Hyperelastic models for elastoplasticity with non-linear isotropic and kinematic hardening at large deformation

International Journal of Solids and Structures

Volumn 35, Issue 25, 1998, Pages 3363-3389

  Svendsen, Bob ^a   Arndt, Stephan ^a   Klingbeil, Dietmar ^a   Sievert, Rainer ^a  

^a BAM FEDERAL INSTITUTE FOR MATERIALS RESEARCH AND TESTING   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; COMPUTER SIMULATION; FINITE ELEMENT METHOD; HARDENING; MATHEMATICAL MODELS; PLASTIC DEFORMATION; SHEAR STRESS; STRAIN;

KINEMATIC HARDENING; NONLINEAR ISOTROPIC;

ELASTOPLASTICITY;

EID: 0032156324     PISSN: 00207683     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0020-7683(98)00009-2     Document Type: Article

References (54)

1. Aifantis, E. (1987) On the physics of plastic deformation. International Journal of Plasticity 3, 211-247.
2. Aifantis, E. (1995) From micro-to macro-plasticity: the scale-invariance approach. J. Eng. Mat. Tech. 117, 352-355.
3. Armstrong, P. J. and Frederick, C. O. (1966) A mathematical representation of the multiaxial Bauschinger effect. General Electricity Generating Board Report No. RD/B/N/731. o. O.
4. Arndt, S., Klingbeil, D. and Svendsen, B. (1997) On the simulation of warm pre-stressing and ductile crack extension by constitutive modelling. Transactions of the 14th International Conference on Structural Mechanics in Reactor Technology, 4, pp. 689-696.
5. Atluri, S. N. (1984) On constitutive relations at finite strain : hypoelasticity and elastoplasticity with isotropic or kinematic hardening. Comp. Methods Appl. Mech. Eng. 43, 137-171.
6. Bammann, D. J. (1990) Modeling temperature and strain rate dependent large deformations of metals. Applied Mechanics Review 43, S312-S319.
7. Bammann, D. J. and Johnson, G. C. (1987) On the kinematics of finite-deformation plasticity. Acta Mechanica 70, 1-13.
8. Bertram, A. (1993) Description of finite inelastic deformations. In MECAMAT '92, "Multiaxial Plasticity", ed. A. Benallal, R. Billardon and D. Marquis, pp. 821-835.
9. Chaboche, J.-L. (1993) Cyclic viscoplastic constitutive relations, Part I: a thermodynamically-consistent formulation. Journal of Applied Mechanics 60, 813-828.
10. Dafalias, Y. F. (1983) A missing link in the macroscopic constitutive formulation of large plastic deformations, Chap. 8. In Plasticity Today, ed. A. Sawczuk and G. Bianchi, pp. 135-151. Elsevier Applied Science, U.K.
11. Dafalias, Y. F. (1985) The plastic spin. Journal of Applied Mechanics 52, 865-871.
12. Dafalias, Y. F. (1993) On multiple spins and texture development. Case study: kinematic and orthotropic hardening. Acta Mechanica 100, 171-194.
13. Dienes, J. K. (1979) On the analysis of rotation and stress rate in deforming bodies. Acta Mechanica 32, 217-232.
14. Dienes, J. K. (1986) A discussion of material rotation and stress rate. Acta Mechanica 65, 1-11.
15. Dogui, A. and Sidoroff, F. (1985) Kinematic hardening in large elastoplastic strain. Eng. Frac. Mech. 21, 685-695.
16. Eterovic, A. L. and Bathe, K. J. (1990) A hyperelastic-based large strain elastoplastic constitutive formulation with combined isotropic-kinematic hardening using logarithmic stresses and strain measures. International Journal of Numerical Methods in Engineering 30, 1099-1115.
17. Green, A. E. and McInnis, B. C. (1967) Generalized hypoplasticity. Proceedings of the Royal Society of Edinburgh A57, 220-230.
18. Green, A. E. and Naghdi, P. M. (1965) A general theory of the elastic-plastic continuum. Arch. Rat. Mech. Anal. A18, 251-281.
19. Haupt, P. (1995) On the thermodynamic representation of viscoplastic material behaviour. Proceedings of the AMSE Materials Division MD 69-1, 503-519.
20. Haupt, P. and Tsakmakis, Ch. (1986) On kinematic hardening and large plastic deformations. International Journal of Plasticity 2, 279-293.
21. Haupt, P. and Tsakmakis, Ch. (1989) On the application of dual variables in continuum mechanics. Continuum Mech. Thermodyn. 1, 165-196.
22. Loret, B. (1983) On the effects of plastic rotation in the finite deformation of anisotropic elastoplastic materials. Mech. Materials 2, 287-304.
23. Lubliner, J. (1973) On the structure of rate equations in materials with internal variables. Acta Mechanica 17, 109-119.
24. Lubliner, J. (1984) A maximum-dissipation principle in generalized plasticity. Acta Mechanica 52, 225-250.
25. Lubliner, J. (1986) On normality rules in large-deformation plasticity. Mech. Mat. 5, 29-34.
26. Mandel, J. (1972) Plasticité classique et viscoplasticité. CISM Course. Springer-Verlag.
27. Mandel, J. (1974) Thermodynamics and plasticity. In Foundations of Continuum Thermodynamics, ed. J. J. Delgado Domingos, M. N. R. Nina and J. H. Whitelaw. MacMillan.
