A return mapping algorithm for cyclic viscoplastic constitutive models

Computer Methods in Applied Mechanics and Engineering

Volumn 195, Issue 1-3, 2006, Pages 148-178

  Nukala, Phani Kumar V V ^a  

^a OAK RIDGE NATIONAL LABORATORY   (United States)

Author keywords

Cyclic constitutive model; Cyclic hardening behavior; Nonlinear kinematic rule; Return mapping algorithms; Viscoplasticity

Indexed keywords

ALGORITHMS; KINEMATICS; LAGRANGE MULTIPLIERS; MATHEMATICAL MODELS; MATRIX ALGEBRA; THERMODYNAMICS;

CYCLIC CONSTITUTIVE MODEL; CYCLIC HARDENING BEHAVIOR; NONLINEAR KINEMATIC RULE; RETURN MAPPING ALGORITHMS;

VISCOPLASTICITY;

ALGORITHM; MATHEMATICAL MODELING; VISCOPLASTICITY;

EID: 27244448610     PISSN: 00457825     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cma.2005.01.009     Document Type: Article

References (41)

1. J. Lemaitre J.L. Chaboche Mechanics of Solid Materials 1990 Cambridge University Press
2. J.L. Chaboche Constitutive equations for cyclic plasticity and cyclic viscoplasticity Int. J. Plasticity 5 1989 247-302
3. N. Ohno Recent topics in constitutive modeling of cyclic plasticity and viscoplasticity Appl. Mech. Rev. 43 1990 283
4. N. Ohno A constitutive model of cyclic plasticity with a non-hardening strain region J. Appl. Mech. 49 1982 721
5. D.L. McDowell A nonlinear kinematic hardening theory for cyclic thermoplasticity and thermoviscoplasticity Int. J. Plasticity 8 1992 695-728
6. J.L. Chaboche Cyclic viscoplastic constitutive equations, Part I: A thermodynamically consistent formulation ASME J. Appl. Mech. 60 1993 813-821
7. J.L. Chaboche Cyclic viscoplastic constitutive equations, Part II: Stored energy-comparison between models and experiments ASME J. Appl. Mech. 60 1993 821-828
8. F. Auricchio R.L. Taylor Two material models for cyclic plasticity: nonlinear kinematic hardening and generalized plasticity Int. J. Plasticity 11 1995 65-98
9. Y. Jiang P. Kurath Characteristics of the Armstrong-Frederick type plasticity models Int. J. Plasticity 12 3 1996 387-415
10. J.L. Chaboche Thermodynamic formulation of constitutive equations and application to the viscoplasticity and viscoelasticity of metals and polymers Int. J. Solids Struct. 34 18 1997 2239-2254
11. F. Auricchio A viscoplastic constitutive equation bounded between two generalized plasticity models Int. J. Plasticity 13 1997 697-721
12. M. Langseth O.S. Hopperstad S. Remseth Cyclic stress-strain behaviour of alloy AA6060, Part I: Uniaxial experiments and modelling Int. J. Plasticity 11 6 1995 725-739
13. M. Langseth O.S. Hopperstad S Remseth Cyclic stress-strain behaviour of alloy AA6060 T4, Part II: Biaxial experiments and modelling Int. J. Plasticity 11 6 1995 741-762
14. M.L. Wilkins Calculation of elastic-plastic flow Methods of Computational Physics vol. 3 1964 Academic Press New York
15. R.D. Krieg, S.W. Key, Implementation of time independent plasticity theory into structural computer programs, in: Constitutive Equations in Viscoplasticity, Computational and Engineering Aspects, AMD-20, ASME, New York, 1986, pp. 125-138.
16. M. Ortiz E.P. Popov Accuracy and stability of integration algorithms for elastoplastic constitutive relations Int. J. Numer. Methods Engrg. 21 1985 1561-1576
17. M. Ortiz J.C. Simo An analysis of a new class of integration algorithms for elastoplastic constitutive relations Int. J. Numer. Methods Engrg. 23 1986 353-366
18. M.A. Crisfield Non-linear Finite Element Analysis for Solids and Structures 1991 John Wiley
19. J.C. Simo R.L. Taylor Consistent tangent operators for rate-independent elastoplasticity Comput. Methods Appl. Mech. Engrg. 48 1985 101-118
