×

zbMATH — the first resource for mathematics

Extended finite element method for quasi-brittle fracture. (English) Zbl 1032.74673
Summary: A methodology for the simulation of quasi-static cohesive crack propagation in quasi-brittle materials is presented. In the framework of the recently proposed extended finite element method, the partition of unity property of nodal shape functions has been exploited to introduce a higher-order displacement discontinuity in a standard finite element model. In this way, a cubic displacement discontinuity, able to reproduce the typical cusp-like shape of the process zone at the tip of a cohesive crack, is allowed to propagate without any need to modify the background finite element mesh. The effectiveness of the proposed method has been assessed by simulating mode-I and mixed-mode experimental tests.

MSC:
74S05 Finite element methods applied to problems in solid mechanics
74R10 Brittle fracture
PDF BibTeX Cite
Full Text: DOI
References:
[1] Nonlocal damage. In Continuum Models for Materials with Microstructure, (ed.). Wiley: New York, 1995; 105-143.
[2] Peerlings, Mechanics of Cohesive-Frictional Materials 3 pp 323– (1998)
[3] Ferrara, Journal of Engineering Mechanics 127 pp 678– (2001)
[4] Comi, European Journal of Mechanics - A/Solids 20 pp 1– (2001)
[5] Comi, International Journal of Solids and Structures 38 pp 6427– (2001)
[6] Jirasek, International Journal for Numerical Methods in Engineering 50 pp 1269– (2001)
[7] Jirasek, International Journal for Numerical Methods in Engineering 50 pp 1291– (2001)
[8] Oliver, Engineering Fracture Mechanics 69 pp 113– (2002)
[9] Cen, Fatigue and Fracture of Engineering Materials and Structures 15 pp 911– (1992)
[10] Maier, Computer Assisted Mechanics and Engineering Science 5 pp 201– (1998)
[11] Belytschko, Computer Methods in Applied Mechanics and Engineering 187 pp 385– (2000)
[12] Bocca, International Journal of Solids and Structures 27 pp 1139– (1991)
[13] Xu, Journal of the Mechanics and Physics of Solids 42 pp 1397– (1994)
[14] Ortiz, International Journal for Numerical Methods in Engineering 44 pp 1267– (1999)
[15] Klisinski, Journal of Engineering Mechanics 117 pp 575– (1991)
[16] Simo, Computational Mechanics 12 pp 277– (1993)
[17] Lotfi, International Journal for Numerical Methods in Engineering 38 pp 1307– (1995)
[18] Bolzon, International Journal for Numerical Methods in Engineering 49 pp 1227– (2000)
[19] Jirasek, Computer Methods in Applied Mechanics and Engineering 188 pp 307– (2000)
[20] Melenk, Computer Methods in Applied Mechanics and Engineering 139 pp 289– (1996)
[21] Duarte, Computers and Structures 77 pp 215– (2000)
[22] Strouboulis, Computer Methods in Applied Mechanics and Engineering 190 pp 4081– (2001)
[23] Moës, International Journal for Numerical Methods in Engineering 46 pp 131– (1999)
[24] Sukumar, International Journal for Numerical Methods in Engineering 48 pp 1549– (2000)
[25] Wells, International Journal for Numerical Methods in Engineering 50 pp 2667– (2001)
[26] Moës, Engineering Fracture Mechanics 69 pp 813– (2002)
[27] Camacho, International Journal of Solids and Structures 33 pp 2899– (1996)
[28] Ruiz, International Journal for Numerical Methods in Engineering 48 pp 963– (2000)
[29] Arun Roy, International Journal of Fracture 110 pp 21– (2001)
[30] Carol, Journal of Engineering Mechanics 123 pp 765– (1997)
[31] Cocchetti, Computer Modeling in Engineering and Sciences 3 pp 279– (2002)
[32] Computational resolution of strong discontinuities. In Proceedings of the Fifth World Congress on Computational Mechanics (WCCM V), Mang HA, Rammerstorfer FG, Eberhardsteiner J (eds). ISBN 3-9501554-0-6, Vienna University of Technology, 2002.
[33] Denarié, Journal of Engineering Mechanics 127 pp 494– (2001)
[34] A PU-FE approach to quasi-brittle fracture. In Proceedings of the 15th AIMETA Congress of Theoretical and Applied Mechanics, Augusti G, Mariano PM, Sepe V, Lacagnina M (eds). Taormina (Italy), 2001.
[35] John, Journal of Structural Engineering 116 pp 585– (1990)
[36] Bolzon, Archive of Applied Mechanics 68 pp 513– (1998)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.