A rigorous bound on error in backward-difference elastoplastic time-integration

Computer Methods in Applied Mechanics and Engineering

Volumn 192, Issue 44-46, 2003, Pages 4909-4927

  Cocchetti, Giuseppe ^a   Perego, Umberto ^a  

^a POLITECNICO DI MILANO   (Italy)

Author keywords

Adaptivity; Backward difference; Elastoplasticity; Error estimation; Time integration

Indexed keywords

ELASTOPLASTICITY; FINITE ELEMENT METHOD; INTEGRATION; MATHEMATICAL MODELS; PROBLEM SOLVING; THEOREM PROVING;

ELASTOPLASTIC STRUCTURES;

STRUCTURAL ANALYSIS;

ELASTOPLASTICITY; MATHEMATICAL METHOD;

EID: 0242286165     PISSN: 00457825     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0045-7825(03)00396-7     Document Type: Article

References (27)

1. Abbo A.J. Sloan S.W. An automatic load stepping algorithm with error control Int. J. Numer. Methods Engrg. 39 1996 1737-1759
2. Armero F. Perez-Foguet A. On the formulation of closest-point projection algorithms in elastoplasticity-part I: the variational structure Int. J. Numer. Methods Engrg. 53 2002 297-329
3. Auricchio F. Beirao de Veiga L. On a new integration scheme for von Mises plasticity with linear hardening Int. J. Numer. Methods Engrg. 56 2003 1375-1396
4. Carter P. Martin J.B. Work bounding functions for plastic materials ASME J. Appl. Mech. 98 1976 434-438
5. Chan A.H.C. Exact stress integration for von Mises elastoplastic model with constant hardening modulus Int. J. Numer. Anal. Methods Geomech. 20 1996 605-613
6. Comi C. Perego U. Fracture energy based bi-dissipative damage model for concrete Int. J. Solids Struct. 38 2001 6427-6454
7. de Borst R. Heeres O.M. A unified approach to the implicit integration of standard, non-standard and viscous plasticity models Int. J. Numer. Anal. Methods Geomech. 26 2002 1059-1070
8. Hong H.-K. Liu C.-S. Internal symmetry in bilinear elastoplasticity Int. J. Non-linear Mech. 34 1999 279-288
9. Hong H.-K. Liu C.-S. Internal symmetry in the constitutive model of perfect elastoplasticity Int. J. Non-linear Mech. 35 2000 447-466
10. Keavey M.A. A canonical form return mapping algorithm for rate independent plasticity Int. J. Numer. Methods Engrg. 53 2002 1491-1510
11. Krieg R.D. Krieg D.B. Accuracies of numerical solution methods for the elastic-perfectly plastic model ASME J. Pressure Vessel Technol. 99 1977 510-515
12. Lee J. Fenves G.L. A return-mapping algorithm for plastic damage models: 3-D and plane stress formulation Int. J. Numer. Methods Engrg. 50 2001 487-506
13. 2 elastoviscoplastic flow Int. J. Numer. Methods Engrg. 51 2001 1283-1298
14. Loret B. Prevost J.H. Accurate numerical solutions for Drucker-Prager elastic-plastic models Comput. Methods Appl. Mech. Engrg. 54 1986 259-277
15. Luccioni L.X. Pestana J.M. Rodriguez-Marek A. An implicit integration algorithm for the finite element implementation of a nonlinear anisotropic material model including hysteretic nonlinearity Comput. Methods Appl. Mech. Engrg. 190 2000 1827-1844
16. Luccioni L.X. Pestana J.M. Taylor R.L. Finite element implementation of non-linear elastoplastic constitutive laws using local and global explicit algorithms with automatic error control Int. J. Numer. Methods Engrg. 50 2001 1191-1212
17. Mahnken R. Tikhomirov D. Stein E. Implicit integration scheme and its consistent linearization for an elastoplastic-damage model with application to concrete Comput. Struct. 75 2000 135-143
18. Ortiz M. Popov E.P. Accuracy and stability of integration algorithms for elastoplastic constitutive relations Int. J. Numer. Methods Engrg. 21 1985 1561-1576
19. Ortiz M. Martin J.B. Symmetry-preserving return mapping algorithms and incrementally extremal paths: a unification of concepts Int. J. Numer. Methods Engrg. 28 1989 1839-1853
20. Owen D.R.J. Hinton E. Finite elements in plasticity-theory and practice 1982 Pineridge Press Swansea, UK
21. Perez-Foguet A. Armero F. On the formulation of closest-point projection algorithms in elastoplasticity-part II: globally convergent schemes Int. J. Numer. Methods Engrg. 53 2002 331-374
22. Saleeb F. Wilt T.E. Li W. Robust integration schemes for generalized viscoplasticity with internal-state variables Comput. Struct. 74 2000 601-628
23. Sawyer J.P.G. Wang C.H. Jones R. An implicit algorithm using explicit correctors for the kinematic hardening model with multiple back stresses Int. J. Numer. Methods Engrg. 50 2001 2093-2107
24. Singh A.K. Pandey P.C. An implicit integration algorithm for plane stress damage coupled elastoplasticity Mech. Res. Commun. 26 1999 693-700
25. Van Langen H. Vermeer P.A. Automatic step size correction for non-associated plasticity problems Int. J. Numer. Methods Engrg. 29 1990 579-598
26. Wilkins M.L. Calculation of elastic-plastic flow Alder B. Fernback S. Rotenberg M. Methods of Computational Physics vol. 3 1964 Academic Press New York
27. Yoder P.J. Whirley R.G. On the numerical implementation of elastoplastic models ASME J. Appl. Mech. 51 1984 283-288