Exact integration of the von Mises elastoplasticity model with combined linear isotropic-kinematic hardening

International Journal of Plasticity

Volumn 25, Issue 6, 2009, Pages 1083-1106

  Kossa, Attila ^a   Szabó, László ^a  

^a BUDAPEST UNIVERSITY OF TECHNOLOGY AND ECONOMICS   (Hungary)

Author keywords

Combined hardening; Consistent tangent; Exact integration; von Mises elastoplasticity

Indexed keywords

AMPLITUDE MODULATION; ELASTICITY; ELASTOPLASTICITY; HARDENING; KINEMATICS; PLASTICITY; SOLS;

ANALYTICAL SOLUTIONS; COMBINED HARDENING; CONSISTENT TANGENT; CONSTANT STRAIN RATES; CONSTANT STRESS; ELASTOPLASTICITY MODELS; EXACT INTEGRATION; EXACT SOLUTIONS; INTEGRATION SCHEMES; ISOTROPIC-KINEMATIC HARDENINGS; NON-LINEAR STRAINS; RADIAL-RETURN METHODS; SEMI-ANALYTICAL SOLUTIONS; SMALL STRAINS; STANDARD FINITE ELEMENTS; STRAIN INCREMENTS; UPDATING ALGORITHMS; VON MISES ELASTOPLASTICITY;

STRAIN RATE;

EID: 63049131571     PISSN: 07496419     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ijplas.2008.08.003     Document Type: Article

References (44)

