Formulation and survey of ALE method in nonlinear solid mechanics

Finite Elements in Analysis and Design

Volumn 24, Issue 4, 1997, Pages 253-269

  Wang, J ^a   Gadala, M S ^a  

^a UNIVERSITY OF BRITISH COLUMBIA   (Canada)

Author keywords

Arbitrary Lagrangian Eulerian method (ALE); Finite deformation; Finite element formulation; Metal forming

Indexed keywords

ANISOTROPY; BOUNDARY CONDITIONS; DEFORMATION; ELASTOPLASTICITY; FINITE ELEMENT METHOD; MATHEMATICAL MODELS; MECHANICS; METAL FORMING; STRAIN;

ARBITRARY LAGRANGIAN-EULERIAN METHOD; FINITE STRAIN DEFORMATION;

NUMERICAL METHODS;

EID: 0031077489     PISSN: 0168874X     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0168-874X(96)00061-3     Document Type: Article

References (40)

1. R. Hill, "Some basic principles in the mechanics of solids without a natural time", J. Mech. Phys. Solids 7, pp. 207-225, 1959.
2. H.D. Hibbitt, P.V. Marcal and J.R. Rice, "A finite element formulation for problems of large strain and large displacement", Int. J. Solid Struct 6, pp. 1069-1086, 1970.
3. R.M. McMeeking and J.R. Rice, "Finite element formulations for problems of large elastic-plastic deformation", Int. J. Solids Struct. 11, pp. 601-616, 1975.
4. J.C. Nagtegaal and J.E. Jong, "Some computational aspects of elastic-plastic large strain analysis", Int. J. Numer. Mech. Eng. 17, pp. 15-41, 1981.
5. M.S. Gadala, M.A. Dokainish and G.AE. Oravas, "Formulation methods of geometric and material nonlinearity problems", Int. J. Numer. Methods Eng. 20, pp. 887-914, 1984.
6. M.S. Gadala, G.AE. Oravas and M.A. Dokainish, "A consistent Eulerian formulation of large deformation problems in static and dynamics", Int. J. Non-linear Mech. 18, pp. 21-35, 1983.
7. M. Abo-Elkhier, G.AE. Oravas and M.A. Dokainish, "A consistent Eulerian formulation for large deformation analysis with reference to metal-extrusion process", Int. J. Non-linear Mech. 23, pp. 37-52, 1988.
8. K.A. Derbalian, E.H. Lee, R.L. Mallet and R.M. McMeeking, "Finite element metal forming analysis with spatially fixed mesh", in: H. Herman (ed.), Application of Numerical Methods for Forming Process, Vol. ASME-AMD 28, pp. 39-47, 1978.
9. Swanson Analysis Systems Inc., Engineering analysis system user's manual, Swanson Analysis Systems Inc., Houston, USA, 1992.
10. Engineering Mechanics Research Corporation, Users manual for NISA II, Numerical integrated elements for systems analysis, Engineering Mechanics Research Corporation, MI, 1992.
11. C.H. Lee and S. Kobayashi, "Elastoplastic analysis of plane-strain and axisymmetric flat punch indentation by the finite element method", Int. J. Mech. Sci. 12, pp. 349-370, 1970.
12. E.H. Lee and R.L. Mallett, "Stress and deformation of metal extrusion process", Comput. Mech. Appl. Mech. Eng. 10, pp. 339-353, 1977.
13. N. Aravas, "The analysis of void growth that leads to central bursts during extrusion", J. Mech. Phys. Solids 34, pp. 55-79, 1986.
14. A.M. Lush, "Numerical grid generation used for remeshing finite element analyses of metal forming", in: S. Sengupta, J. Hauser, P.R. Eiseman and J.F. Thompson (eds.), Numerical Grid Generation in Computational Fluid Mechanics' 88 2nd Conference on Grid Generation in Computational Fluid Dynamics, Swansea, UK, pp. 1029-1038, 1988.
15. J. Cheng and N. Kikuchi, "A mesh re-zoning technique for finite element simulations of metal forming process", Int. J. Numer. Methods Eng. 23, pp. 219-288, 1986.
16. J.C.J.M. Gelten and I.A.W.A. Konter, "Application of mesh-rezoning in the updated Lagrangian method to metal forming analysis", in: J.F.T. Pitman (ed.), Numerical Methods in Industrial Forming Processes, Pineridge Press, Swansea, pp. 511-521, 1982.
17. Y. Kanto and G. Tagawa, "A dynamic of contact buckling analysis by the penalty finite element method", Int. J. Numer. Methods Eng. 29, pp. 755-774, 1990.
18. B. Nour-Omid and P. Wriggers, "A two-level iteration method for solution of contact problems", Comput. Methods Appl. Mech. Eng. 54, pp. 131-144, 1986.
