On the implicit integration of rate-dependent inelastic constitutive models

International Journal for Numerical Methods in Engineering

Volumn 62, Issue 13, 2005, Pages 1832-1856

  Kouhia, Reijo ^a   Marjamäki, Pekka ^a   Kivilahti, Jorma ^a  

^a AALTO UNIVERSITY   (Finland)

Author keywords

Backward Euler method; Creep; Discontinuous Galerkin methods; Implicit integration; Implicit Runge Kutta methods

Indexed keywords

ALGORITHMS; GALERKIN METHODS; MATHEMATICAL MODELS; NUMERICAL METHODS; RUNGE KUTTA METHODS;

BACKWARD EULER METHOD; RATE-DEPENDENT INELASTIC CONSTITUTIVE MODELS; RATE-DEPENDENT INELASTIC CREEP MODELS; RUNGA-KUTTA TIME INTEGRATORS;

INTEGRATION;

CREEP; MATHEMATICAL METHOD;

EID: 15844366556     PISSN: 00295981     EISSN: None     Source Type: Journal    
DOI: 10.1002/nme.1252     Document Type: Article

References (30)

1. Chaboche JL, Cailletaud G. Integration methods for complex plastic constitutive equations. Computer Methods in Applied Mechanics and Engineering 1996; 133:125-155.
2. Simo JC, Hughes TJR. Computational Inelasticity. Springer: New York, 1998.
3. Wallin M, Ristinmaa M. Accurate stress updating algorithm based on constant strain rate assumption. Computer Methods in Applied Mechanics and Engineering 2001; 190(42):5583-5601.
4. Krieg RD, Krieg DB. Accuracies of numerical solution methods for the elastic-perfectly plastic model. Journal of Pressure Vessel Technology 1977; 101:510-515.
5. Schreyer HL, Kulak RF, Kramer JM. Accurate numerical solutions for elastic-plastic models. Journal of Pressure Vessel Technology 1979; 101:226-234.
6. Yoder PJ, Whirley RL. On the numerical implementation of elastoplastic models. Journal of Applied Mechanics 1984; 51:283-287.
7. Runesson K, Sture S, Willam K. Integration in computational plasticity. Computers and Structures 1988; 30(1/2):119-130.
8. Hackl K, Schmidt-Baldassari M. Time integration algorithms for evolution equations in finite strain plasticity. In Trends in Computational Structural Mechanics, Wall WA et al. (eds). CIMNE, Barcelona, 2001; 128-139.
9. Schmidt-Baldassari M, Hackl K. Advanced time integration algorithms for rate independent finite strain elastoplasticity. Preprint 03-1, Ruhr-Universität Bochum, Lehrstuhl für Allgemeine mechanik, 2003.
10. Cyr NA, Teter RD. Finite element elastic-plastic-creep analysis of two-dimensional continuum with temperature dependent material properties. Computers and Structures 1973; 3:849-863.
11. Zienkiewicz OC, Cormeau I. Visco-plasticity-plasticity and creep in elastic solids-a unified numerical solution approach. International Journal for Numerical Methods in Engineering 1974; 8:821-845.
12. Cormeau I. Numerical stability in quasi-static elasto/visco-plasticity. International Journal for Numerical Methods in Engineering 1975; 9:109-127.
13. Nguyen QS. On the elasto-plastic initial boundary value problem and its numerical integration. International Journal for Numerical Methods in Engineering 1977; 11:817-832.
14. Hughes TJR, Taylor RL. Unconditionally stable algorithms for quasi-static elasto/visco-plastic finite element analysis. Computers and Structures 1978; 8:169-173.
15. Kanchi MB, Zienkiewicz OC, Owen DRJ. The visco-plastic approach to problems of plasticity and creep involving geometric non-linear effects. International Journal for Numerical Methods in Engineering 1978; 12:169-181.
16. Kirchner E, Kollmann FG. Application of modern time integrators to Hart's inelastic model. International Journal of Plasticity 1999; 15:647-666.
17. Kirchner E, Simeon B. A higher-order time integration method for viscoplasticity. Computer Methods in Applied Mechanics and Engineering 1999; 175:1-18.
18. Eriksson K, Estep D, Hansbo P, Johnsson C. Computational Differential Equations. Studentlitteratur: Lund, 1996.
19. Anand L, Brown S. Constitutive equations for large deformations of metals at high temperatures. In Constitutive Models of Deformation Chandra J, Srivastav RP (eds). SIAM: Philadelphia, 1987; 1-26.
20. Brown SB, Kim KH, Anand L. An internal variable constitutive model for hot working of metals. International Journal of Plasticity 1989; 5:91-130.
21. Frear DR, Burchett SN, Neilsen MK, Stephens JJ. Microstructurally based finite element simulation of solder joint behaviour. Soldering and Surface Mount Technology 1997; 1(25):39-42.
22. Burchett SN, Neilsen MK, Frear DR, Stephens JJ. Computational continuum modelling of solder interconnects. In Design and Reliability of Solders and Solder Interconnects, Mahidhara RK et al. (eds). The Minerals, Metals and Materials Society: Warrendale, PA, 1997; 171-178.
23. Schreyer HL. Unconditionally stable time integration of creep constitutive equations. Eccomas 2000, Barcelona, 11-14 September 2000, CD-ROM Proceedings.
24. Schreyer HL. On time integration of viscoplastic constitutive models suitable for creep. International Journal for Numerical Methods in Engineering 2002; 53(3):637-652.
25. Hairer E, Wanner G. Solving Ordinary Differential Equations II, Stiff and Differential-Algebraic Problems (2nd edn). Springer: Berlin, 1991.
26. Johnson C, Hansbo P. Adaptive finite element methods in computational mechanics. Computer Methods in Applied Mechanics and Engineering 1992; 101:143-181.
27. Rannacher R, Suttmeier F-T. A posteriori error estimation and mesh adaptation for finite element models in elasto-plasticity. Computer Methods in Applied Mechanics and Engineering 1999; 176:333-361.
28. Garofalo F. Fundamentals of Creep and Creep-Rupture in Metals. The MacMillan Co.: New York, 1965.
29. Clark MA, Alden TH. Deformation enhanced grain growth in a superplastic Sn-1% Bi alloy. Acta Metallurgica 1973; 21:1195-1206.
30. Miller A. An inelastic constitutive model for monotonic, cyclic and creep deformations: part I-equations development and analytical procedures. Journal of Engineering Materials Technology 1976; 98:97-105.