20. J.C. Simo R.L. Taylor A return mapping algorithm for plane stress elastoplasticity Int. J. Numer. Methods Engrg. 22 1986 649-670
21. J.C. Simo S. Govindjee Exact closed-form solution of the return mapping algorithm in plane stress elasto-viscoplasticity Engrg. Comput. 5 1988 254-258
22. J.C. Simo S. Govindjee Non-linear B-stability and symmetry preserving return mapping algorithms for plasticity and viscoplasticity Int. J. Numer. Methods Engrg. 31 1991 151-176
23. 2-flow theory Comput. Struct. 43 1992 1117-1133
24. Q.S. Germain P. Nguyen P. Suquet Continuum thermodynamics ASME J. Appl. Mech. 50 1983 1010-1020
25. Phani Kumar V.V. Nukala, Donald W. White, Consistent reduction of von-Mises-type constitutive relations onto stress and strain constrained configuration subspaces, unpublished.
26. I. Doghri Fully implicit integration and consistent tangent modulus in elasto-plasticity Int. J. Numer. Methods Engrg. 36 1993 3915-3932
27. S. Hartmann P. Haupt Stress computation and consistent tangent operator using non-linear kinematic hardening models Int. J. Numer. Methods Engrg. 36 1993 3801-3814
28. O.S. Hopperstad S. Remseth A return mapping algorithm for a class of cyclic plasticity models Int. J. Numer. Methods Engrg. 38 1995 549-564
29. J.L. Chaboche G. Cailletaud Integration methods for complex plastic constitutive equations Comput. Methods Appl. Mech. Engrg. 133 1996 125-155
30. S. Hartmann G. Luhrs P. Haupt An efficient stress algorithm with applications in viscoplasticity and plasticity Int. J. Numer. Methods Engrg. 40 1997 991-1013
31. J.P.G. Sawyer C.H. Wang R. Jones An implicit algorithm using explicit correctors for the kinematic hardening model with multiple back stresses Int. J. Numer. Methods Engrg. 50 2001 2093-2107
32. G. Luhrs S. Hartmann P. Haupt On the numerical treatment of finite deformations in elastoviscoplasticity Comput. Methods Appl. Mech. Engrg. 144 1997 1-21
33. B. Svendsen S. Arndt D. Klingbeil R. Sievert Hyperelastic models for elastoplasticity with nonlinear isotropic and kinematic hardening at large deformation Int. J. Solids Struct. 35 1998 3363-3389
34. W. Dettmer S. Reese On the theoretical and numerical modelling of Armstrong-Frederick kinematic hardening in the finite strain regime Comput. Methods Appl. Mech. Engrg. 193 2004 87-116
35. N.R. Hansen H.L. Schreyer A thermodynamically consistent framework for theories of elasto-plasticity coupled with damage Int. J. Solids Struct. 31 1994 359-389
36. N. Ohno J.D. Wang Kinematic hardening rules for simulation of ratcheting behavior Eur. J. Mech. A/Solids 13 4 1994 519-531
37. J.E. Dennis R.L. Schnable Numerical Methods for Unconstrained Optimization and Nonlinear Equations 1983 Prentice-Hall Englewood Cliffs, NJ
38. Bradley N. Maker, NIKE3D: A nonlinear implicit three-dimensional finite element code for solid and structural mechanics, Rept. ucrl-ma-105268, rev 1, University of California, Lawrence Livermore National Laboratory, 1995.
39. H.S. Lamba O.M. Sidebottom Cyclic plasticity for nonproportional paths. Part I: Cyclic hardening, erasure of memory, and subsequent strain hardening experiments J. Engrg. Mater. Technol. 100 1978 96-103
40. H.S. Lamba O.M. Sidebottom Cyclic plasticity for nonproportional paths. Part II: Comparison with predictions of three incremental plasticity models J. Engrg. Mater. Technol. 100 1978 104-110
41. A. Billinghurst J.R.L. Williams G. Chen N.S. Trahair Inelastic uniform torsion of steel members J. Struct. Mech. 8 January 1991 61-92