×

zbMATH — the first resource for mathematics

Stabilized global-local X-FEM for 3D non-planar frictional crack using relevant meshes. (English) Zbl 1242.74121
Summary: A stabilized global-local quasi-static contact algorithm for 3D non-planar frictional crack is presented in the X-FEM/level set framework. A three-field weak formulation is considered and allows an independent discretization of the bulk and the crack interface. Then, a fine discretization of the interface can be defined according to the possible complex contact state along the crack faces independently from the mesh in the bulk. Furthermore, an efficient stabilized non-linear LATIN solver dedicated to contact and friction is proposed. It allows solving in a unified framework frictionless and frictional contact at the crack interface with a symmetric formulation, no iterations on the local stage (unilateral contact law with/without friction), no calculation of any global tangent operator, and improved convergence rate. 2D and 3D patch tests are presented to illustrate the relevance of the proposed model and an actual 3D frictional crack problem under cyclic fretting loading is modeled.

MSC:
74S05 Finite element methods applied to problems in solid mechanics
74R10 Brittle fracture
74M10 Friction in solid mechanics
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Ribeaucourt, A new fatigue frictional contact crack propagation model with the coupled XFEM/LATIN method, Computer Methods in Applied Mechanics and Engineering 196 (33-34) pp 3230– (2007) · Zbl 1173.74385 · doi:10.1016/j.cma.2007.03.004
[2] Giner, Extended finite element method for fretting fatigue crack propagation, International Journal of Solids and Structures 5 (22-23) pp 5675– (2008) · Zbl 1177.74364 · doi:10.1016/j.ijsolstr.2008.06.009
[3] Giner, Numerical modelling of crack-contact interaction in 2D incomplete fretting contacts using X-FEM, Tribology International 2 pp 1269– (2009) · doi:10.1016/j.triboint.2009.04.003
[4] Giner, Crack face contact in X-FEM using a segment-to-segment approach, International Journal for Numerical Methods in Engineering 2 (11) pp 1424– (2009) · Zbl 1188.74057
[5] Baietto, A multi-model X-FEM strategy dedicated to frictional crack growth under cyclic fretting fatigue loadings, International Journal of Solids and Structures 7 (10) pp 1405– (2010) · Zbl 1193.74146 · doi:10.1016/j.ijsolstr.2010.02.003
[6] Pierres, 3D two scale X-FEM crack model with interfacial frictional contact: application to fretting-fatigue, Tribology International 43 (10) pp 1831– (2010) · doi:10.1016/j.triboint.2010.05.004
[7] Moes, Non-planar 3D crack growth with the extended finite element and level sets. Part I: mechanical model, International Journal for Numerical Methods in Engineering 53 pp 2549– (2002) · Zbl 1169.74621 · doi:10.1002/nme.429
[8] Gravouil, Non-planar 3D crack growth with the extended finite element and level sets. Part 2: level set update, International Journal for Numerical Methods in Engineering 53 pp 2569– (2002) · Zbl 1169.74621 · doi:10.1002/nme.430
[9] Duflot, A study on the representation of cracks with level sets, International Journal for Numerical Methods in Engineering 70 pp 1261– (2007) · Zbl 1194.74516 · doi:10.1002/nme.1915
[10] Rannou, A local multigrid X-FEM strategy for 3-D crack propagation, International Journal for Numerical Methods in Engineering 77 pp 1641– (2008)
[11] Rannou, Three dimensional experimental and numerical multiscale analysis of a fatigue crack, Computer Methods in Applied Mechanics and Engineering 199 pp 1307– (2010) · Zbl 1227.74056 · doi:10.1016/j.cma.2009.09.013
[12] Baietto, 3D crack network during the scratching of a polymer: comparison between experimental results and localized multigrid X-FEM, Tribology International (2010)
[13] Dolbow, n extended finite element method for modelling crack growth with frictional contact, Computer Methods in Applied Mechanics and Engineering 53 pp 6825– (2001) · Zbl 1033.74042 · doi:10.1016/S0045-7825(01)00260-2
[14] Bechet, A stable Lagrange multiplier space for stiff interface conditions within the extended finite element method, International Journal for Numerical Methods in Engineering 78 pp 931– (2009) · Zbl 1183.74259 · doi:10.1002/nme.2515
[15] Kim, A mortared finite element method for frictional contact on arbitrary interfaces, Computational Mechanics 39 (3) pp 223– (2007) · Zbl 1178.74169 · doi:10.1007/s00466-005-0019-4
[16] Moes, Imposing Dirichlet boundary conditions in the extended finite element method, International Journal for Numerical Methods in Engineering 67 pp 1641– (2006) · Zbl 1113.74072 · doi:10.1002/nme.1675
[17] Siavelis, Robust implementation of contact under friction and large sliding with the extended finite element method, European Journal of Computational Mechanics 19 (1-3) pp 189– (2010) · Zbl 1426.74305
[18] GĂ©niaut, A stable 3D contact formulation for cracks using X-FEM, European Journal of Computational Mechanics 16 (1) pp 259– (2007)
[19] Nistor, An X-FEM approach for large sliding contact along discontinuities, International Journal for Numerical Methods in Engineering 78 (12) pp 1407– (2009) · Zbl 1183.74301 · doi:10.1002/nme.2532
