×

Extended finite element method coupled with face-based strain smoothing technique for three-dimensional fracture problems. (English) Zbl 1352.74370

Summary: In this work, the extended finite element method (XFEM) is for the first time coupled with face-based strain-smoothing technique to solve three-dimensional fracture problems. This proposed method, which is called face-based smoothed XFEM here, is expected to combine both the advantages of XFEM and strain-smoothing technique. In XFEM, arbitrary crack geometry can be modeled and crack advance can be simulated without remeshing. Strain-smoothing technique can eliminate the integration of singular term over the volume around the crack front, thanks to the transformation of volume integration into area integration. Special smoothing scheme is implemented in the crack front smoothing domain. Three examples are presented to test the accuracy, efficiency, and convergence rate of the face-based smoothed XFEM. From the results, it is clear that smoothing technique can improve the performance of XFEM for three-dimensional fracture problems.

MSC:

74S05 Finite element methods applied to problems in solid mechanics
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
74R10 Brittle fracture
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Belytschko, Elastic crack growth in finite elements with minimal remeshing, 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
[2] Moës, A finite element method for crack growth without remeshing, 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
[3] Elguedj, Appropriate extended functions for XFEM simulation of plastic fracture mechanics, Computer Methods in Applied Mechanics and Engineering 195 pp 501– (2006) · Zbl 1222.74041 · doi:10.1016/j.cma.2005.02.007
[4] Bordas, Three-dimensional crack initiation, propagation, branching and junction in non-linear materials by an extended meshfree method without asymptotic enrichment, Engineering Fracture Mechanics 75 pp 943– (2008) · doi:10.1016/j.engfracmech.2007.05.010
[5] Rabczuk, A three-dimensional meshfree method for continuous multiple-crack initiation, propagation and junction in statics and dynamics, Computational Mechanics 40 pp 473– (2007) · Zbl 1161.74054 · doi:10.1007/s00466-006-0122-1
[6] Rabczuk, A simple and robust three-dimensional cracking-particle method without enrichment, Computer Methods in Applied Mechanics and Engineering 199 pp 2437– (2009) · Zbl 1231.74493 · doi:10.1016/j.cma.2010.03.031
[7] Chessa, An enriched finite element method for axisymmetric two-phase flow with surface tension, Journal of Computational Physics 58 pp 2041– (2003) · Zbl 1032.76591
[8] Chopp, Fatigue crack propagation of multiple coplanar cracks with the coupled extended finite element/fast marching method, International Journal of Engineering Science 41 pp 845– (2003) · Zbl 1211.74199 · doi:10.1016/S0020-7225(02)00322-1
[9] Merle, Solving thermal and phase change problems with the extended finite element method, Computational Mechanics 28 pp 339– (2002) · Zbl 1073.76589 · doi:10.1007/s00466-002-0298-y
[10] Ji, A hybrid extended finite element/level set method for modeling phase transformations, International Journal for Numerical Methods in Engineering 54 pp 1209– (2002) · Zbl 1098.76572 · doi:10.1002/nme.468
[11] Chen, A stabilized conforming nodal integration for Galerkin meshfree methods, International Journal for Numerical Methods in Engineering 50 pp 435– (2001) · Zbl 1011.74081 · doi:10.1002/1097-0207(20010120)50:2<435::AID-NME32>3.0.CO;2-A
[12] Liu, A normed G space and weakened weak formulation of a cell-based smoothed point interpolation method, International Journal of Computational Mechanics 6 pp 147– (2009) · Zbl 1264.74285
[13] Liu, A G space theory and weakened weak (W2) form for a unified formulation of compatible and incompatible methods, part I: theory and part II: applications to solid mechanics problems, International Journal for Numerical Methods in Engineering 81 pp 1093– (2010)
[14] Liu, Smoothed Finite Element Method (2010) · doi:10.1201/EBK1439820278
