×

zbMATH — the first resource for mathematics

An extended finite element library. (English) Zbl 1194.74367
Summary: This paper presents and exercises a general structure for an object-oriented-enriched finite element code. The programming environment provides a robust tool for extended finite element (XFEM) computations and a modular and extensible system. The programme structure has been designed to meet all natural requirements for modularity, extensibility, and robustness. To facilitate mesh – geometry interactions with hundreds of enrichment items, a mesh generator and mesh database are included. The salient features of the programme are: flexibility in the integration schemes (subtriangles, subquadrilaterals, independent near-tip, and discontinuous quadrature rules); domain integral methods for homogeneous and bi-material interface cracks arbitrarily oriented with respect to the mesh; geometry is described and updated by level sets, vector level sets or a standard method; standard and enriched approximations are independent; enrichment detection schemes: topological, geometrical, narrow-band, etc.; multi-material problem with an arbitrary number of interfaces and slip-interfaces; nonlinear material models such as J2 plasticity with linear, isotropic and kinematic hardening. To illustrate the possible applications of our paradigm, we present 2D linear elastic fracture mechanics for hundreds of cracks with local near-tip refinement, and crack propagation in two dimensions as well as complex 3D industrial problems.

MSC:
74S05 Finite element methods applied to problems in solid mechanics
74-04 Software, source code, etc. for problems pertaining to mechanics of deformable solids
74R10 Brittle fracture
Software:
Doxygen; XFEM
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Babuška, International Journal for Numerical Methods in Engineering 40 pp 727– (1997)
[2] Belytschko, International Journal for Numerical Methods in Engineering 45 pp 601– (1999)
[3] Moës, International Journal for Numerical Methods in Engineering 46 pp 131– (1999)
[4] Strouboulis, Computer Methods in Applied Mechanics and Engineering 181 pp 43– (2000)
[5] Strouboulis, International Journal for Numerical Methods in Engineering 47 pp 1401– (2000)
[6] Hansbo, Computer Methods in Applied Mechanics and Engineering 193 pp 3523– (2004) · Zbl 1068.74076
[7] Areias, Computer Methods in Applied Mechanics and Engineering 195 pp 1275– (2006)
[8] Mergheim, Communications in Numerical Methods in Engineering (2006)
[9] Mergheim, International Journal for Numerical Methods in Engineering (2006)
[10] Mergheim, International Journal for Numerical Methods in Engineering 63 pp 276– (2005)
[11] de Borst, Engineering Fracture Mechanics 73 pp 160– (2006)
[12] Belytschko, International Journal for Numerical Methods in Engineering 50 pp 993– (2001)
[13] Sukumar, International Journal of Solids and Structures 40 pp 7513– (2003)
[14] Legrain, International Journal for Numerical Methods in Engineering 63 pp 290– (2005)
[15] Areias, Computational Mechanics 35 pp 54– (2004)
[16] Sukumar, Engineering Fracture Mechanics 70 pp 29– (2003)
[17] Moës, International Journal for Numerical Methods in Engineering 53 pp 2549– (2002)
[18] Gravouil, International Journal for Numerical Methods in Engineering 53 pp 2569– (2002)
[19] Areias, International Journal for Numerical Methods in Engineering 63 pp 760– (2005)
[20] Chopp, International Journal of Engineering Science 41 pp 845– (2003)
[21] Dolbow, International Journal of Solids and Structures 37 pp 7161– (2000)
[22] Moës, Engineering Fracture Mechanics 69 pp 813– (2002)
[23] Remmers, Computational Mechanics 31 pp 69– (2003)
[24] Zi, International Journal for Numerical Methods in Engineering 57 pp 2221– (2003)
[25] de Borst, Engineering Fracture Mechanics 70 pp 1743– (2003)
[26] Wells, International Journal for Numerical Methods in Engineering 50 pp 2667– (2001)
[27] de Borst, International Journal for Numerical Methods in Engineering 60 pp 289– (2004)
[28] Tijssens, European Journal of Mechanics A, Solids 19 pp 761– (2000)
[29] Sukumar, International Journal for Numerical Methods in Engineering 59 pp 1075– (2003)
[30] Sukumar, International Journal for Numerical Methods in Engineering 190 pp 6183– (2001)
[31] Daux, International Journal for Numerical Methods in Engineering 48 pp 1741– (1999)
[32] Sukumar, International Journal for Numerical Methods in Engineering 56 pp 2015– (2003)
[33] Areias, International Journal for Numerical Methods in Engineering 66 pp 878– (2006)
[34] Dolbow, Computer Methods in Applied Mechanics and Engineering 19 pp 6825– (2001)
[35] Une stratégie de calcul pour les structures fissurées: analyse locale-globale et approche multiéchelle pour la fissuration. Ph.D. Thesis, ENS-Cachan, 2005.
