Consistent finite elastoplasticity theory combining additive and multiplicative decomposition of the stretching and the deformation gradient

International journal of plasticity

Volumn 16, Issue 2, 2000, Pages 143-177

  Xiao, H ^a   Bruhns, O T ^a   Meyers, A ^a  

^a RUHR UNIVERSITY BOCHUM   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

HARDENING; KINEMATICS; PLASTIC DEFORMATION; STRESS ANALYSIS;

DEFORMATION GRADIENTS; FINITE DEFORMATION ELASTOPLASTICITY THEORY;

ELASTOPLASTICITY;

EID: 0033874267     PISSN: 07496419     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0749-6419(99)00045-5     Document Type: Article

References (53)

1. Agah-Tehrani A., Lee E.H., Mallett R.L., Onat E.T. The theory of elastic-plastic deformation at finite strain with induced anisotropy modeled as combined isotropic-kinematical hardening. J. Mech. Phys. Solids. 35:1987;519-539.
2. Backmann M.E. From the relation between stress and finite elastic and plastic strains under impulsive loading. J. Appl. Phys. 35:1964;2524-2533.
3. Brannon R.M. Caveats concerning conjugate stress and strain measures for frame indifferent anisotropic elasticity. Acta Mech. 129:1998;107-116.
4. Bruhns O.T., Diehl H. An internal variable theory of inelastic behaviour at high rates of strain. Arch. Mech. 41:1989;427-460.
5. Bruhns O.T., Xiao H., Meyers A. Self-consistent Eulerian rate type elastoplasticity models based upon the logarithmic stress rate. Int. J. Plasticity. 15:1999;479-520.
6. p in plasticity ASME J. Appl. Mech. 47:1980;672-675.
7. Casey J., Naghdi P.M. Discussion of Lubarda and Lee (1981), cited below. ASME J. Appl. Mech. 48:1981;983-984.
8. Casey J., Naghdi P.M. On the use of invariance requirements for intermediate configurations associated with the polar decomposition of a deformation gradient. Q. Appl. Math. 41:1983;339-342.
9. Casey J., Naghdi P.M. A prescription for the identification of finite plastic strain. Int. J. Engng. Sci. 30:1992;1257-1278.
10. Dafalias Y.F. Issues in constitutive formulation at large elastoplastic deformation. Part 1: Kinematics. Acta Mech. 69:1987;119-138.
11. Dafalias Y.F. Issues in constitutive formulation at large elastoplastic deformation. Part 2: Kinetics. Acta Mech. 73:1988;121-146.
12. Dienes J.K. On the analysis of rotation and stress rate in deforming bodies. Acta Mech. 32:1979;217-232.
13. Dienes, J.K., 1986. A discussion of material rotation and stress rate. Acta Mech. 65, 1-11.
14. Drucker, D.C., 1988. Conventional and unconventional plastic response and representation. Appl. Mech. Rev. 41, 151-167.
15. Green A.E., Naghdi P.M. A general theory of an elastic-plastic continuum. Arch. Rat. Mech. Anal. 18:1965;251-281.
16. Green, A.E., Naghdi, P.M. 1966. A thermodynamic development of elastic-plastic continua. In: Parker, H., Sedov, L.I. (Eds.), Proc. IUTAM Symposum on Irreversible Aspects of Continuum Mechanics and Transfer of Physical Characteristics in Moving Fluids, Springer-Verlag, pp. 117-131.
17. Green A.E., Naghdi P.M. Some remarks on elastic-plastic deformation at finite strain. Int. J. Engng. Sci. 9:1971;1219-1229.
18. Guo Z.H. Rates of stretch tensors. J. Elasticity. 14:1984;263-267.
19. Guo Z.H., Lehmann Th., Liang H.Y., Man C.S. Twirl tensors and the tensor equation. AX-XA=C J. Elasticity. 27:1992;227-245.
20. Hill R. Aspects of invariance in solid mechanics. Advances in Appl. Mech. 18:1978;1-75.
21. Hoger A., Carlson D.E. Determination of the stretch and rotation in the polar decomposition of the deformation gradient. Q. Appl. Math. 42:1984;113-117.
22. Hoger A. The stress conjugate to the logarithmic strain, Int. J. Solids Struct. 23:1987;1645-1656.
23. Khan A.S., Huang S.J. Continuum Theory of Plasticity. 1995;John Wiley & Sons, New York.
24. Kröner E. Allgemeine Kontinuumstheorie der Versetzungen und Eigenspannungen. Arch. Rat. Mech. Anal. 4:1960;273-334.