[20] Arnold, Mixed finite element methods for elliptic problems, Computer Methods in Applied Mechanics and Engineering 82 (1-3) pp 281– (1990) · Zbl 0729.73198 · doi:10.1016/0045-7825(90)90168-L
[21] Brezzi, A discourse on the stability conditions for mixed finite element formulations, Computer Methods in Applied Mechanics and Engineering 82 (1-3) pp 27– (1990) · Zbl 0736.73062 · doi:10.1016/0045-7825(90)90157-H
[22] Auricchio, Encyclopedia of Computational Mechanics, Volume 1: Fundamentals pp 237– (2004)
[23] Hild, Stabilized lagrange multiplier method for the finite element approximation of contact problems in elastostatics, Numerical Mathematics 15 (1) pp 101– (2010) · Zbl 1194.74408 · doi:10.1007/s00211-009-0273-z
[24] Sanders, On methods for stabilizing constraints over enriched interfaces in elasticity, International Journal for Numerical Methods in Engineering 78 pp 1009– (2009) · Zbl 1183.74313 · doi:10.1002/nme.2514
[25] Franca, Pressure bubbles stabilization features in the Stokes problem, Computer Methods in Applied Mechanics and Engineering 192 (16-18) pp 1929– (2003) · Zbl 1029.76032 · doi:10.1016/S0045-7825(02)00628-X
[26] Hughes, Multiscale phenomena: Green’s functions, the Dirichlet-to-Neumann formulation, subgrid scale models, bubbles and the origins of stabilized methods, Computer Methods in Applied Mechanics and Engineering 127 (1-4) pp 387– (1995) · Zbl 0866.76044 · doi:10.1016/0045-7825(95)00844-9
[27] Tezduyar, Stabilized finite element formulations for incompressible flow computations, Advances in Applied Mechanics 28 (1) pp 1– (1991) · Zbl 0747.76069 · doi:10.1016/S0065-2156(08)70153-4
[28] Liu, Stabilized low-order finite elements for frictional contact with the extended finite element method, Computer Methods in Applied Mechanics and Engineering 199 (37-40) pp 2456– (2010) · Zbl 1231.74426 · doi:10.1016/j.cma.2010.03.030
[29] Liu, A contact algorithm for frictional crack propagation with the extended finite element method, International Journal for Numerical Methods in Engineering 76 (10) pp 1489– (2008) · Zbl 1195.74186 · doi:10.1002/nme.2376
[30] Pierres, A two-scale extended finite element method for modeling 3D crack growth with interfacial contact, Computer Methods in Applied Mechanics and Engineering 199 (17-20) pp 1165– (2010) · Zbl 1227.74088 · doi:10.1016/j.cma.2009.12.006
[31] Elguedj, A mixed augmented Lagrangian-extended finite element method for modelling elastic-plastic fatigue crack growth with unilateral contact, International Journal for Numerical Methods in Engineering 71 pp 1569– (2007) · Zbl 1194.74387 · doi:10.1002/nme.2002
[32] Elguedj, Appropriate extended functions for X-FEM simulation of plastic fracture mechanics, Computers Methods in Applied Mechanics and Engineering 195 pp 501– (2005) · Zbl 1222.74041 · doi:10.1016/j.cma.2005.02.007
[33] Hansbo, A finite element method for the simulation of strong and weak discontinuities in solid mechanics, Computer Methods in Applied Mechanics and Engineering 193 pp 3523– (2004) · Zbl 1068.74076 · doi:10.1016/j.cma.2003.12.041
[34] Champaney L Modular analysis of assemblages of three-dimensional structures with unilateral contact conditions 1996
[35] Ladeveze, Nonlinear Computational Structural Mechanics-New Approaches and Non-incremental Methods of Calculation (1999) · doi:10.1007/978-1-4612-1432-8
[36] Ladeveze, A multiscale computational approach for contact problems, Computer Methods in Applied Mechanics and Engineering 191 pp 4869– (2002) · Zbl 1018.74036 · doi:10.1016/S0045-7825(02)00406-1
[37] Boucard, A suitable computational strategy for the parametric analysis of problems with multiple contact, International Journal for Numerical Methods in Engineering 57 pp 1259– (2003) · Zbl 1062.74607 · doi:10.1002/nme.724
[38] McDevitt, A mortar-finite element formulation for frictional contact problems, International Journal for Numerical Methods in Engineering 48 (10) pp 1525– (2000) · Zbl 0972.74067 · doi:10.1002/1097-0207(20000810)48:10<1525::AID-NME953>3.0.CO;2-Y
[39] Combescure, An algorithm to solve transient structural non-linear problems for non-matching time-space domains, Computers and Structures 81 pp 1211– (2003) · doi:10.1016/S0045-7949(03)00037-3
[40] Dureisseix, Information transfer between incompatible finite element meshes: application to coupled thermo-viscoelasticity, Computer Methods in Applied Mechanics and Engineering 195 pp 6523– (2006) · Zbl 1124.74046 · doi:10.1016/j.cma.2006.02.003
[41] Legrain, Stability of incompressible formulations enriched with X-FEM, Computer Methods in Applied Mechanics and Engineering 197 (21-24) pp 1835– (2008) · Zbl 1194.74426 · doi:10.1016/j.cma.2007.08.032
[42] Hughes, The Finite Element Method: Linear Static and Dynamic Finite Element Analysis (1987) · Zbl 0634.73056
[43] Bathe, Finite Element Procedures (1996)
[44] Brezzi, Mixed and Hybrid Finite Element Methods (1991) · Zbl 0788.73002 · doi:10.1007/978-1-4612-3172-1
[45] Ottosen, Introduction to the Finite Element Method (1992) · Zbl 0806.73001
[46] Zienkiewicz, The Finite Element Method, vol. 1-The Basis (2000) · Zbl 0962.76056
[47] Pierres E Baietto M-C Gravouil A 3D experimental and X-FEM frictional contact fatigue crack model. Prediction of fretting problems 2011
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.