Error estimation and adaptivity for discontinuous failure

International Journal for Numerical Methods in Engineering

Volumn 78, Issue 5, 2009, Pages 528-563

  Pannachet, T ^a   Sluys, L J ^b   Askes, H ^c  

^a KHON KAEN UNIVERSITY   (Thailand)

^b DELFT UNIVERSITY OF TECHNOLOGY   (Netherlands)

^c UNIVERSITY OF SHEFFIELD   (United Kingdom)

Author keywords

Cohesive crack; Cohesive zone model; Discontinuity; Error estimation; Finite element method; Mesh adaptivity; Partition of unity; Quasi brittle materials

Indexed keywords

COHESIVE CRACK; COHESIVE ZONE MODEL; DISCONTINUITY; ERROR ESTIMATION; MESH ADAPTIVITY; PARTITION OF UNITY; QUASI-BRITTLE MATERIALS;

BRITTLE FRACTURE; BRITTLENESS; CRACKS; ERROR ANALYSIS; ESTIMATION;

FINITE ELEMENT METHOD;

EID: 65449137503     PISSN: 00295981     EISSN: 10970207     Source Type: Journal    
DOI: 10.1002/nme.2495     Document Type: Article

References (45)

1. Griffith AA. The theory of rupture. Proceedings of the First International Conference of Applied Mechanics, Delft, The Netherlands, 1924; 55-63.
2. Irwin GR. Analysis of stresses and strains near the end of a crack traversing a plate. Journal of Applied Mechanics, Transactions of the ASME 1957; 24:361-364.
3. Rice JR. A path independent integral and the approximate analysis of strain concentrations by notches and cracks. Journal of Applied Mechanics, Transactions of the ASME 1968; 35:379-386.
4. Rice JR. Mathematical analysis in the mechanics of fracture. In Fracture - An Advanced Treatise, vol. 2, Liebowitz H (ed.). Academic Press: New York, 1968; 191-308.
5. Dugdale DS. Yielding of steel sheets containing slits. Journal of the Mechanics and Physics of Solids 1960; 8:100-108.
6. Barenblatt GI. The mathematical theory of equilibrium cracks in brittle fracture. Advances in Applied Mechanics 1962; 7:55-129.
7. Hillerborg A, Modeer M, Petersson PE. Analysis of crack formation and crack growth in concrete by means of fracture mechanics and finite elements. Cement and Concrete Research 1976; 6:773-782.
8. Karihaloo BL, Xiao QZ. Accurate simulation of frictionless and frictional cohesive crack growth in quasi-brittle materials using XFEM. In Discretization Methods for Evolving Discontinuities, Combescure A, De Borst R, Belytschko T (eds). Springer: Dordrecht, 2007; 233-254.
9. Belytschko T, Black T. Elastic crack growth in finite elements with minimal remeshing. International Journal for Numerical Methods in Engineering 1999; 45:601-620.
10. Moës N, Dolbow J, Belytschko T. A finite element method for crack growth without remeshing. International Journal for Numerical Methods in Engineering 1999; 46:131-150.
11. Wells GN, Sluys LJ. A new method for modelling cohesive cracks using finite elements. International Journal for Numerical Methods in Engineering 2001; 50:2667-2682.
12. Rots JG. Smeared and discrete representations of localized fracture. International Journal of Fracture 1991; 51:45-59.
13. Wells GN. Discontinuous modelling of strain localisation and failure. Ph.D. Dissertation, Delft University of Technology, The Netherlands, 2001. (Downloadable from http://www.library.tudelft.nl/ dissertations.)
14. Pannachet T, Askes H, Sluys LJ. p-version error estimation for linear elasticity. Computational Mechanics 2008; DOI: 10.1007/ s00466-008-0333-8.
15. Pannachet T. Error estimation and adaptive spatial discretisation for quasi-brittle failure. Ph.D. Dissertation, Delft University of Technology, The Netherlands, 2006. (Downloadable from http://www.library.tudelft.nl/dissertations.)
16. Duarte CA, Reno LG, Simone A. A high-order generalized FEM for through-the-thickness branched cracks. International Journal for Numerical Methods in Engineering 2007; 72(3):325-351.
17. Szabó B, Babuŝka I. Finite Element Analysis. Wiley: New York, 1991.
18. Pannachet T, Askes H. Partition-of-unity based p-adaptivity and error estimation in the finite element method. WCCM V - Fifth World Congress on Computational Mechanics, Vienna, Austria, 2002.
19. Runge C. Über empirische Funktionen und die Interpolation zwischen äquidistanten Ordinaten. Zeitschrift für Mathematik und Physik 1901; 46:224-243.
20. Stazi FL, Budyn E, Chessa J, Belytschko T. An extended finite element method with higher-order elements for curved cracks. Computational Mechanics 2003; 31:38-48.
21. Laborde P, Pommier J, Renard Y, Salaün M. High-order extended finite element method for cracked domains. International Journal for Numerical Methods in Engineering 2005; 64:354-381.