28. Maugin, G. (1992) The Thermodynamics of Plasticity and Fracture. Cambridge University Press.
29. Miehe, C. (1994) On the representation of Prandtl-Reuss tensors within the framework of multiplicative elastoplasticity. International Journal of Plasticity 10, 609-621.
30. Miehe, C. (1996) Exponential map algorithm for stress updates in anisotropic multiplicative elastoplasticity for single crystals. International Journl of Numerical Methods in Engineering 39, 3367-3390.
31. Nagtegaal, J. C. and DeJong, J. E. (1981) Some aspects of nonisotropic work hardening in finite strain plasticity. In Proceedings of the Workshop on Plasticity of Metals at Finite Strain, pp. 65-106. Div. Appl. Mech. Standford University.
32. Noll, W. (1967) Material uniform inhomogeneous material bodies. Arch. Rat. Mech. Anal. 27, 1-32.
33. Noll, W. (1972) A new mathematical theory of simple materials. Arch. Rat. Mech. Anal. 48, 1-50.
34. Paulun, J. E. and Pecherski, R. B. (1987) On the application of the plastic spin concept for the description of anisotropic hardening in finite deformation plasticity. International Journal of Plasticity 3, 303-314.
35. Paulun, J. E. and Pecherski, R. B. (1992) On the relation for the plastic spin. Arch. Appl. Mech. 62, 376-385.
36. Perić, D. (1992) On consistent stress rates in solid mechanics: computational implications. International Journal of Numerical Methods in Engineering 33, 799-817.
37. Sievert, R. (1997) Considerations on the back-stress at large strain and non-isothermal loading. Report BAM-V.31 97/2. Federal Institute for Materials Research and Testing, Berlin.
38. Simo, J. C. (1988a) A framework for finite strain elastoplasticity based on the multiplicative decomposition and hyperelastic relations. Part I: formulation. Comp. Methods Appl. Mech. Eng. 66(2), 199-219.
39. Simo, J. C. (1988b) A framework of finite strain elastoplasticity based on the multiplicative decomposition and hyperelastic relations. Part II: computational aspects. Comp. Methods Appl. Mech. Eng. 66(3), 1-31.
40. Simo, J. C. (1992) Algorithms for static and dynamic multiplicative plasticity that preserve the classical return mappings schemes of the infinitesimal theory. Comp. Methods Appl. Mech. Eng. 99, 61-112.
41. Simo, J. C. and Meschke, G. (1993) A new class of algorithms for classical plasticity extended to finite strains. Application to geomaterials. Comp. Mech. 11, 253-278.
42. Simo, J. C. and Miehe, C. (1991) Coupled associative thermoplasticity at finite strains. Formulation, numerical analysis and implementation. Comp. Methods Appl. Mech. Eng. 98, 41-104.
43. Simo, J. C. and Ortiz, M. (1985) A unified approach to finite deformation elastoplastic analysis based on the use of hyperelastic constitutive relations. Comp. Methods Appl. Mech. Eng. 49, 221-245.
44. Simo, J. C. and Pister, M. (1984) Remarks on rate constitutive equations for finite deformation problems: computational implications. Comp. Methods Appl. Mech. Eng. 46, 201-215.
45. Svendsen, B. (1998a) A thermodynamic formulation of finite-deformation elastoplasticity with hardening based on the concept of material isomorphism. International Journal of Plasticity, in press.
46. Svendsen, B. (1998b) On material isomorphism, material symmetry and material uniformity in finite-deformation elastoplasticity. International Journal of Engineering Science, submitted.
47. Svendsen, B. and Tsakmakis, Ch. (1994) On the generalization of constitutive relations from small to large deformations. Z. angew. Math. Mech. 74, T320-T322.
48. Szabó, L. and Balla, M. (1992) Comparison of some stress rates. International Journal of Solids and Structures 25, 279-297.
49. Truesdell, C. and Noll, W. (1992) The Non-Linear Field Theories of Mechanics, 2nd edn. Springer.
50. Tvergaard, V. and Van der Giessen, E. (1991) Effect of plastic spin on localization predictions for a porous ductile material. Journal of the Mechanics and Physics of Solids 39, 763-781.
51. Tsakmakis, Ch. (1996) Kinematic hardening rules at large deformations, Part I: a constitutive approach. Cont. Mech. Thermodyn. 8, 215-231.
52. Van der Giessen, E. (1991) Micromechanical and thermodynamic aspects of the plastic spin. International Journal of Plasticity 7, 365-386.
53. Weber, G. and Anand, L. (1990) Finite deformation constitutive equations and a time integration procedure for isotropic, hyperelastic-viscoelastic solid. Comp. Methods Appl. Mech. Eng. 79, 173-202.
54. Zavaliangos, A. and Anand, L. (1993) Thermo-elasto-viscoplasticity of isotropic porous metal. Journal of the Mechanics and Physics of Solids 41, 1087-1118.