) 255-281
32. Oñate E. A stabilized finite element method for incompressible viscous flows using a finite increment calculus formulation. Comput. Methods Appl. Mech. Engrg. 182 1-2 (2000) 355-370
33. Oñate E., and García J. A finite element method for fluid-structure interaction with surface waves using a finite calculus formulation. Comput. Methods Appl. Mech. Engrg. 191 (2001) 635-660
34. E. Oñate, J. García, S.R. Idelsohn, F. Del Pin, FIC formulations for finite element analysis of incompressible flows. Eulerian, ALE and Lagrangian approaches, Comput. Methods Appl. Mech. Engrg., submitted for publication.
35. Oñate E., Arteaga J., García J., and Flores R. Error estimation and mesh adaptivity in incompressible viscous flows using a residual power approach. Comput. Methods Appl. Mech. Engrg. 195 (2006) 339-362
36. Oñate E., Taylor R.L., Zienkiewicz O.C., and Rojek J. A residual correction method based on finite calculus. Engrg. Comput. 20 5/6 (2003) 629-658
37. Oñate E., Rojek J., Taylor R.L., and Zienkiewicz O.C. Finite calculus formulation for incompressible solids using linear triangles and tetrahedra. Int. J. Numer. Methods Engrg. 59 (2004) 1473-1500
38. Idelsohn S.R., Oñate E., and Del Pin F. A lagrangian meshless finite element method applied to fluid-structure interaction problems. Comput. Struct. 81 (2003) 655-671
39. Oñate E., Idelsohn S.R., Del Pin F., and Aubry R. The particle finite element method. An overview. Int. J. Comput. Methods 1 2 (2004) 267-307
40. Idelsohn S.R., Oñate E., and Del Pin F. The particle finite element method: a powerful tool to solve incompressible flows with free-surfaces and breaking waves. Int. J. Numer. Methods Engrg. 61 (2004) 964-989
41. Aubry R., Idelsohn S.R., and Oñate E. Particle finite element method in fluid mechanics including thermal convection-diffusion. Comput. Struct. 83 17-18 (2005) 1459-1475
42. Oñate E., Sacco C., and Idelsohn S. A finite point method for incompressible flow problems. Comput. Visualizat. Sci. 2 (2000) 67-75
43. Zienkiewicz O.C., Jain P.C., and Oñate E. Flow of solids during forming and extrusion: some aspects of numerical solutions. Int. J. Solids Struct. 14 (1978) 15-38
44. Zienkiewicz O.C., Oñate E., and Heinrich J.C. A general formulation for coupled thermal flow of metals using finite elements. Int. J. Numer. Methods Engrg. 17 (1981) 1497-1514
45. Codina R. Pressure stability in fractional step finite element method for incompressible flows. J. Comput. Phys. 170 (2001) 112-140
46. Oñate E., and Manzan M. A general procedure for deriving stabilized space-time finite element methods for advective-diffusive problems. Int. J. Numer. Methods Fluids 31 (1999) 203-221
47. Codina R., Schaefer U., and Oñate E. Mould filling simulation using finite elements. Int. J. Numer. Methods Engrg. 4 (1994) 291-310
48. Codina R., and Soto O. Finite element simulation of the filling of thin moulds. Int. J. Numer. Methods Engrg. 46 (1999) 1559-1573
49. Agelet de Saracibar C., Cervera M., and Chiumenti M. On the Formulation of coupled thermoplastic problems with phase-change. Int. J. Plastic. 15 (1999) 1-34
50. Cervera M., AgeletdeSaracibar C., and Chiumenti M. Thermo-mechanical analysis of industrial solidification processes. Int. J. Numer. Methods Engrg. 46 (1999) 1575-1591
51. Agelet de Saracibar C., Cervera M., and Chiumenti M. On the constitutive modeling of coupled thermo-mechanical phase-change problems. Int. J. Plastic. 17 (2001) 1565-1622
52. Calvo N., Idelsohn S.R., and Oñate E. The extended Delaunay tesselation. Engrg. Comput. 20 5/6 (2003) 583-600
53. Idelsohn S.R., Oñate E., Calvo N., and del Pin F. The meshless finite element method. Int. J. Numer. Methods Engrg. 58 (2003) 893-912
54. MARC/Autoforge User's Guide 2.2, 1999.
55. Edelsbrunner H., and Mucke E.P. Three dimensional alpha shapes. ACM Trans. Graphics 13 (1999) 43-72
56. VULCAN, Finite element system for casting simulation, Quantech ATZ, Barcelona, Spain, 2003. Available from: .
57. J.C. Cante, J. Oliver, C. González, Powder forming simulation with the particle finite element method, in: Z.H. Yao, M.W. Yuan, W.X. Zhong (Eds.), Computational Mechanics, CD-Rom Proceedings of the WCCM VI, Beijing, September 5-10, 2004.
58. J. Rojek, E. Oñate, R.L. Taylor, CBS based stabilization in explicit solid mechanics, Int. J. Numer. Mech. Engrg. in press.