25. Lee E.H., Liu D.T. Finite strain elastic-plastic theory with application to plane-wave analysis. J. Appl. Phys. 38:1967;19-27.
26. Lee E.H. Elastic-plastic deformation at finite strains. ASME J. Appl. Mech. 36:1969;1-6.
27. Lee E.H. Some comments on elastic-plastic analysis. Int. J. Solids Struct. 17:1981;859-872.
28. Lehmann Th. Anisotrope plastische Formänderungen. Romanian J. Tech. Sci. Appl. Mech. 17:1972;1077-1086.
29. Lehmann Th. Einige Bemerkungen zu einer allgemeinen Klasse von Stoffgesetzen für große elasto-plastische Formänderungen. Ing.-Arch. 41:1972;297-310.
30. Lehmann Th., Guo Z.H., Liang H.Y. The conjugacy between Cauchy stress and logarithm of the left stretch tensor. Eur. J. Mech., A/Solids. 10:1991;297-310.
31. Lubarda V.A., Lee E.H. A correct definition of elastic and plastic deformation and its computational significance. ASME J. Appl. Mech. 48:1981;35-40.
32. Naghdi P.M. A critical review of the state of finite plasticity. ZAMP. 41:1990;315-394.
33. Nagtegaal, J.C., de Jong, J.E. 1982. Some aspects of non-isotropic work-hardening in finite strain plasticity. In: Lee, E.H., Mallett, R.L. (Eds.), Proc. of the Workshop on Plasticity of Metals at Finite Strain: Theory, experiment and computation, Stanford University, pp. 65-102.
34. Neale K.W. Phenomenological constitutive laws in finite plasticity. SM Archives. 6:1981;79-128.
35. Nemat-Nasser S. Decomposition of strain measures and their rates in finite deformation elastoplasticity. Int. J. Solids Struct. 15:1979;155-166.
36. Nemat-Nasser S. On finite deformation elastoplasticity. Int. J. Solids Struct. 18:1982;857-872.
37. Nemat-Nesser S. On finite plastic flow of crystalline solids and geomaterials. ASME J. Appl. Mech. 50:1983;1114-1126.
38. Nemat-Nasser S. Certain basic issues in finite-deformation continuum plasticity. Meccanica. 24:1990;223-229.
39. Nemat-Nasser S. Phenomenological theories of elastoplasticity and strain localization at high strain rates. Appl. Mech. Rev. 45:1992;S19-S45.
40. Ogden R.W. Nonlinear elastic deformations. 1984;Chichester, Ellis Horwood.
41. Reinhardt W.D., Dubey R.N. Eulerian strain-rate as a rate of logarithmic strain. Mech. Res. Commun. 22:1995;165-170.
42. Reinhardt W.D., Dubey R.N. Coordinate-independent representation of spin tensors in continuum mechanics. J. Elasticity. 42:1996;133-144.
43. Simo J.C., Pister K.S. Remarks on rate constitutive equations for finite deformation problem: computational implications. Comp. Meth. Appl. Mech. Engng. 46:1984;201-215.
44. -12 and more general isotropic tensor functions of C J. Elasticity. 15:1985;319-323.
45. Willis J.R. Some constitutive equations applicable to problems of large dynamic plastic deformation. J. Mech. Phys. Solids. 17:1969;359-369.
46. Xiao H. Unified explicit basis-free expressions for time rate and conjugate stress of an arbitrary Hill's strain. Int. J. Solids Struct. 32:1995;3327-3340.
47. Xiao H., Bruhns O.T., Meyers A. A new aspect in the kinematics of large deformation. Gupta N.K. Plasticity and impact mechanics. 1996;100-109 New Age Intern Publ. Ltd, New Delhi.
48. Xiao H., Bruhns O.T., Meyers A. Hypo-elasticity model based upon the logarithmic stress rate. J. Elasticity. 47:1997;51-68.
49. Xiao H., Bruhns O.T., Meyers A. Logarithmic strain, logarithmic spin and logarithmic rate. Acta Mech. 124:1997;89-105.
50. Xiao H., Bruhns O.T., Meyers A. On objective corotational rates and their defining spin tensors. Int. J. Solids Struct. 35:1998;4001-4014.
51. Xiao H., Bruhns O.T., Meyers A. Strain rates and material spins. J. Elasticity. 52:1998;1-41.
52. Xiao H., Bruhns O.T., Meyers A. Objective corotational rates and unified work-conjugacy relation between Lagrangean and Eulerian strain and stress measures. Arch. Mech. 50:1998;1015-1045.
53. *=λ(trD)I+2μD and its significance to finite inelasticity. Acta Mech. 138, 31-50.