Efficient and modular algorithms in modeling finite inelastic deformations: Objective integration, parameter identification and sub-stepping techniques

Computer Methods in Applied Mechanics and Engineering

Volumn 196, Issue 17-20, 2007, Pages 2269-2283

  Seifert, T ^a   Schenk, T ^b   Schmidt, I ^a  

^a FRAUNHOFER INSTITUTE FOR MECHANICS OF MATERIALS IWM   (Germany)

^b NETHERLANDS INSTITUTE FOR METALS RESEARCH   (Netherlands)

Author keywords

Material modeling; Modular algorithms; Sub stepping

Indexed keywords

ALGORITHMS; COMPUTER SIMULATION; FINITE ELEMENT METHOD; INTEGRATION; STRAIN RATE;

FINITE INELASTIC DEFORMATIONS; INELASTIC MATERIAL DEFORMATION; MATERIAL MODELING; MODULAR ALGORITHMS;

DEFORMATION;

ALGORITHMS; COMPUTER SIMULATION; DEFORMATION; FINITE ELEMENT METHOD; INTEGRATION; STRAIN RATE;

EID: 33846940739     PISSN: 00457825     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cma.2006.12.002     Document Type: Article

References (46)

1. ABAQUS Theory Manual, Version 6.6, Hibbit, Karlson & Sorensen, Inc., 2006.
2. P.J. Armstrong, C.O. Frederik, A mathematical representation of the multiaxial Bauschinger effect, Central Electricity Generating Board, Report RD/B/N 731, 1966.
3. Atluri S.N. On constitutive relations at finite strain: Hypo-elasticity and elasto-plasticity with isotropic and kinematic hardening. Comput. Methods Appl. Mech. Engrg. 43 (1984) 137-171
4. Bertsekas D.P. Projected Newton methods for optimization with simple constraints. SIAM J. Control Opt. 20 (1982) 221-246
5. Bertsekas D.P. Nonlinear Programming. second ed. (2003), Athena Scientific, Belmont, Massachusetts
6. Bruhns O.T., and Anding D.K. On the simultaneous estimation of model parameters used in constitutive laws for inelastic material behaviour. Int. J. Plast. 15 (1999) 1311-1340
7. Chaboche J.L. Time-independent constitutive theories for cyclic plasticity. Int. J. Plast. 2 (1986) 149-188
8. Chaboche J.L. Constitutive equations for cyclic plasticity and cyclic viscoplasticity. Int. J. Plast. 2 (1989) 149-188
9. Dennis J.R., and Schnabel R.B. Numerical Methods for Unconstrained Optimization and Nonlinear Equations (1983), Prentice-Hall, Inc., Englewood Cliffs, NJ
10. Fish J., and Shek K. Computational aspects of incrementally objective algorithms for large deformation plasticity. Int. J. Numer. Methods Engrg. 44 (1999) 839-851
11. Gurson A.L. Continuum theory of ductile rupture by void nucleation and growth - I. Yield criteria and flow rules for porous ductile media. J. Engrg. Mater. Technol. 99 (1977) 2-15
12. Haupt P., Kamlah M., and Tsakmakis C. Continuous representation of hardening properties in cyclic plasticity. Int. J. Plast. 8 (1992) 803-817
13. Healy B.E., and Dodds R.H. A large strain plasticity model for implicit finite element analysis. Comput. Mech. 9 (1992) 95-112
14. J. Heinold, K.-W. Gaede, Ingenieur-Statistik, Dritte Auflage, R. Oldenburg, München, Wien., 1972.
15. Hughes T.J.R. Numerical implementation of constitutive models: rate independent deviatoric plasticity. In: Nemat-Nasser S., Asaro R.J., and Hegemier G.A. (Eds). Theoretical Foundation for Large-scale Computations of Nonlinear Material Behavior (1984), Martinus Nijhoff Publishers, Dortrecht Boston Lancaster
16. Hughes T.J.R., and Winget J. Finite rotation effects in numerical integration of rate constitutive equations arising in large-deformation analysis. Int. J. Numer. Methods Engrg. 15 (1980) 1862-1867
17. Jiang Y., and Sehitoglu H. Modeling of cyclic ratchetting plasticity, Part I: Development of constitutive relations. J. Appl. Mech. 63 (1996) 720-725
18. Johnson G.C., and Bammann D.J. A discussion of stress rates in finite deformation problems. Int. J. Solids Struct. 20 (1984) 725-737
19. Keavey M.A. A canonical form return mapping algorithm for rate independent plasticity. Int. J. Numer. Methods Engrg. 53 (2002) 1491-1510
20. Kreissig R. Numerische Methoden für die Parameteridentifikation. ZAMM 78 (1998) 555-557
21. Kreissig R., Benedix U., and Görke U.-J. Statistical aspects of the identification of material parameters for elasto-plastic models. Arch. Appl. Mech. 71 (2001) 123-134
22. Luenberger D.G. Linear and Nonlinear Programming. second ed. (2003), Kluwer Academic Publishers
