Abstract
The extended finite element method (X-FEM) has been developed to minimize requirements on the mesh in a problem with a displacement discontinuity. We present the development carried out to take advantage of the X-FEM approach in simplifying the meshing of complex 3D networks of discontinuities with junctions. Contact with large sliding along the branched discontinuities is discussed. Solutions are proposed and discussed to solve some matrix conditioning issues. Several examples are presented in this paper in order to prove the efficiency of the proposed approach.
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References
Alart P, Curnier A (1991) A mixed formulation for frictional contact problems prone to Newton like solution methods. Comput Methods Appl Mech Eng 92: 353–375
Babuška I (1973) The finite element method with Lagrangian multipliers. Numer Math 20(3): 179–192
Béchet E, Minnebo H, Moës N, Burgardt B (2005) Improved implementation and robustness study of the X-FEM for stress analysis around cracks. Int J Numer Methods Eng 64(8): 1033–1056
Béchet E, Moës N, Wohlmuth B (2009) A stable Lagrange multiplier space for stiff interface conditions within the extended finite element method. Int J Numer Methods Eng 78(8): 931–954
Ben Dhia H, Zarroug M (2002) Hybrid frictional contact particles-in elements. Eur J Comput Mech 11: 417–430
Brezzi F, Fortin M (1991) Mixed and hybrid finite element methods. Spriner, New York
Chapelle D, Bathe KJ (1993) The inf-sup test. Comput Struct 47(4/5): 537–545
Daux C, Moës N, Dolbow J, Sukumar N, Belytschko T (2000) Arbitrary branched and intersecting cracks with the extended finite element method. Int J Numer Methods Eng 48: 1741–1760
Destuynder P, Djaoua M (1981) Sur une Interprétation Mathématique de l’Intégrale de Rice en Théorie de la Rupture Fragile. Math Methods Appl Sci 3(1): 70–87
Dolbow J, Moës N, Belytschko T (2001) An extended finite element method for modeling crack growth with frictional contact. Comput Methods Appl Mech Eng 190: 6825–6846
Duarte CA, Reno LG, Simone A (2007) A high-order generalized FEM for through-the-thickness branched cracks. Int J Numer Methods Eng 72: 325–351
Dulac JC, Gringarten E (2011) Approach couples fluid flow, Geomechanical simulations in 3-D reservoir modeling. The American Oil & Gas Reporter
Dumont G (2001) Algorithme des contraintes actives et contact unilatéral sans frottement. Euro J Comput Mech 4(1): 55–73
Erdogan F, Sih G (1963) On the crack extension in plates under plane loading and transverse shear. Trans ASME J Basic Eng 85(2): 519–527
Gosz M, Moran B (2002) An interaction energy integral method for computation of mixed-mode stress intensity factors along non-planar crack fronts in three dimensions. Eng Fract Mech 69: 299–319
Géniaut S, Massin P, Moës N (2005) Fissuration avec X-FEM et contact. In: Actes du 7ème Colloque National en Calcul des Structures, Giens
Géniaut S, Massin P, Moës N (2007) A stable 3D contact formulation for cracks using X-FEM. Eur J Comput Mech 16(2): 259–275
Khoei AR, Nikbakht M (2006) Contact friction modeling with the extended finite element method (X-FEM). J Mater Process Technol 177: 58–62
Laborde P, Pommier J, Renard Y, Salaün M (2005) High-order extended finite element method for cracked domains. Int J Numer Methods Eng 64(3): 354–381
Lasserre JB (1998) Integration on a convex polytope. Proc Am Math Soc 126(8): 2433–2441
Lepage F (2003) Génération de maillages tridimensionnels pour la simulation des phénomènes physiques en géosciences. PhD thesis, Institut National Polytechnique de Lorraine
Liu F, Borja R (2008) A contact algorithm for frictional crack propagation with the extended finite element method. Int J Numer Methods Eng 76: 1489–1512
Moës N, Dolbow J, Belytschko T (1999) A finite element method for crack growth without remeshing. Int J Numer Methods Eng 46: 131–150
Moës N, Gravouil A, Belytschko T (2002) Non-planar 3D crack growth by the extended finite element and level sets—part I: mechanical. Int J Numer Methods Eng 53: 2549–2568
Moës N, Béchet , Tourbier M (2006) Imposing Dirichlet boundary conditions in the extended finite element method. Int J Numer Methods Eng 67(12): 1641–1669
Mourad HM, Dolbow J, Harari I (2007) A bubble-stabilized finite element method for Dirichlet constraints on embedded interfaces. Int J Numer Methods Eng 69(4): 772–793
Mousavi SE, Sukumar N (2011) Numerical integration of polynomials and discontinuous functions on irregular convex polygons and polyhedrons. Comput Mech 47(5): 535–554
Mousavi S, Grinspun E, Sukumar N (2010) Higher-order extended finite elements with harmonic enrichment functions for complex crack problems. Int J Numer Methods Eng 86(4-5): 560–574
Nistor I, Guiton MLE, Massin P, Moës N, Géniaut S (2009) An X-FEM approach for large sliding contact along discontinuities. Int J Numer Methods Eng 78(12): 1407–1435
Nuismer R (1975) An energy release rate criterion for mixed mode fracture. Int J Fract 11(2): 245–250
Pierrès E, Baietto MC, Gravouil A (2010) A two-scale extended finite element method for modelling 3D crack growth with interfacial contact. Comput Methods Appl Mech Eng 199(17-20): 1165–1177
Rice JR (1968) A path independent integral and the approximate analysis of strain concentration by notches and cracks. J Appl Mech 35: 379–386
Sanders JD, Dolbow JE, Laursen TA (2009) On methods for stabilizing constraints over enriched interfaces in elasticity. Int J Numer Methods Eng 78: 1009–1036
Stern M, Becker EB, Dunham RS (1976) A contour integral computation of mixed-mode stress intensity factors. Int J Fract 12(3): 359–368
Siavelis M, Massin P, Guiton MLE, Mazet S, Moës N (2010) Robust implementation of contact under friction and large sliding with the eXtended finite element method. Eur J Comput Mech 19(1-2-3): 189–203
Sih G (1974) Strain-energy-density factor applied to mixed mode crack problems. Int J Fract 10: 305–321
Simone A, Duarte CA, Vander Giessen E (2006) A generalized finite element method for polycrystals with discontinuous grain boundaries. Int J Numer Methods Eng 67: 1122–1145
Solberg JM, Papadopoulos P (2005) An analysis of dual formulations for the finite element solution of two-body contact problems. Comput Methods Appl Mech Eng 194: 2734–2780
Ventura G (2006) On the elimination of quadrature subcells for discontinuous functions in the eXtended finite-element method. Int J Numer Methods Eng 66: 761–795
Wriggers P (2002) Computational contact mechanics. Wiley, New York
Yavuz A, Phoenix S, TerMaath S (2006) Multiple crack analysis in finite plates. AIAA J 44(11): 2535–2541
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Siavelis, M., Guiton, M.L.E., Massin, P. et al. Large sliding contact along branched discontinuities with X-FEM. Comput Mech 52, 201–219 (2013). https://doi.org/10.1007/s00466-012-0807-6
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DOI: https://doi.org/10.1007/s00466-012-0807-6