19. J. Padovan and R. Moscarello, Pantographing self adaptive GAP elements, Comput. Struct. 20, pp. 745-758, 1985.
20. M. Abo-Elkhier, On the numerical solution of nonlinear problems in continuum mechanics, Ph.D. Thesis, McMaster University, 1985.
21. J.T. Oden and H.J. Braucnli, "On the calculation of consistent stress distributions in finite element approximations", Int. J. Numer. Mech. Eng. 3, pp. 317-325, 1971.
22. W.F. Noh, "A time-dependent two-space-dimensional coupled Eulerian-Lagrangian code", in: B. Alderb, (ed.), Methods in Computational Physics, Vol. 3, Academic Press, New York, 1964.
23. T. Belytschko and J.M. Kennedy, "Computer methods for subassembly simulation", Nucl. Eng. Des. 47, pp. 17-38, 1978.
24. R.B. Haber and H.M. Koh, "Explicit expression for release rates using virtual crack extension", Int. J. Numer. Methods Eng. 21, pp. 301-305, 1985.
25. R.B. Haber and J.F. Abel, "Contact-slip analysis using mixed displacements", ASME J. Eng. Mech. 109, pp. 441-429, 1983.
26. J. Huetink, P.T. Vreede and J.V.D. Lugt, "Progress in mixed Eulerian-Lagrangian finite element simulation of forming process", Int. J. Numer. Methods Eng. 30, pp. 1441-1457, 1990.
27. J. Huetink, "Analysis of metal forming processes based on a combined Eulerian-Lagrangian finite formulation", in: J.F.T. Pittman (ed.), Numerical Methods in Industrial Forming Processes, Pineridge, Swansea, pp. 501-509, 1982.
28. R.B. Harber, "A mixed Eulerian-Lagrangian displacement model for large-deformation analysis in solid mechanics", Comput. Methods Appl. Mech. Eng. 43, pp. 277-292, 1984.
29. T. Yamada and F. Kikuchi, "An arbitrary Langrangian-Eulerian finite element method for incompressible hyperelasticity", Comput. Methods Appl. Mech. Eng. 102, pp. 149-177, 1993.
30. P.J.G. Schreurs, F.E. Veldpaus and W.A.M. Brekelmans, "An arbitrary Eulerian Lagrangian finite element model for the simulation of geometric nonlinear hyperelastic and elasto-plastic deformation processes", in: J.F.T. Pittman (ed.), Numerical Methods in Industrial Forming Processes, Pineridge, Swansea, pp. 491-500, 1982.
31. P.J.G. Schreurs, F.E. Veldpaus and W.A.M. Brekelmans, "Simulation of forming processes, using the arbitrary Eulerian-Lagrangian formulation", Comput. Methods Appl. Mech. Eng. 58, pp. 19-36, 1986.
32. T.J.R. Hughes, W.K. Liu and T.K. Zimmermann, "Lagrangian-Eulerian finite element formulation for incompressible viscous flows", Comput. Methods Appl. Mech. Eng. 29, pp. 329-349, 1981.
33. W.K. Liu, H. Chang, J. Chen and T. Belytschko, "Arbitrary Lagrangian-Eulerian petrov-Galerkin finite elements for nonlinear continua", Comput. Methods Appl. Mech. Eng. 68, pp. 259-310, 1988.
34. W.K. Liu, J.S. Chen, T. Belytschko and Y.F. Zhang, "Adaptive finite elements with particular reference to external work rate on frictional Interface", Comput. Mech. Appl. Mech. Eng. 93, pp. 1186-1216, 1991.
35. S. Ghosh and N. Kikuchi, "An arbitrary Lagrangian-Eulerian finite method for large deformation analysis of elastic-viscoplastic solids", Comput. Methods Appl. Mech. Eng. 86, pp. 127-188, 1991.
36. S. Ghosh and N. Kikuchi, "Finite element formulation for the simulation of hot sheet metal forming process", Int. J. Eng. Sci. 26, pp. 143-161, 1988.
37. S. Ghosh, "Finite element simulation of some extrusion processes using the arbitrary Lagrangian-Eulerian description", J. Mat. Shaping Technol. 8, pp. 53-64, 1990.
38. R. Couch and R. Sharp, "Application of ALE techniques to metal forming simulations", in Advanced Computational Methods for Materials Modeling, American Society of Mechanical Engineers, Applied Mechanics Division, Vol. AMD 186, pp. 133-149, 1993.
39. A. Huerta and F. Casadei, "New ALE applications in non-linear fast-transient solid dynamic", Eng. Comput. 11, pp. 317-345, 1994.
40. C. Truesdell and R. Toupin, The classical field theories, In: Encyclopedia of Physics, Vol. III/1, Springer, Berlin, pp. 552-610, 1960.