Analysis of transfer procedures in elastoplasticity based on the error in the constitutive equations: Theory and numerical illustration

International Journal for Numerical Methods in Engineering

Volumn 60, Issue 9, 2004, Pages 1595-1631

  Orlando, A ^a   Peric D ^a  

^a SWANSEA UNIVERSITY   (United Kingdom)

Author keywords

Associative rate independent plasticity; Displacement finite element solution; Error in the constitutive equations; Transfer operators

Indexed keywords

APPROXIMATION THEORY; CHARACTERIZATION; FINITE ELEMENT METHOD;

CONSTITUTIVE EQUATIONS; TRANSFER OPERATORS;

ELASTOPLASTICITY;

FINITE ELEMENT ANALYSIS; PLASTICITY;

EID: 3142675247     PISSN: 00295981     EISSN: None     Source Type: Journal    
DOI: 10.1002/nme.1021     Document Type: Article

References (43)

1. Zienkiewicz OC, Zhu JZ. A simple error estimator and adaptive procedure for practical engineering analysis. International Journal for Numerical Methods in Engineering 1987; 24:337-357.
2. Zienkiewicz OC, Liu YC, Huang GC. Error estimation and adaptivity in flow formulation for forming problems. International Journal for Numerical Methods in Engineering 1988; 25:23-42.
3. Ortiz M, Quigley JJ. Adaptive mesh refinement in strain localization problems. Computer Methods in Applied Mechanics and Engineering 1991; 90:781-804.
4. Perić D, Yu J, Owen DRJ. On error estimates and adaptivity in elastoplastic solids: applications to the numerical simulation of strain localization in classical and Cosserat continua. International Journal for Numerical Methods in Engineering 1994; 37:1351-1379.
5. Johnson C, Hansbo P. Adaptive finite element methods in computational mechanics. Computer Methods in Applied Mechanics and Engineering 1992; 101:143-181.
6. Repin SI, Xanthis L. A posteriori error estimation for elasto-plastic problems based on duality theory. Computer Methods in Applied Mechanics and Engineering 1996; 138:317-339.
7. Rannacher R, Suttmeier FT. A posteriori error control in finite element methods via duality techniques: application to perfect plasticity. Computational Mechanics 1998; 21:123-133.
8. Alberty J, Carstensen C. Numerical analysis of time-depending primal elastoplasticity with hardening. SIAM Journal on Numerical Analysis 2000; 37:1271-1294.
9. Rannacher R, Suttmeier FT. 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.
10. Barthold FJ, Schmidt M, Stein E. Error indicators and mesh refinements for finite-element-computations of elastoplastic deformations. Computational Mechanics 1998; 22:225-238.
11. Ladevèze P. Comparaison de modèles de milieux continus. Ph.D. Thesis, Université Pierre et Marie Curie-Paris 6, France, 1975.
12. Ladevèze P. Sur une famille d'algorithmes en mécanique des structures. Comptes Rendus Académie des Sciences, II 1985; 300:41-44.
13. Ladevèze P. La méthode à grand incrément de temps pour l'analyse des structures à comportement non linéaire décrit par variables internes. Comptes Rendus Académie des Sciences, II 1989; 309:1095-1099.
14. Ladevèze P, Moës N, Douchin B. Constitutive relation error estimators for (visco)plastic finite element analysis with softening. Computer Methods in Applied Mechanics and Engineering 1999; 176:247-264.
15. Orlando A, Perić D. A study on a posteriori error estimation for elastoplastic solids. In Proceedings of the 6th International Conference on Computational Plasticity-COMPLAS VI, Barcelona, 2000.
16. Cirak F, Ramm E. A posteriori error estimation and adaptivity for elastoplasticity using the reciprocal theorem. International Journal for Numerical Methods in Engineering 2000; 47:379-393.
17. Eriksson K, Johnson C. Adaptive finite element methods for parabolic problems I: a linear model problem. SIAM Journal on Numerical Analysis 1991; 28:43-77.
18. Eriksson K, Estep D, Hansbo P, Johnson C. Computational Differential Equation. Cambridge University Press: Cambridge, 1996.
