Robust integration schemes for generalized viscoplasticity with internal-state variables

Computers and Structures

Volumn 74, Issue 5, 2000, Pages 601-628

  Saleeb, A F ^a   Wilt, T E ^a   Li, W ^a  

^a University of Akron   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; ANISOTROPY; FINITE ELEMENT METHOD; INTEGRATION; ITERATIVE METHODS; MATHEMATICAL MODELS; STIFFNESS;

GENERALIZED VISCOPLASTICITY; INTERNAL STATE VARIABLES;

VISCOPLASTICITY;

EID: 0033904680     PISSN: 00457949     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0045-7949(99)00020-6     Document Type: Article

References (33)

1. Coleman B.D., Gurtin M.E. Thermodynamics with internal state variables. J. Chem. Phys. 47:(2):1967;597-613.
2. Lubliner J. On the structure of rate equations of materials with internal variables. Acta Mechanica. 17:1973;109-119.
3. Germain P., Nguyen Q.S., Suquet P. Continuum thermodynamics. J. Appl. Mech. ASME. 50:1983;1010-1120.
4. Lemaitre J., Chaboche J.L. Mechanics of solid materials. 1990;Cambridge University Press, Cambridge.
5. Chaboche J.L. Constitutive equations for cyclic viscoplasticity. Int. J. Plasticity. 5:1989;247-302.
6. Arnold S.M., Saleeb A.F. On the thermodynamic framework of generalized, coupled thermoelastic-viscoplastic-damage modeling. Int. J. Plasticity. 10:(3):1994;263-278.
7. Arnold S.M., Saleeb A.F., Wilt T.E. A modeling investigation of thermal and strain induced recovery and nonlinear hardening in potential based viscoplasticity. J. Eng. Mater. Tech. ASME. 117:1995;157-167.
8. Arnold SM, Saleeb AF, Castelli MG, A fully associative, nonlinear, kinematic, unified viscoplastic model for titanium based matrices: life prediction methodology for titanium matrix composites, ASTM STP 1253, Johnson WS, Larsen JM, Cox BN, 1996.
9. Arnold SM, Saleeb AF, Castelli MG, A fully associative, nonisothermal, nonlinear kinematic, unified viscoplastic model for titanium based matrices: thermomechanicsl fatigue behavior of materials, vol. 2, ASTM STP 1263, Verilli MJ, Castelli MG, Philadelphia, 1995.
10. Robinson D.N., Duffy S.F. Continuum deformation theory for high-temperature metallic composites. J. Eng. Mech. ASCE. 116:(4):1990;832-844.
11. Robinson D.N., Duffy S.F., Ellis J.R. A viscoplastic constitutive theory for metal-Matrix composites atb high-temperature. Sehitoglu H., Zamrik S.Y. Thermal stress, material deformation, and thermomechanical fatigue. vol. 123:1987;49-56 ASME-PVP, New York.
12. Freed A.D., Walker K.P. Viscoplasticity with creep and plasticity bounds. Int. J. Plasticity. 9:1993;213-242.
13. Simo J.C., Taylor R.L. A return mapping algorithm for plane stress elastoplasticity. Int. J. Num. Meth. Eng. 22:1986;649-670.
14. Simo J.C., Taylor R.L. Consistent tangent operators for rate-independent elastoplasticity. Comp. Meth. Appl. Mech. Eng. 48:1985;101-118.
15. Simo J.C. Nonlinear stability of the time-discrete variational problem in nonlinear heat conduction, plasticity, and elastoplasticity. Comput. Meth. Appl. Mech. Eng. 88:1991;111-131.
16. Ju J.W. Consistent tangent moduli for a class of viscoplasticity. J. Eng. Mech. ASCE. 116:1990;1704-1779.
17. Ortiz M., Popov E.P. Accuracy and stability of integration algorithms for elastoplastic constitutive relations. Int. J. Num. Meth. Eng. 21:1985;1561-1576.
18. Burlet H., Cailletaud G. Numerical techniques for cyclic plasticity at variable temperature. Eng. Comput. 3:1986;143-153.
19. Loret B., Hammoum F., Dafalias Y.F. A note on the accuracy of stress-point algorithms for anisotropic elastic-plastic solids. Comput. Meth. Appl. Mech. Eng. 98:1992;399-409.
20. Lush A.M., Weber G., Anand L. An implicit time-integration procedure for a set of internal variable constitutive equations for isotropic elasto-viscoplasticity. Int. J. Plasticity. 5:1987;521-549.
21. Caddemi S., Martin J.B. Convergence of the Newton-Raphson algorithm in elastic-plastic incremental analysis. Int. J. Num. Meth. Eng. 31:1991;177-191.
22. Hornberger K., Stamm H. An implicit integration algorithm with a projection method for viscoplastic constitutive equations. Int. J. Num. Meth. Eng. 28:1989;2397-2421.
23. Auricchio F., Taylor R.L. A generalized elastoplastic plate theory and its algorithmic implementation. Int. J. Numer. Meth. Eng. 37:1994;2583-2608.
24. Freed AD, Walker KP. Exponential integration algorithms applied to viscoplasticity, NASA TM 104461, 3rd International Conference on Computational Plasticity, Barcelona, 1992.
25. Saleeb A.F., Wilt T.E. Analysis of the anisotropic viscoplastic-damage response of composite laminates-continuum basis and computational algorithm. Int. J. Num. Meth. Eng. 36:1993;1629-1660.
26. Kojic M., Bathe K.J. The 'effective-stress function' algorithm for thermo-elasto-plasticity and creep. Int. J. Numer. Meth. Eng. 24:1987;1509-1532.
27. Bathe K.J. Finite element procedures. 1996;Prentice-Hall, Englewood Cliffs, NJ.
28. Spencer A.J.M. Continuum theory of the mechanics of fiber-reinforced composites. 1984;Springer-Verlag, Berlin.
29. Saleeb AF, Wilt TE, Li W. An Implicit time-stepping scheme for generalized viscoplasticity with dynamic recovery, Computational Mechanics 1998;21(6):429-440.
30. Crisfield M.A. Nonlinear finite element method of structures and solids, Chichester. 1991;Wiley, New York.
31. Wilt T.E., Saleeb A.F., Chang T.Y.P. A mixed element for plates and shells. Comput. Struct. 37:1990;597-612.
32. Arya VK. Efficient and accurate explicit integration algorithms with application to viscoplastic models. NASA CR 195342, 1994.
33. Lamba H.S., Sidebottom O.M. Cyclic plasticity for nonproportional paths, part I and II. J. Eng. Materials Tech. 100:1978;93-111.