Bounds on history-dependent or independent local quantities in viscoelasticity problems solved by approximate methods

International Journal for Numerical Methods in Engineering

Volumn 71, Issue 12, 2007, Pages 1387-1411

  Chamoin, L ^a   Ladeveze P ^a,b  

^a CNRS   (France)

^b UNIVERSITÉ PARIS SACLAY   (France)

Author keywords

Dissipation error; Evolution problems; Finite elements; Output of interest; Verification

Indexed keywords

APPROXIMATION THEORY; BOUNDARY CONDITIONS; ERROR ANALYSIS; FINITE ELEMENT METHOD;

DISSIPATION ERRORS; EVOLUTION PROBLEMS; EXTRACTION TECHNIQUES; OUTPUTS OF INTEREST;

VISCOELASTICITY;

APPROXIMATION THEORY; BOUNDARY CONDITIONS; ERROR ANALYSIS; FINITE ELEMENT METHOD; VISCOELASTICITY;

EID: 34548675800     PISSN: 00295981     EISSN: 10970207     Source Type: Journal    
DOI: 10.1002/nme.1978     Document Type: Article

References (25)

1. Babugka I, Strouboulis T. The Finite Element Method and its Reliability. Oxford University Press: Oxford, 2001.
2. Ladevèze P, Pelle J-P. Mastering Calculations in Linear and Nonlinear Mechanics. Springer: New York, 2004.
3. Wiberg NE, Diez P. Preface. Computer Methods in Applied Mechanics and Engineering 2006; 195(4-6):205-206.
4. Paraschivoiu M, Peraire J, Pateta AT. A posteriori finite element bounds for linear functional outputs of elliptic partial differential equations. Computer Methods in Applied Mechanics and Engineering 1997; 150:289-312.
5. Rannacher R, Suttmeier FT. A posteriori error control and mesh adaptation for finite element models in elasticity and elasto-plasticity. In Advances in Adaptative Computational Method in Mechanics, Ladevèze, Oden (eds). Elsevier: Amsterdam, 1998; 275-292.
6. Cirak F, Ramm E. A posteriori error estimation and adaptivity for linear elasticity using the reciprocal theorem. Computer Methods in Applied Mechanics and Engineering 1998; 156:351-362.
7. Prudhomme S, Oden JT. On goal-oriented error estimation for elliptic problems: application to the control of pointwise errors. Computer Methods in Applied Mechanics and Engineering 1999; 176:313-331.
8. Ladevèze P, Rougeot P, Blanchard P, Moreau JP. Local error estimators for finite element linear analysis. Computer Methods in Applied Mechanics and Engineering 1999; 176:231-246.
9. Strouboulis T, Babuška I, Datta D, Copps K, Gangaraj SK. A posteriori estimation and adaptive control of the error in the quantity of interest - Part 1: A posteriori estimation of the error in the Von Mises stress and the stress intensity factors. Computer Methods in Applied Mechanics and Engineering 2000; 181:261-294.
10. Parès N, Bonet J, Huerta A, Peraire J. The computation of bounds for linear-functional outputs of weak solutions to the two-dimensional elasticity equations. Computer Methods in Applied Mechanics anal Engineering 2006; 195(4-6):406-429.
11. Johnson C, Hansbo P. Adaptative finite element methods for small strain elasto-plasticity. Proceedings of the IUTAM Conference on Finite Inelastic Deformations Theory and Applications, Hannover, Allemagne, 1991.
12. Becker R, Rannacher R. An optimal control approach to shape a posteriori error estimation in finite element methods. In Acta Numerica, Isereles A (ed.). Cambridge University Press: Cambridge, 2001; 10:1-120.
13. Ladevèze P. The Large time increments method for analysis of structures with nonlinear behavior described by internal variables (in French). Comptes Rendus Académie des Sciences, Paris 1989; 309(II):1095-1099.
14. Ladevèze P, Moës N. A new a posteriori error estimation for non-linear time-dependent finite element analysis. Computer Methods in Applied Mechanics and Engineering 1998; 157:45-68.
15. Ladevèze P, Moës N, Douchin B. Constitutive relation error estimations for (visco) plasticity finite element analysis with softening. Computer Methods in Applied Mechanics and Engineering 1999; 176:247-264.
16. Ladevèze P. Upper error bounds on calculated outputs of interest for linear and non-linear structural problems. Comptes Rendus Académie des Sciences - Mécanique, Paris 2006; 334:399-407.
17. Ladevèze P, Rougée P. Plasticity and viscoplasticity under periodic loading: properties and computation of the limit cycle (in French). Comptes Rendus Académie des Sciences - Mécanique, Paris 1985; 301(II):891-894.
18. Duvaut G, Lions JL. Inequalities in Mechanics and Physics. Springer: Berlin, Heidelberg, 1976.
19. Moreau JJ. On unilateral constraints friction and plasticity. New Variational Techniques in Mathematical Physics, edizioni Cremonese, Rome, Italy, 1974; 175-322.
20. Halphen B, Nguyen QS. On generalized standard materials (in French). Journal de Mécanique 1975; 14:39-62.
21. Lemaître J, Chaboche JL. Mechanics of Solid Materials. Cambridge Press: Cambridge, 1994.
22. Ladevèze P. Nonlinear Computational Structural Mechanics - New Approaches and Non-Incremental Methods of Calculation. Springer: New York, 1999.
23. Drucker DC. On the postulate of stability of material in the mechanics of continua. Journal of Mechanics 1964; 3(2):235-249.
24. Stein E, Ohmnimus S, Walhom E. Local error estimates of fem for displacements and stresses in linear elasticity by solving local Neumann problems. International Journal for Numerical Methods in Engineering 2001; 52:727-746.
25. Strouboulis T, Babuška I, Copps K. The design and analysis of the generalized finite element method. Computer Methods in Applied Mechanics and Engineering 2000; 181:43-69.