A formulation of anisotropic continuum elastoplasticity at finite strains. Part I: Modelling

International Journal of Plasticity

Volumn 22, Issue 12, 2006, Pages 2346-2365

  Sansour, Carlo ^a   Karšaj, Igor ^b   Sorić, Jurica ^b  

^a UNIVERSITY OF NOTTINGHAM   (United Kingdom)

^b UNIVERSITY OF ZAGREB   (Croatia)

Author keywords

Anisotropic plasticity; Finite strains; Isotropic hardening; Multiplicative inelasticity; Orthotropic yield function

Indexed keywords

ANISOTROPY; NUMERICAL ANALYSIS; PLASTIC PRODUCTS; STRAIN;

ANISOTROPIC PLASTICITY; FINITE STRAINS; ISOTROPIC HARDENING; MULTIPLICATIVE INELASTICITY; ORTHOTROPIC YIELD FUNCTION;

ELASTOPLASTICITY;

EID: 33747793383     PISSN: 07496419     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ijplas.2006.04.002     Document Type: Article

References (58)

1. Banabic D. An improved analytical description of orthotropy in metallic sheets. Int. J. Plasticity 21 (2005) 493-512
2. Barlat F., Maeda Y., Chung K., Yanagawa M., Brem J.C., Hayashida Y., Lege D.J., Matsui K., Murtha S.J., Hattori S., Becker R.C., and Makosey S. Yield function development for aluminum alloy sheets. J. Mech. Phys. Solids 45 (1997) 1727-1763
3. Bertram A. An alternative approach to finite plasticity based on material isomorphisms. Int. J. Plasticity 15 (1999) 353-374
4. Besseling J. A thermodynamic approach to rheology. In: Parkus H., and Seddov L.I. (Eds). Irreversible Aspects of Continuum Mechanics (1968), Springer, Wien
5. Boehler J.P. Applications of Tensor Functions in Solid Mechanics (1987), Springer Verlag, Wien
6. Bron F., and Besson J. A yield function for anisotropic materials application to aluminum alloys. Int. J. Plasticity 20 (2004) 937-963
7. Bucher A., Goerke U.-J., and Kreissig R. A material model for finite elasto-plastic deformations considering a substructure. Int. J. Plasticity 20 (2004) 619-642
8. Cleja-Tigoiu S., and Maugin G. Eshelbys stress tensors in finite elastoplasticity. Acta Mech. 139 (2000) 231-249
9. Cleja-Tigoiu S., and Soos E. Elastoviscoplastic models with relaxed configurations and internal state variables. Appl. Mech. Rev. 43 (1990) 131-151
10. Dafalias Y. Plastic spin: necessity or redundancy. Int. J. Plasticity 14 (1998) 909-931
11. Dafalias Y. Orientational evolution of plastic orthotropy in sheet metals. J. Mech. Phys. Solids 48 (2000) 2231-2255
12. Darrieulat M., and Montheillet F. A texture based continuum approach for predicting the plastic behaviour of rolled sheet. Int. J. Plasticity 19 (2003) 517-546
13. Eidel B., and Gruttmann F. Elastoplastic orthotropy at finite strains: multiplicative formulation and numerical implementation. Comput. Mater. Sci. 28 (2003) 732-742
14. Haupt P. On the concept of an intermediate configuration and its application to a representation of viscoelastic-plastic material behaviour. Int. J. Plasticity 1 (1985) 279-293
15. Haupt P., and Kersten T. On the modelling of anisotropic material behaviour in viscoplasticity. Int. J. Plasticity 19 (2003) 1885-1915
16. Helling D.E., Miller A.K., and Stout M.G. An experimental investigation of the yield loci of 1100-0 aluminum, 70:30 brass and an overaged 2024 aluminum alloy after various prestrain. J. Eng. Mater. Technol., ASME 108 (1986) 313-320
17. Hill R. The Mathematical Theory of Plasticity (1950), Oxford University Press, London
18. Hu W. An orthotropic yield criterion in a 3-d general stress state. Int. J. Plasticity 21 (2005) 1771-1796
19. Hull D., and Clyne T.W. An Introduction to Composite Materials (1996), Cambridge University Press
20. Ikegami K. Experimental plasticity on the anisotropy of metals. In: Boehler J.P. (Ed). Proceedings of the Euromech Colloquium 115 (1982), Editions du Centre National de la Recherche Scientifique, Paris 201-227
21. Ishikawa H. Subsequent yield surface probed from its current center. Int. J. Plasticity 13 (1997) 533-549
22. Itskov M. On the application of the additive decomposition of generalized strain measures in large strain plasticity. Mech. Res. Commun. 31 (2004) 507-517
23. Karafillis A.P., and Boyce M.C. A general anisotropic yield criterion using bounds and a transformation weighting tensor. J. Mech. Phys. Solids 41 (1993) 1859-1886
24. Khan A.S., and Wang X. An experimental study on subsequent yield surface after finite shear prestraining. Int. J. Plasticity 9 (1993) 889-905
25. Kocks U.F., Tome C.N., and Wenk H.-R. Texture and Anisotropy (1998), Cambridge University Press
26. Kowalczyk K., and Gambin W. Model of plastic anisotropy evolution with texture-dependent yield surfaceá. Int. J. Plasticity 20 (2004) 19-54
27. Kröner E. Allgemeine kontinuumstheorie der versetzungen und eigenspannungen. Arch. Rat. Mech. Anal. 4 (1960) 273-334