[15] Le, A cell-based smoothed finite element method for kinematic limit analysis, International Journal for Numerical Methods in Engineering 83 pp 1651– (2010) · Zbl 1202.74177 · doi:10.1002/nme.2897
[16] Liu, A novel singular node-based smoothed finite element method (NS-FEM) for upper bound solutions of fracture problems, International Journal for Numerical Methods in Engineering 83 pp 1466– (2010) · Zbl 1202.74179 · doi:10.1002/nme.2868
[17] Chen, A singular edge-based smoothed finite element method (ES-FEM) for bimaterial interface cracks, Computational Mechanics 45 pp 109– (2010) · Zbl 1398.74316 · doi:10.1007/s00466-009-0422-3
[18] Liu, An edge-based smoothed finite element method (ES-FEM) for static, free and forced vibration analyses of solids, Journal of Sound and Vibration 320 (4-5) pp 1100– (2008) · doi:10.1016/j.jsv.2008.08.027
[19] Cui, Bending and vibration responses of laminated composite plates using an edge-based smoothing technique, Engineering Analysis with Boundary Elements 35 pp 818– (2011) · Zbl 1259.74029 · doi:10.1016/j.enganabound.2011.01.007
[20] Jiang, An edge-based smoothed XFEM for fracture in composite materials, International Journal of Fracture 179 (1-2) pp 179– (2013) · doi:10.1007/s10704-012-9786-z
[21] Chen, Extended finite element method with edge-based strain smoothing (ESm-XFEM) for linear elastic crack growth, Computer Methods in Applied Mechanics and Engineering 209-212 pp 250– (2012) · Zbl 1243.74170 · doi:10.1016/j.cma.2011.08.013
[22] Nguyen-Thoi, A face-based smoothed finite element method (FS-FEM) for 3D linear and geometrically non-linear solid mechanics problems using 4-node tetrahedral elements, International Journal for Numerical Methods in Engineering 78 pp 324– (2009) · Zbl 1183.74299 · doi:10.1002/nme.2491
[23] Nguyen-Thoi, A face-based smoothed finite element method (FS-FEM) for visco-elastoplastic analyses of 3D solids using tetrahedral mesh, Computer Methods in Applied Mechanics and Engineering 198 pp 3479– (2009) · Zbl 1230.74193 · doi:10.1016/j.cma.2009.07.001
[24] Parks, A stiffness derivative finite element technique for determination of crack tip stress intensity factor, International Journal of Fracture 10 pp 487– (1974) · doi:10.1007/BF00155252
[25] Parks, The virtual crack extension method for nonlinear material behavior, Computer Methods in Applied Mechanics and Engineering 12 pp 353– (1977) · Zbl 0368.73085 · doi:10.1016/0045-7825(77)90023-8
[26] Hellen, On the method of virtual crack extension, International Journal for Numerical Methods in Engineering 9 pp 187– (1975) · Zbl 0293.73049 · doi:10.1002/nme.1620090114
[27] Hellen TK, Virtual crack extension methods for non-linear materials, International Journal for Numerical Methods in Engineering 28 pp 929– (1989) · doi:10.1002/nme.1620280414
[28] Rybicki, A finite element calculation of stress intensity factors by modified crack closure integral, Engineering Fracture Mechanics 9 pp 931– (1977) · doi:10.1016/0013-7944(77)90013-3
[29] Shivakumar, Virtual crack closure technique for calculating stress-intensity factors for cracked three-dimensional bodies, International Journal of Fracture 36 pp R43– (1988)
[30] Raju, Three-dimensional elastic analysis of a composite double cantilever beam specimen, American Institute of Aeronautics and Astronautics Jl 26 pp 1493– (1988) · doi:10.2514/3.10068
[31] Buchholz, Accuracy Reliability and Training in FEM-Technology pp 650– (1984)
[32] Rice, A path-independent integral and the approximate analyses of strain concentration by notches and cracks, Journal of Applied Mechanics 35 pp 376– (1968) · doi:10.1115/1.3601206
[33] Cherepanov, Crack propagation in continuous media, Journal of Applied Mathematics and Mechanics 31 pp 503– (1967) · Zbl 0288.73078 · doi:10.1016/0021-8928(67)90034-2
[34] Eshelby, Solid State Physics pp 79– (1956)
[35] Cherepanov, Mechanics of brittle fracture (1979)
[36] Anderson, Fracture Mechanics: Fundamentals and applications, 3. ed. (2004)
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. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.