1. Abramowitz M., and Stegun I.A. Handbook of Mathematical Functions. Applied Mathematics Series vol. 55 (1968), Dover Publications, New York Chapter 5
2. Armstrong, P.J., Frederick, C.O., 1966. A mathematical representation of the multiaxial Bauschinger effect. Report RD/B/N731, CEGB, Central Electricity Generating Board, Berkeley, UK.
3. Artioli E., Auricchio F., and Beir ãoda Veiga L. A novel 'optimal' exponential-based integration algorithm for von-Mises plasticity with linear hardening: theoretical analysis on yield consistency, accuracy, convergence and numerical investigations. Int. J. Numer. Methods Eng. 67 (2006) 449-498
4. 2 plasticity with linear hardening. Int. J. Numer. Methods Eng. 72 (2007) 422-463
5. Auricchio F., and Beirão da Veiga L. On a new integration scheme for von-Mises plasticity with linear hardening. Int. J. Numer. Methods Eng. 56 (2003) 1375-1396
6. Auricchio F., and Taylor R.L. Two material models for cyclic plasticity: nonlinear kinematic hardening and generalized plasticity. Int. J. Plasticity 11 (1995) 65-98
7. Axelsson K., and Samuelsson A. Finite element analysis of elastic-plastic materials displaying mixed hardening. Int. J. Numer. Methods Eng. 14 (1979) 211-225
8. Caddemi S. Computational aspects of the integration of the von Mises linear hardening constitutive laws. Int. J. Plasticity 10 (1994) 935-956
9. Carosio A., Willam K., and Etse G. On the consistency of viscoplastic formulations. Int. J. Solids Struct. 37 (2000) 7349-7369
10. Chaboche J.L. A review of some plasticity and viscoplasticity constitutive theories. Int. J. Plasticity 1 (2008) 10.1016/j.ijplas.2008.03.009
11. Chan A.H.C. Exact stress integration for von Mises elasto-plastic model with constant hardening modulus. Int. J. Numer. Anal. Methods Geomech. 20 (1996) 605-613
12. Chen W.F., and Han D.J. Plasticity for Structural Engineers (1988), Springer, New York
13. Cocchetti G., and Perego U. A rigorous bound on error in backward-difference elastoplastic time-integration. Comput. Methods Appl. Mech. Eng. 192 (2003) 4909-4927
14. Dominici D. Nested derivatives: a simple method for computing series expansions of inverse functions. Int. J. Math. Math. Sci. 2003 (2003) 3699-3715
15. Dunne F., and Petrinic N. Introduction to Computational Plasticity (2005), Oxford University Press, New York
16. Gratacos P., Montmitonnet P., and Chenot J.L. An integration scheme for Prandtl-Reuss elastoplastic constitutive equations. Int. J. Numer. Methods Eng. 33 (1992) 943-961
17. Hiley R.A., and Rouainia M. Explicit Runge-Kutta methods for the integration of rate-type constitutive equations. Comput. Mech. 42 (2008) 53-66
18. Hong H.K., and Liu C.S. Prandtl-Reuss elastoplasticity: on-off switch and superposition formulae. Int. J. Solids Struct. 34 (1997) 4281-4304
19. Khan A.S., and Huang S. Continuum Theory of Plasticity (1995), John Wiley & Sons, New York
20. Khoei A.R., and Jamali N. On the implementation of a multi-surface kinematic hardening plasticity and its applications. Int. J. Plasticity 21 (2005) 1741-1770
21. Krieg R.D., and Krieg D.B. Accuracies of numerical solution methods for the elastic-perfectly plastic model. J. Pressure Vessel Technol. (ASME) 99 (1977) 510-515
22. Krieg R.D., and Xu S. Plane stress linear hardening plasticity theory. Finite Elements Anal. Des. 27 (1997) 41-67
23. Liu C.S. A consistent numerical scheme for Mises mixed hardening constitutive equations. Int. J. Plasticity 20 (2004) 663-704
24. Loret B., and Prevost J.H. Accurate numerical solution for Drucker-Prager elastic-plastic models. Comput. Methods Appl. Mech. Eng. 54 (1986) 259-277
25. Mukherjee S., and Liu C.S. Computational isotropic-workhardening rate-independent elastoplasticity. J. Appl. Mech. 70 (2003) 644-648
26. Nemat-Nasser S. Plasticity. A Treatise on Finite Deformation of Heterogeneous Inelastic Materials (2004), Cambridge University Press, Cambridge
27. Ponthot J.P. Unified stress update algorithms for the numerical simulation of large deformation elasto-plastic and elasto-viscoplastic processes. Int. J. Plasticity 18 (2002) 91-126
28. Reuss E. Berücksichtigung der elastischen Formänderung in der Plastizitätstheorie. Zeits. Angew. Math. Mech. (ZAMM) 10 (1930) 266-274
29. Rezaiee-Pajand M., and Nasirai C. On the integration schemes for Drucker-Prager's elastoplastic models based on exponential maps. Int. J. Numer. Methods Eng. 74 (2008) 799-826
30. Ristinmaa M. Tangent Modulus in Finite Element Calculations for Non-Linear Materials. LUTFD2/(TFHT-3033), Div. of Solid Mechanics (1990), Lund University
31. Ristinmaa M., and Tryding J. Exact integration of constitutive equations in elasto-plasticity. Int. J. Numer. Methods Eng. 36 (1993) 2525-2544
32. Romashchenko V.A., Lepikhin P.P., and Ivashchenko K.B. Exact solution of problems of flow theory with isotropic-kinematic hardening. Part 1. Setting the loading trajectory in the space of stress. Strength Mater. 31 (1999) 582-591
33. Simo J.C., and Hughes T.J.R. Computational Inelasticity (1998), Springer, Berlin
34. Spanier J., and Oldham K.N. An Atlas of Functions (1987), Springer, Berlin
35. Stein E., de Borst R., and Hughes T.J.R. Encyclopedia of Computational Mechanics vol. 2 (2004), John Wiley & Sons, New York
36. 2 flow theory of plasticity with linear isotropic hardening. Comput. Methods Appl. Mech. Eng.
37. Szabó L., and Kovács A. Numerical implementation of Prager's kinematic hardening model in exactly integrated form for elastic-plastic analysis. Comput. Struct. 26 (1987) 815-822
38. Wallin M., and Ristinmaa M. Accurate stress updating algorithm based on constant strain rate assumption. Comput. Methods Appl. Mech. Eng. 190 (2001) 5583-5601
39. Wallin M., and Ristinmaa M. An alternative method for the integration of continuum damage evolution laws. Comput. Mech. 41 (2008) 347-359
40. Wang, X., Chang, L., 1985. Exact integration of constitutive equations of kinematic hardening material and its extended applications. SMIRT-8, Brussels, Proc. Paper L2/3, pp. 65-70.
41. Wei Z., Peric D., and Owen D.R.J. Consistent linearization for the exact stress update of Prandtl-Reuss non-hardening elastoplastic models. Int. J. Numer. Methods Eng. 39 (1996) 1219-1235
42. Wolfram Research, Inc., 2005. Mathematica Edition: Version 5.2. Wolfram Research, Inc., Champaign, IL.
43. Yoder P.J., and Whirley R.G. On the numerical implementation of elastoplastic models. J. Appl. Mech. 51 (1984) 283-288
44. Yang Y., Muraleetharan K.K., and Yu H.S. Generalized trapezoidal numerical integration of an advanced soil model. Int. J. Numer. Anal. Methods Geomech. 32 (2008) 43-64