Modeling of finite strain viscoplasticity based on the logarithmic corotational description

Archive of Applied Mechanics

Volumn 75, Issue 10-12, 2006, Pages 693-708

  Lin, R C ^a   Betten, J ^b   Brocks, W ^c  

^a DALIAN MARITIME UNIVERSITY   (China)

^b RWTH AACHEN UNIVERSITY   (Germany)

^c INSTITUTE OF MATERIALS RESEARCH   (Germany)

Author keywords

Internal dissipation; Logarithmic corotational rate; Viscoplasticity

Indexed keywords

ALGORITHMS; DEFORMATION; HARDENING; STRAIN; TENSORS;

INTERNAL DISSIPATION; LOGARITHMIC COROTATIONAL RATE; LOGARITHMIC COROTATIONAL RATES; LOGARITHMIC STRAIN;

VISCOPLASTICITY;

EID: 33749366029     PISSN: 09391533     EISSN: 14320681     Source Type: Journal    
DOI: 10.1007/s00419-006-0044-6     Document Type: Article

References (38)

1. ABAQUS Manual: getting started with ABAQUS 6.4. Hibbitt, Karlsson & Sorensen, Pawtucket, RI (2003)
2. ABAQUS Theory Manual 5.8. Hibbitt, Karlsson & Sorensen, Pawtucket, RI (1998)
3. Arzt, M., Brocks, W., Mohr, R., Qi, W.: User material routine for simulating anisothermal elasto-viscoplasticity and damage. Technical Note GKSS/WMG/99/11. Institute of Material Research, GKSS Research Center (1999)
4. Asaro, R.J.: Geometrical effects in the inhomogeneous deformation of ductile single crystals. Acta Metall. 27, 445-453 (1979)
5. Asaro, R.J.: Micromechanics of crystals and polycrystals. In: Advances in Applied Mechanics, vol. 23. Academic, New York (1983)
6. Asaro, R.J., Rice, J.R.: Strain localization in ductile single crystals. J. Mech. Phys. Solids 25, 309-338 (1977)
7. Betten, J.: Interpolation methods for tensor functions. In: Avula, X.J.R. (ed.) Mathematical Modelling in Science and Technology, pp. 52-57. Pergamon, New York (1984)
8. Betten, J.: Generalization of nonlinear matherial laws found in experiments to multiaxial states of stress. Eur. J. Mech. A Solids 8, 325-339 (1989)
9. Betten, J.: Kontinuumsmechanik, 2. Aufl. Springer, Berlin Heidelberg New York (2001)
10. Betten, J.: Creep Mechanics, 2nd edn. Springer, Berlin Heidelberg New York (2005)
11. Chaboche, J.L.: Viscoplastic constitutive equations for the description of cyclic and anisotropic behaviour of metals. In: Bull de 1'Acad Polonaise des Sciences, Série Sc et Tech, 17th Polish Conference on Solids Mechanics, Szczyrk, Poland, pp. 33-41 (1975)
12. Chaboche, J.L.: Constitutive equations for cyclic plasticity and cyclic viscoplasticity. Int. J. Plast. 5, 247-302 (1989)
13. Chaboche, J.L.: Cyclic viscoplastic constitutive equations, part I: a thermodynamically consistent formulation. ASME J. Appl. Mech. 60, 813-821 (1993)
14. Chaboche, J.L.: Cyclic viscoplastic constitutive equations, part II: stored energy - comparison between models and experiments. ASME J. Appl. Mech. 60, 822-828 (1993)
15. Chaboche, J.L.: Thermodynamic formulation of constitutive equations and application to the viscoplasticity and viscoelasticity of metals and polymers. Int. J. Solids Struct. 34, 2239-2254 (1997)
16. Chaboche, J.L., Jung, O.: Application of a kinematic hardening viscoplasticity model with thresholds to the residual stress relaxation. Int. J. Plast. 13, 785-807 (1998)
17. Chaboche, J.L., Rousselier, G.: On the plastic and viscoplastic constitutive equations. I. rules developed with internal variable concept. ASME J. Press. Vessel Tech. 34, 153-158 (1983)
18. Chaboche, J.L., Rousselier, G.: On the plastic and viscoplastic constitutive equations. II. application of internal variable concepts to the 316 stainless steel. ASME J. Press. Vessel Tech. 34, 159-164 (1983)