28. Kuroda M. Interpretation of the behavior of metals under large plastic shear deformations: a macroscopic approach. Int. J. Plasticity 13 (1997) 359-383
29. Kuroda M. Interpretation of the behavior of metals under large plastic shear deformations: comparison of macroscopic predictions to physically based prediction. Int. J. Plasticity 15 (1999) 1217-1236
30. Lee E. Elastic-plastic deformation at finite strains. ASME J. Appl. Mech. 36 (1969) 1-6
31. Lemaitre J., and Chaboche J.-L. Mechanics of Solid Materials (1990), Cambridge University Press, London
32. Liu I.-S. On representations of anisotropic invariants. Int. J. Eng. Sci. 20 (1982) 1099-1109
33. Maugin G.A. Eshelby stress in elastoplasticity and ductile fracture. Int. J. Plasticity 10 (1994) 393-408
34. Menzel A., and Steinmann P. On the spatial formulation of anisotropic multiplicative elasto-plasticity. Comput. Meth. Appl. Mech. Eng. 192 (2003) 3431-3470
35. Miastkowski J., and Szczepinski W. An experimental study of yield surfaces of pre-strained brass. Int. J. Solids Struct. 1 (1965) 189-194
36. Mollica F., and Srinivasa A.R. A general framework for generating convex yield surfaces for anisotropic metals. Acta Mech. 154 (2002) 61-84
37. Ning J., and Aifantis E. Anisotropic yield and plastic flow of polycrystalline solids. Int. J. Plasticity 12 (1996) 1221-1240
38. Oller S., Car E., and Lubliner J. Definition of a general implicit orthotropic yield criterion. Comput. Meth. Appl. Mech. Eng. 192 (2003) 895-912
39. Papadopoulos P., and Lu J. On the formulation and numerical solution of problems in anisotropic finite plasticity. Comput. Meth. Appl. Mech. Eng. 190 (2001) 4889-4910
40. Phillips A., and Moon H. An experimental investigation concerning yield surfaces and loading surfaces. Acta Mech. 27 (1977) 91-102
41. Phillips R. Crystals, Defects, and Microstructures-modelling Across Scales (2001), Cambridge University Press
42. Qui H.P.T., and Lippmann H. Plastic spin and evaluation of an anisotropic yield condition. Int. J. Mech. Sci. 43 (2001) 1969-1983
43. Rubin M.B. Plasticity theory formulated in terms of physically based micro-structural variables - Part I theory. Int. J. Solids Struct. 19 (1994) 2615-2634
44. Sansour C., and Bocko J. On the numerical implications of multiplicative inelasticity with an anisotropic elastic constitutive law. Int. J. Num. Meth. Eng. 58 (2003) 2131-2160
45. Sansour, C., Karšaj, I., Sorić, J., submitted for publication. On an invariant formulation for anisotropic elastoplasticity at finite strains.
46. Sansour C., and Kollmann F.G. Anisotropic formulations for finite strain viscoplasticity. Applications to shells. In: Wall W.A., Bletzinger K.-U., and Schweizerhof K. (Eds). Trends in Computational Structural Mechanics (2001), CIMNE, Barcelona 198-207
47. Scheidler M., and Wright T.W. A continuum framework for finite viscoplasticity. Int. J. Plasticity 17 (2001) 1033-1085
48. Schroeder J., Gruttmann F., and Löblein J. A simple orthotropic finite elasto-plasticity model based on generalized stress-strain measures. Comput. Mech. 30 (2002) 38-64
49. Smith G. On isotropic functions of symmetric tensors, skew-symmetric tensors and vectors. Int. J. Eng. Sci. 9 (1971) 899-916
50. Spencer A. Theory of invariants. In: Eringen C. (Ed). Continuum Physics vol. I (1971), Academic Press, New York 239-353
51. Stoughton T.B., and Yoon J.W. A pressure-sensitive yield criterion under a non-associated floe rule for sheet metal forming. Int. J. Plasticity 20 (2004) 705-731
52. Svendsen B. On the modelling of anisotropic elastic and inelastic material behaviour at large strain. Int. J. Solids Struct. 38 (2001) 9579-9599
53. Tsakmakis C. Description of plastic anisotropy effects at large deformations - part i: restrictions imposed by the second law and the postulate of il'iushin. Int. J. Plasticity 20 (2004) 167-198
54. Tugcu P., Neale K.W., Wu P.D., and Inal K. Crystal plasticity simulation of the hydrostatic bulge test. Int. J. Plasticity 20 (2004) 1603-1653
55. van der Giesen E. Continuum models for large deformation plasticity. Part i: large deformation plasticity and the concept of a natural reference state. Eur. J. Mech. A/Solids 8 (1989) 14-34
56. Wang C. A new representation theorem for isotropic functions. Arch. Rat. Mech. Anal. 36 (1970) 166-197
57. Zbib H., and Aifantis E. On the concept of relative and plastic spins and its implications to large deformation theories. Acta Mech. 75 (1988) 15-56
58. Zheng Q.-S. Theory of representation for tensor functions - A unified invariant approach to constitutive equations. Appl. Mech. Rev. 47 (1994) 545-587