22. Simone A. Partition of unity based discontinuous elements for interface phenomena: computational issues. Communications in Numerical Methods in Engineering 2004; 20(6):465-478.
23. Simone A, Sluys LJ. The use of displacement discontinuities in a rate-dependent medium. Computer Methods in Applied Mechanics and Engineering 2004; 193(27-29):3015-3033.
24. 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.
25. Zienkiewicz OC, Zhu JZ. The superconvergent patch recovery (SPR) and adaptive finite element refinement. Computer Methods in Applied Mechanics and Engineering 1992; 101:207-224.
26. Babuŝka I, Rheinboldt C. A posteriori error estimates for the finite element method. International Journal for Numerical Methods in Engineering 1978; 12:1597-1615.
27. Díez P, Egozcue JJ, Huerta A. A posteriori error estimation for standard finite element analysis. Computer Methods in Applied Mechanics and Engineering 1998; 163:141-157.
28. Bordas S, Duflot M, Le P. A simple a posteriori error estimator for the extended finite element method. Communications in Numerical Methods in Engineering 2007; DOI: 10.1002/cnm.1001.
29. Bordas S, Duflot M. Derivative recovery and a posteriori error estimation in extended finite element methods. Computer Methods in Applied Mechanics and Engineering 2007; 196:3381-3399.
30. Ródenas JJ, González-Estrada OA, Tarancón JE, Fuenmayor FJ. A recovery type error estimator for the extended finite element method based on singular+smooth stress field splitting. International Journal for Numerical Methods in Engineering 2008; Published Online: March 20 2008 9:52AM. DOI: 10.1002/nme.2313.
31. Duflot M, Bordas S. A posteriori error estimation for extended finite elements by an extended global recovery. International Journal for Numerical Methods in Engineering 2008; Published Online: June 19 2008 5:42AM. DOI: 10.1002/nme.2332.
32. Huerta A, Díez P. Error estimation including pollution assessment for nonlinear finite element analysis. Computer Methods in Applied Mechanics and Engineering 2000; 181:21-41.
33. 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.
34. Heintz P, Samuelsson K. On adaptive strategies and error control in fracture mechanics. Computers and Structures 2004; 82:485-497.
35. Rüter M, Stein E. Adaptive finite element analysis of crack propagation in elastic fracture mechanics based on averaging techniques. Computational Material Science 2004; 31:247-257.
36. Rüter M, Korotov S, Steenbock C. Goal-oriented error estimates based on different FE spaces for the primal and the dual problems with applications to fracture mechanics. Computational Mechanics 2007; 39:787-797.
37. Li L-Y, Bettess P, Bull JW, Bond T, Applegarth I. Theoretical formulations for adaptive finite element computations. Communications in Numerical Methods in Engineering 1995; 11:857-868.
38. Elguedj T, Gravouil A, Combescure A. Appropriate extended functions for X-FEM simulation of plastic fracture mechanics. Computer Methods in Applied Mechanics and Engineering 2006; 195:501-515.
39. Li L-Y, Bettess P. Notes on mesh optimal criteria in adaptive finite element computation. Communications in Numerical Methods in Engineering 1995; 11:911-915.
40. Zi G, Belytschko T. New crack-tip elements for XFEM and applications to cohesive cracks. International Journal for Numerical Methods in Engineering 2003; 57:2221-2240.
41. Liu GR, Nguyen TT, Dai KY, Lam KY. Theoretical aspects of the smoothed finite element method (SFEM). International Journal for Numerical Methods in Engineering 2007; 71:902-930.
42. Hung N-X, Bordas S, Hung N-D. Smooth finite element methods: convergence, accuracy and properties. International Journal for Numerical Methods in Engineering 2008; 74:175-208.
43. Sukumar N, Moës N, Belytschko T, Moran B. Extended finite element method for three-dimensional crack modelling. International Journal for Numerical Methods in Engineering 2000; 48(11):1549-1570.
44. Moës N, Gravouil A, Belytschko T. Non-planar 3D crack growth by the extended finite element and level sets. Part I. Mechanical model. International Journal for Numerical Methods in Engineering 2002; 53(11):2549-2568.
45. Gravouil A, Moës N, Belytschko T. Non-planar 3D crack growth by the extended finite element and level sets. Part II. Level set. International Journal for Numerical Methods in Engineering 2002; 53(11):2569-2586.