23. Mahnken R., and Stein E. The identification of parameters for visco-plastic models via finite-element methods and gradient methods. Modell. Simul. Mater. Sci. Engrg. 2 (1994) 597-616
24. Mahnken R., and Stein E. Parameter identification for viscoplastic models based on analytical derivatives of a least-squares functional and stability investigations. Int. J. Plast. 12 (1996) 451-479
25. Mahnken R., and Stein E. A unified approach for parameter identification of inelastic material models in the frame of the finite element method. Comput. Methods Appl. Mech. Engrg. 136 (1996) 225-258
26. Mahnken R., and Stein E. Parameter identification for finite deformation elasto-plasticity in principal directions. Comput. Methods Appl. Mech. Engrg. 147 (1997) 17-39
27. Miehe C. Numerical computation of algorithmic (consistent) tangent moduli in large-strain computational inelasticity. Comput. Methods Appl. Mech. Engrg. 134 (1996) 223-240
28. Nagtegaal J.C. On the implementation of inelastic constitutive equations with special reference to large deformation problems. Comput. Methods Appl. Mech. Engrg. 33 (1981) 469-484
29. Nagtegaal J.C., and de Jong J.E. Some aspects on nonisotropic work-hardening in finite strain plasticity. In: Kee L.H., and Mallett R.L. (Eds). Plasticity of Metals at Finite Strain: Theory Computation and Experience (1982), Stanford University/Rensselaer Polytechnic Institute 65-102
30. Ohno N., and Wang J.-D. Kinematic hardening rules with critical state of dynamic recovery, Part I: Formulation and basic features for ratchetting behaviour. Int. J. Plast. 9 (1993) 375-390
31. Ortiz M., and Popov E.P. Accuracy and stability of integration algorithms for elastic-plastic constitutive relations. Int. J. Numer. Methods Engrg. 21 (1985) 1561-1576
32. Ortiz M., and Simo J.C. An analysis of a new class of integration algorithms for elastoplastic constitutive relations. Int. J. Numer. Methods Engrg. 23 (1986) 353-366
33. Perez-Foguet A., Rodriguez-Ferran A., and Huerta A. Numerical differentiation for local and global tangent operators in computational plasticity. Comput. Methods Appl. Mech. Engrg. 190 (2000) 4627-4647
34. Perez-Foguet A., Rodriguez-Ferran A., and Huerta A. Consistent tangent matrices for substepping schemes. Comput. Methods Appl. Mech. Engrg. 190 (2001) 4627-4647
35. Press W.H., Teukolsky S.A., Vetterling W.T., and Flannery B.P. Numerical Recipies in Fortran 77. second ed. (1992), Cambridge University Press
36. Reed K.W., and Atluri S.N. Constitutive modelling and computational implementation for finite strain plasticity. Int. J. Plast. 1 (1985) 63-87
37. G. Scheday, Theorie und Numerik der Parameteridentifikation von Materialmodellen der finiten Elastizität und Inelastizität auf der Grundlage optischer Feldmessmethoden, Institut für Mechanik (Bauwesen) der Universität Stuttgart, Bericht I-11, 2003.
38. M. Sester, Fortschrittliche Werkstoffmodelle im Rahmen der Kontinuumsmechanik, Bericht W 8/95, Fraunhofer-Institut für Werkstoffmechanik, Freiburg, 1995.
39. Simo J.C., and Pister K.S. Remarks on rate constitutive equations for finite deformation problems: computational implications. Comput. Methods Appl. Mech. Engrg. 46 (1984) 201-215
40. Simo J.C., and Taylor R.L. Consistent tangent operators for rate-independent elastoplasticity. Comput. Methods Appl. Mech. Engrg. 48 (1985) 101-118
41. Simo J.C., and Hughes T.J.R. Computational Inelasticity. second ed. (2000), Springer-Verlag
42. Springmann M., and Kuna M. Determination of ductile damage parameters by local deformation fields measurement and simulation. Arch. Appl. Mech. (2006) 1-23
43. Weber G.G., Lush A.M., Zavaliangos A., and Anand L. An objective time-integration procedure for isotropic rate-independent and rate-dependent elastic-plastic constitutive equations. Int. J. Plast. 6 (1990) 701-744
44. Weber G.G., and Anand L. Finite deformation constitutive equations and a time integration procedure for isotropic, hyperelastic-viscoplastic solids. Comput. Methods Appl. Mech. Engrg. 79 (1990) 173-202
45. S. Weygand, H. Riedel, B. Eberhard, G. Wouters, Numerical simulation of the drawing process of tungsten wires, in: 16th International Plansee Seminar, vol. 1, 2005, pp. 55-66.
46. Yildirim N., Akcay F., Hüseyin O., and Yildirim D. Parameter estimation of nonlinear models in biochemistry: a comparative study on optimization methods. Appl. Math. Comput. 140 (2003) 29-36