An improved iterative method for large strain viscoplastic problems

International Journal for Numerical Methods in Engineering

Volumn 44, Issue 2, 1999, Pages 155-176

  Cao, H L ^a   Potier Ferry, M ^a  

^a UNIVERSITÉ DE LORRAINE   (France)

Author keywords

Adaptive step; Newton Raphson method; Perturbation technique; Viscoplasticity

Indexed keywords

BENDING (DEFORMATION); ITERATIVE METHODS; NUMERICAL ANALYSIS; STRAIN;

LARGE STRAIN VISCOPLASTIC PROBLEM; NEWTON-RAPHSON METHOD;

VISCOPLASTICITY;

EID: 0032761625     PISSN: 00295981     EISSN: None     Source Type: Journal    
DOI: 10.1002/(SICI)1097-0207(19990120)44:2<155::AID-NME484>3.0.CO;2-M     Document Type: Article

References (18)

1. N. M. Wang, 'A rigid-plastic rate-sensitive finite element method for modelling sheet metal forming processes', in J. F. T. Pittman, O. C. Zienkiewicz, R. D. Wood and J. M. Alexander (eds.), Numerical Analysis of Forming Processes, Wiley, London, 1984, pp. 117-164.
2. S. Kobayashi, 'Thermoviscoplastic analysis of metal forming problems by the finite element method', in J. F. T. Pittman, O. C. Zienkiewicz, R. D. Wood and I. M. Alexander (eds.), Numerical Analysis of Forming Processes Wiley London 1984, pp. 45-69.
3. O. C. Zienkiewicz, 'Flow formulation for numerical solution of forming processes', in J. F. T. Pittman, O. C. Zienkiewicz, R. D. Wood and J. M. Alexander (eds.), Numerical Analysis of Forming Processes, Wiley London, 1984, pp. 1-44.
4. K. Chung and R. H. Wagoner, 'Numerical improvement of viscoplastic, non-linear, finite element analysis' Int. J. Mech. Sci., 29, 45-59 (1987).
5. C. Bohatier and J. L. Chenot, 'Finite element formulation for non-steady-state viscoplastic deformation', Int. J. Numer. Meth. Engng., 21, 1697-1708 (1985).
6. A. C. Walker, 'A nonlinear finite element analysis of shallow circular arches', Int. J. Solids Struct., 5, 97-107 (1969).
7. J. Connor and N. Morin, 'Perturbation techniques in the analysis of geometrically nonlinear shells', Proc. 1970 IUTAM Conf. High Speed Computing of Elastic Structures, Université de Liège, 1971, pp. 683-705.
8. L. Azrar, B. Cochelin, N. Damil and M. Potier-Ferry, 'An asymptotic numerical method to compute the post-buckling behaviour of elastic plates and shells', Int. J. Numer. Meth. Engng., 36, 1251-1277 (1993).
9. Y. Yokoo, T. Nakamura and K. Uetani, 'The incremental perturbation method for large displacement analysis of elastic-plastic structures', Int. J. Numer. Meth. Engng., 10, 503-525 (1976).
10. N. Damil and M. Potier-Ferry, 'A new method to compute perturbed bifurcation: Application to buckling of imperfect elastic structures', Int. J. Engng. Sci., 28, 704-719 (1990).
11. B. Cochelin, N. Damil and M. Potier-Ferry, 'The asymptotic numerical method, an efficient perturbation technique for non-linear structural mechanics', Revue Européenne des Elements Finis, 3, 281-297 (1994).
12. M. Potier-Ferry, H. L. Cao, J. Descamps and N. Damil, 'An asymptotic numerical method for numerical analysis of large deformation viscoplastic problems', Comput. Struct., submitted.
13. N. Mole, J. L. Chenot and L. Fourment, 'A velocity based approach including acceleration to the finite element computation of viscoplastic problems', Int. J. Numer. Meth. Engng., 39, 3439-3451 (1996).
14. Y. J. Kim and D. Y. Yang, 'A rigid-plastic finite element formulation considering the effect of geometric change and its application to hydrostatic bulging', Int. J. Mech. Sci., 27, 453-463 (1985).
15. H. Iseki, T. Jimma and T. Murota, 'Finite element method of analysis of the hydrostatic bulging of a sheet metal', Bull. JSME, 20, 285-291 (1977).
16. G. Powell and J. Simons, 'Improved iteration strategy for non-linear structures', Int. J. Numer. Meth. Engng., 17, 1455-1467 (1996).
17. M. Potier-Ferry, N. Damil, B. Braikat, J. Descamps, J. M. Cadou, H. L. Cao and A. Elhage Hussein, 'Traitement des fortes non-linéarités par la méthode asymptotique numérique', Compte Rendus de l'Académie des Sciences, 324, 171-177 (1997).
18. J. Descamps, H. L. Cao and M. Potier-Ferry, 'An asymptotic numerical method to solve large strain viscoplastic problems'. Proc. 5th int. Conf. on Computational Plasticity. Models Software and Applications, Barcelona, 1997 pp. 393-400.