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Arbitrary branched and intersecting cracks with the extended finite element method. (English) Zbl 0989.74066
Summary: We preent some extensions of a new technique for the finite element modelling of cracks with multiple branches, multiple holes and cracks emanating from holes. This extended finite element method allows the representation of crack discontinuities and voids independently of the mesh. A standard displacement based approximation is enriched by incorporating discontinuous fields through a partition of unity method. We also develop a methodology that constructs the enriched approximation based on the interaction of discontinuous geometric features with the mesh. Computations of stress intensity factors in different examples involving branched and intersecting cracks as well as cracks emanating from holes demonstrate the accuracy and robustness of the proposed technique.

##### MSC:
 74S05 Finite element methods applied to problems in solid mechanics 74R10 Brittle fracture 74G70 Stress concentrations, singularities in solid mechanics
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##### References:
 [1] Barsoum, International Journal for Numerical Methods in Engineering 11 pp 85– (1977) · Zbl 0348.73030 · doi:10.1002/nme.1620110109 [2] Kwon, Computers and Structures 31 pp 467– (1989) · doi:10.1016/0045-7949(89)90394-5 [3] Boundary Element Analysis in Computational Fracture Mechanics. Kluwer: Dordrecht, 1988. · Zbl 0648.73039 · doi:10.1007/978-94-009-1385-1 [4] An improved method of collocation for the stress analysis of cracked plates with various shaped boundaries. Technical Report TN D-6376, NASA, 1971. [5] Nisitani, Journal Aeronautical Society of India (Special Issue on Fracture Mechanics) 37 pp 21– (1985) [6] Integral transform methods. In: Methods of Analysis and Solutions of Crack Problems. Nordhoff International: Leyden, 1973. [7] Vitek, International Journal of Fracture 13 pp 481– (1977) · doi:10.1007/BF00040874 [8] Chen, Engineering Fracture Mechanics 52 pp 791– (1995) · doi:10.1016/0013-7944(95)00052-W [9] Obata, Journal of Applied Mechanics and Transactions ASME 56 pp 858– (1989) · doi:10.1115/1.3176182 [10] Fleming, International Journal for Numerical Methods in Engineering 40 pp 1483– (1997) · doi:10.1002/(SICI)1097-0207(19970430)40:8<1483::AID-NME123>3.0.CO;2-6 [11] Belytschko, International Journal for Numerical Methods in Engineering 45 pp 601– (1999) · Zbl 0943.74061 · doi:10.1002/(SICI)1097-0207(19990620)45:5<601::AID-NME598>3.0.CO;2-S [12] Mo?s, International Journal for Numerical Methods in Engineering 46 pp 131– (1999) · Zbl 0955.74066 · doi:10.1002/(SICI)1097-0207(19990910)46:1<131::AID-NME726>3.0.CO;2-J [13] An extended finite element method with discontinuous enrichment for applied mechanics. Ph.D. Thesis, Theoretical and applied mechanics, Northwestern University, 1999. [14] Melenk, Computer Methods in Applied Mechanics and Engineering 39 pp 289– (1996) · Zbl 0881.65099 · doi:10.1016/S0045-7825(96)01087-0 [15] Strouboulis, International Journal for Numerical Methods in Engineering 47 pp 1401– (2000) · Zbl 0955.65080 · doi:10.1002/(SICI)1097-0207(20000320)47:8<1401::AID-NME835>3.0.CO;2-8 [16] Strouboulis, Computer Methods in Applied Mechanics and Engineering 181 pp 43– (2000) · Zbl 0983.65127 · doi:10.1016/S0045-7825(99)00072-9 [17] Duarte, Computer Methods in Applied Mechanics and Engineering (2000) [18] Oden, Computer Methods in Applied Mechanics and Engineering 153 pp 117– (1998) · Zbl 0956.74062 · doi:10.1016/S0045-7825(97)00039-X [19] Yau, Journal of Applied Mechanics 47 pp 335– (1980) · Zbl 0463.73103 · doi:10.1115/1.3153665 [20] Shih, Journal of Applied Mechanics 55 pp 299– (1988) · doi:10.1115/1.3173676 [21] Kitagawa, Transactions of the Japan Society of Mechanical Engineering 41 pp 1641– (1975) · doi:10.1299/kikai1938.41.1641 [22] Lo, Journal of Applied Mechanics 45 pp 797– (1978) · Zbl 0392.73087 · doi:10.1115/1.3424421 [23] Theocaris, Engineering Fracture Mechanics 20 pp 583– (1984) · doi:10.1016/0013-7944(84)90033-X [24] Gmsh finite element grid generator, 1998, available at http: //scorec.rpi.edu/?remacle/Gmsh_Eng.html. [25] Cheung, Computational Mechanics 10 pp 335– (1992) · Zbl 0775.73335 · doi:10.1007/BF00364254 [26] Ouchterlong, Engineering Fracture Mechanics 8 pp 447– (1976) · doi:10.1016/0013-7944(76)90026-6 [27] Bowie, Journal of Mathematical Physics 35 pp 60– (1956) · Zbl 0072.18904 · doi:10.1002/sapm195635160 [28] Woo, Engineering Fracture Mechanics 32 pp 279– (1989) · doi:10.1016/0013-7944(89)90300-7
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