19. Fitzgerald, J.E.: A tensorial Hencky measure of strain and strain rate for finite deformations. J. Appl. Phys. 51, 5111-5115 (1980)
20. Lehmann, Th., Guo, Z.H., Liang, H.Y.: The conjugacy bewteen Cauchy stress and logarithm of the left stretch tensor. Eur. J. Mech. A Solids 10, 395-404 (1991)
21. Lemaitre, J., Chaboche, J.L.: Mechanics of Solids Materials. Cambridge University Press, London (1990)
22. Lin, R.C.: Viscoelastic and elastic-viscoelastic-elastoplastic constitutive characterizations of polymers at finite strains: theoretical and numerical aspects. PhD Thesis, University of the Federal Armed Forces Hamburg (2002)
23. Lin, R.C.: Numerical study of consistency of rate constitutive equations with elasticity at finite deformation. Int. J. Numer. Methods Eng. 55, 1053-1077 (2002)
24. Lin, R.C.: Analytical stress solutions of a closed deformation path with stretching and shearing using the hypoelastic formulations. Eur. J. Mech. A Solids 22, 443-461 (2003)
25. Lin, R.C., Brocks, W.: On a finite viscoplastic theory based on anew internal dissipation inequality. Int. J. Plast. 20, 1281-1311 (2004)
26. Lin, R.C., Schomburg, U.: A finite elastic-viscoelastic-elastoplastic material law with damage: theoretical and numerical aspects. Comput. Methods Appl. Mech. Eng. 192, 1591-1627 (2003)
27. Lin, R.C., Brocks, W., Betten, J.: On internal dissipation inequalities and finite strain inelastic constitutive laws: theoretical and numerical comparisons. Int. J. Plast. (2006)
28. Lion, A.: A physically based method to represent the thermo-mechanical behaviour of elastomers. Acta Mech. 123, 1-25 (1997a)
29. Miehe, C.: A constitutive frame of elastoplasticity at large strains based on the notation of a plastic metric. Int. J. Solids Struct. 35, 3859-3897 (1998)
30. Olschewski, J., Sievert, R., Meersmaun, J., Ziebs, J.: Selection, cablibration and verification of viscoplastic constitutive models used for advanced blading methodology. In: Bachelet, E., et al. (eds.) High Temperature Materials for Power Engineering, pp. 1051-1060. Kluwer, Dordrecht (1990)
31. Olschewski, J., Sievert, R., Bertram, A.: A comparison of the predictive capabilities of two unified constitutive models at elevated temperatures. In: Desai, C.S., et al. (eds.) Constitutive Laws for Engineering Materials. Proceedings of the 3rd International Conference on Constitutive Laws for Engineering Materials: Theory and Applications, New York (1991)
32. Simo, J.C.: Algorithms for static and dynamic multiplicative plasticity that preserve the classical return mapping schemes of the infinitesimal theory. Comput. Methods Appl. Mech. Eng. 99, 61-112 (1992)
33. Simo, J.C.: Numerical analysis and simulation of plasticity. In: Ciarlet, P.O., Lions, J.L. (eds.) Handbook of Numerical Analyis, vol. IV. Elsevier, Amsterdam (1998)
34. Simo, J.C., Hughes, T.J.R.: Computational Inelasticity. Springer, Berlin Heidelberg New York (1998)
35. Simo, J.C., Miehe, C.: Associative coupled thermoplasticity at finite strains: formulation, numerical Analysis and implementation. Comput. Methods Appl. Mech. Eng. 98, 41-104 (1992)
36. Simo, J.C., Pister, K.S.: Remarks on rate constitutive equations for finite deformation problems: computational implicatons. Comput. Methods Appl. Mech. Eng. 46, 201-215 (1984)
37. Xiao, H., Bruhns, O.T., Meyers, A.: On objective corotational rates and their defining spin tensors. Int. J. Solids Struct. 35, 4001-4014 (1998)
38. Xiao, H., Bruhns O.T., Meyers, A.: Strain rates and material spins. J. Elast. 52, 1-41 (1998)