[36] Chessa, International Journal for Numerical Methods in Engineering 53 pp 1957– (2002)
[37] Extended Finite Element and level set methods with applications to growth of cracks and biofilms. Ph.D. Thesis, Northwestern University, December 2003. http://www.civil.gla.ac.uk/bordas/publications.html
[38] Duddu, International Journal for Numerical Methods in Engineering (2006)
[39] Dolbow, Mechanics and Physics of Solids 52 pp 51– (2003)
[40] Legay, Computer Methods in Applied Mechanics and Engineering 195 pp 2070– (2006)
[41] Cavin, International Journal for Numerical Methods in Engineering 64 pp 304– (2006)
[42] Réthoré, International Journal for Numerical Methods in Engineering 64 pp 260– (2005)
[43] Réthoré, International Journal for Numerical Methods in Engineering 63 pp 631– (2005)
[44] Walhorn, Computers and Structures 83 pp 2100– (2005)
[45] Legay, International Journal for Numerical Methods in Engineering 64 pp 991– (2005)
[46] Ji, International Journal for Numerical Methods in Engineering 61 pp 2508– (2004)
[47] . Recent developments of the extended/generalized FEM and a comparison with the FEM. In Development and Applications of Solid Mechanics, University of Science and Technology of China Press: Hefei, China, 2005; 303–324. ISBN: 7-312-01842-4.
[48] Karihaloo, Computers and Structures 81 pp 119– (2003)
[49] An object oriented approach to the XFEM with applications to fracture mechanics. Master’s Thesis, EMMC-Hochiminh University of Technology, Vietnam, November 2005 (available on request).
[50] Zimmermann, Computer Methods in Applied Mechanics and Engineering 93 pp 291– (1992)
[51] Bordas, Engineering Fracture Mechanics 73 pp 1176– (2006)
[52] Stazi, Computational Mechanics 31 pp 38– (2003)
[53] Laborde, International Journal for Numerical Methods in Engineering 190 pp 6183– (2004)
[54] Béchet, International Journal for Numerical Methods in Engineering 64 pp 1033– (2005)
[55] Ventura, International Journal for Numerical Methods in Engineering 66 pp 761– (2006)
[56] . Enriched finite element short course: class notes. In The Extended Finite Element Method, A New Approach to Numerical Analysis in Mechanics: Course Notes. Organized by S. Bordas and A. Legay through the EPFL school of continuing education, Lausanne, Switzerland, 7–9 December 2005. http://www.civil.gla.ac.uk/bordas/publications.html
[57] Doxygen, a documentation system for C++, C, Java, Objective-C, Python, IDL (Corba and Microsoft flavors) and to some extent PHP, C#, and D, 1997–2006. http://www.stack.nl/dimitri/doxygen/
[58] Devillers, Computational Geometry: Theory and Applications 2 pp 55– (1992) · Zbl 0773.68066
[59] Dunant, European Journal of Computational Mechanics (Special Issue on Partition of Unity Enrichment in Finite Elements) (2006)
[60] Stolarska, International Journal for Numerical Methods in Engineering 51 pp 943– (2001)
[61] Duflot, International Journal for Numerical Methods in Engineering (2006)
[62] Chessa, International Journal for Numerical Methods in Engineering 57 pp 1015– (2003)
[63] , . Morphological aspects of fatigue crack propagation. Part II–effects of stress biaxiality and welding residual stresses. Technical Report, Department of Naval Architecture and Ocean Engineering, Yokohama National University, Japan, 1995.
[64] Fleming, International Journal for Numerical Methods in Engineering 40 pp 1483– (1997)
[65] Bouchard, Computer Methods in Applied Mechanics and Engineering 192 pp 3887– (2003)
[66] Rabczuk, Computational Mechanics (2006)
[67] NASA. Nasgro, 2003. NASA Johnson Space Center and Southwest Research Institute (SwRI), information available at http://www.nasgro.swri.org/
[68] Bordas, Engineering with Computers (2006)
[69] , . Static strength analysis of aerospace castings. Design and Quality Assurance of Premium Quality Aerospace Castings, FAA Contract DTFA03-98-F-IA025, 2003. Northwestern University, Center for Quality Engineering and Failure Prevention, McCormick School of Engineering and Applied Science. http://www.civil.gla.ac.uk/bordas/publications.html
[70] , . Damage tolerance assessment of complex aerospace structures. Design and Quality Assurance of Premium Quality Aerospace Castings, FAA Contract DTFA03-98-F-IA025, 2003. Northwestern University, Center for Quality Engineering and Failure Prevention, McCormick School of Engineering and Applied Science. http://www.civil.gla.ac.uk/bordas/publications.html
[71] , . Integrated design approach of aerospace castings. Design and Quality Assurance of Premium Quality Aerospace Castings, FAA Contract DTFA03-98-F-IA025, 2003. Northwestern University, Center for Quality Engineering and Failure Prevention, McCormick School of Engineering and Applied Science. http://www.civil.gla.ac.uk/bordas/publications.html
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.