19. Chen Z, Nochetto RH, Schmidt A. Error control and adaptivity for a phase relaxation model. ESAIM-Mathematical Modelling and Numerical Analysis-Modelisation Mathematique et Analyse Numerique 2000; 34:775-797.
20. Wiberg NE, Li XD. Adaptive finite element procedures for linear and non-linear dynamics. International Journal for Numerical Methods in Engineering 1999; 46:1781-1802.
21. Perić D, Hochard Ch, Dutko M, Owen DRJ. Transfer operators for evolving meshes in small strain elasto-plasticity. Computer Methods in Applied Mechanics and Engineering 1996; 137:331-344.
22. Rashid MM. Material state remapping in computational solid mechanics. International Journal for Numerical Methods in Engineering 2002; 55:431-450.
23. Ladevèze P. Nonlinear Computational Structural Mechanics. Springer: Berlin, 1999.
24. Halphen B, Nguyen QS. Sur les materiaux standards generalises. Journal de Mécanique 1975; 14:39-63.
25. Rockafellar RT. Convex Analysis. Princeton University Press: Princeton, 1970.
26. Ekeland I, Temam R. Convex Analysis and Variational Problems. North-Holland: Amsterdam, 1976.
27. Lemaitre J, Chaboche JL. Mechanics of Solid Materials. Cambridge University Press: Cambridge, 1990.
28. Coleman BD, Gurtin ME. Thermodynamics with internal state variables. The Journal of Chemical Physics 1967; 47:597-613.
29. Germain P, Nguyen QS, Suquet P. Continuum thermodynamics. Journal of Applied Mechanics-Transactions of the ASME 1983; 50:1010-1020.
30. Ladevèze P, Pelle JP. La Maitrise du Calcul en Mécanique Linéaire et Non Linéaire, Hermes Science Publications: Paris, 2001.
31. Bataille J, Kestin J. Irreversible processes and physical interpretation of rational thermodynamics. Journal of Non-equilibrium Thermodynamics 1979; 4:229-258.
32. Orlando A. Analysis of adaptive finite element solutions in elastoplasticity with reference to transfer operation techniques. Ph.D. Thesis C/Ph/258/02, University of Wales, Swansea. UK, in preparation.
33. Mikusinski J, Sikorski R. The Elementary Theory of Distributions. Panstwowe Wydawnictwo Naukowe: Warsawa, 1957.
34. Zienkiewicz OC, Taylor RL. The Finite Element Method (5th edn), vol. 1-3. Butterworth-Heinemann: Stoneham, MA, 2000.
35. Camacho GT, Ortiz M. Adaptive Lagrangian modelling of ballistic penetration of metallic targets. Computer Methods in Applied Mechanics and Engineering 1997; 142:269-301.
36. Radovitzky R, Ortiz M. Error estimation and adaptive meshing in strongly nonlinear dynamic problems. Computer Methods in Applied Mechanics and Engineering 1999; 172:203-240.
37. Fraeijs de Veubeke B. Displacement and equilibrium models in the finite element method. In Stress Analysis, Zienkiewicz OC, Holister GS (eds), Chapter 9. Wiley: New York, 1965; 145-197.
38. Lee N, Bathe KJ. Error indicators and adaptive remeshing in large deformation finite element analysis. Finite Elements in Analysis and Design 1994; 16:99-139.
39. Ladevèze P, Moës N. A new a posteriori error estimation for nonlinear time dependent finite element analysis. Computer Methods in Applied Mechanics and Engineering 1997; 157:45-68.
40. Ladevèze P, Leguillon D. Error estimate procedure in the finite element method and applications. SIAM Journal on Numerical Analysis 1983; 20:485-509.
41. Ladéveze P, Coffignal G, Pelle JP. Accuracy of elastoplastic and dynamic analysis. In Accuracy Estimates and Adaptive Refinements in Finite Element Computations, Babuska I, Zienkiewicz OC, Gago J, de A. Oliveira ER (eds), Chapter 11. Wiley: New York, 1986; 181-203.
42. Babuska I, Rheinboldt WC. A posteriori error estimates for the finite element method. International Journal for Numerical Methods in Engineering 1978; 12:1597-1615.
43. Coffignal G. Optimisation et Fiabilité des Calculs Eléments Finis en Elastoplasticité. Ph.D. Thesis, Université Pierre et Marie Curie-Paris 6, France, 1987.