Error estimation of stress intensity factors for mixed-mode cracks

International Journal for Numerical Methods in Engineering

Volumn 68, Issue 3, 2006, Pages 299-316

  Gallimard, Laurent ^a   Panetier, J ^a  

^a CNRS   (France)

Author keywords

Finite element method; Fracture; Goal oriented error estimation; Stress intensity factors

Indexed keywords

A POSTERIORI ERROR ESTIMATOR; ARBITRARY CROWN; ERROR ESTIMATION;

ELASTICITY; ERROR ANALYSIS; FINITE ELEMENT METHOD; FRACTURE; INTEGRAL EQUATIONS; STRESS INTENSITY FACTORS;

CRACKS;

CRACKS; ELASTICITY; ERROR ANALYSIS; FINITE ELEMENT METHOD; FRACTURE; INTEGRAL EQUATIONS; STRESS INTENSITY FACTORS;

EID: 33749543901     PISSN: 00295981     EISSN: 10970207     Source Type: Journal    
DOI: 10.1002/nme.1705     Document Type: Article

References (25)

1. Babuška I, Rheinboldt WC. A posteriori estimates for the finite element method. International Journal for Numerical Methods in Engineering 1978; 12:1597-1615.
2. Ladevèze P, Pelle JP. Méthode de calcul par encadrement des fréquences propres de structures élastiques. Comptes Rendus de l'Académie des Sciences Série II. Paris 1983; 296:1757-1760.
3. 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.
4. Babuška I, Miller A. The post-processing approach of the finite element method part ii: The calculation of the stress intensity factor. International Journal for Numerical Methods in Engineering 1982; 20:1111-1129.
5. Kelly DW, Isles JD. Procedures for residual equilibration and local error estimation in the finite element method. Communications in Applied Numerical Methods 1989; 5:497-505.
6. Rannacher R, Stuttmeier FT. A feedback approach to error control in finite element methods: application to linear elasticity. Computational Mechanics 1997; 19:434-446.
7. Rannacher R, Stuttmeier FT. A posteriori error control and mesh adaptation for f.e. models in elasticity and elastoplasticity. In Advances in Adaptive Computational Methods in Mechanics, Ladevèze P, Oden JT (eds), Studies in Applied Mechanics, vol. 47. Elsevier: Amsterdam, 1998; 275-292.
8. Peraire J, Patera A. Bounds for linear-functional outputs of coercive partial differential equations: local indicators and adaptive refinement. In Advances in Adaptive Computational Methods, Ladevèze P, Oden JT (eds). Elsevier: Amsterdam, 1998; 199-216.
9. 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.
10. Ladevèze P, Rougeot P, Blanchard P, Moreau JP. Local error estimators for finite element analysis. Computer Methods in Applied Mechanics and Engineering 1999; 176:231-246.
11. Ohnimus S, Stein E, Walhorn 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.
12. Prudhomme S, Oden JT, Westermann T, Bass J, Botkin ME. Practical methods for a posteriori error estimation in engineering applications. International Journal for Numerical Methods in Engineering 2003; 56:1193-1224.
13. Strouboulis T, Babuška I, Datta DK, Copps K, Gangaraj SK. A posteriori estimation and adaptative 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 factor. Computer Methods in Applied Mechanics and Engineering 2000; 180:261-274.
14. Heintz P, Larsson P, Hansbo P, Runesson K. On adaptive strategies and error control in fractures mechanics. Technical Report, Chalmers Finite Element Center, Chalmers University of Technology, 2002, preprint 2002-14.
15. Heintz P, Samuelsson K. On adaptive strategies and error control in fracture mechanics. Computers and Structures 2004; 82:485-497.
16. Ruter M, Stein E. Goal-oriented a posteriori error in linear elastic fracture mechanics. Computer Methods in Applied Mechanics and Engineering 2006; 195:251-278.
17. Xuan ZC, Parés N, Peraire J. Computing upper and lower bounds for the J-integral in two-dimensional linear elasticity. Computer Methods in Applied Mechanics and Engineering 2006; 195:430-443.
18. Sih GC, Rice JR. The bending of plates of dissimilar materials with crack. Journal of Applied Mechanics 1964; 477-482.
19. Stern M, Becker EB, Dunham RS. A contour integral computation of mixed-mode stress intensity factors. International Journal of Fracture 1976; 12(3):359-368.
20. Ladevèze P, Pelle JP, Rougeot P. Error estimation and mesh optimization for classical finite elements. Engineering Computation 1991; 8:69-80.
21. Ladevèze P, Rougeot P. New advances on a posteriori error on constitutive relation in f.e. analysis. Computer Methods in Applied Mechanics and Engineering 1997; 150:239-249.
22. Florentin E, Gallimard L, Pelle JP. Evaluation of the local quality of stresses in 3d finite element analysis. Computer Methods in Applied Mechanics and Engineering 2002; 191:4441-4457.
23. Prager W, Synge JL. Approximation in elasticity based on the concept of functions space. Quarterly of Applied Mathematics 1947; 5:261-269.
24. Florentin E, Gallimard L, Pelle JP. Etude de la qualité locale de différentes versions de l'estimateur d'erreur en relation de comportement. Revue européenne des éléments finis 2003; 12(6):761-783.
25. Murakami Y. Stress Intensity Factors Handbook. Pergamon Press: Oxford, 1986.