University of California, Davis

Introduction
Home
CV
Publications
Directions

Research
NEM X-FEM MAXENT
POLYFEM
QUANTUM

Teaching
ECI212A ENG104

Programming
C++ C++ FAQ
STL Python
PS CTAN CPAN

Links
E-Journals
Linux RPMs
Websters
Dilbert

Societies
USACM IUTAM

Sports
Running [Marathons]
Chess TT NBA

Weather
Davis

Google



EXTENDED FINITE ELEMENT METHOD


In the extended finite element method (X-FEM), a standard displacement based finite element approximation is enriched by additional (special) functions using the framework of partition of unity. It is a particular instance of the partition of unity finite element method (PUFEM) or the generalized finite element method (GFEM). In the X-FEM, the finite element mesh need not conform to the internal boundaries (cracks, material interfaces, voids, etc.), and hence a single mesh suffices for modeling as well as capturing the evolution of material interfaces and cracks in two- and three-dimensions. The striking advantages are that the finite element framework (sparsity and symmetry of the stiffness matrix) is retained, and a single-field variational principle is used. The initial developments of the X-FEM took place at Northwestern University (NU); here's a touch of nostalgia on the NU-connection. If you're interested in learning about this method, an excellent source is the X-FEM page at Aachen.

Publications

  • S. Banerjee and N. Sukumar (2017), "Exact Integration Scheme for Planewave-Enriched Partition of Unity Finite Element Method to Solve the Helmholtz Problem," Computer Methods in Applied Mechanics and Engineering, Vol. 317, pp. 619–648. [PDF]
  • E. B. Chin, J. B. Lasserre and N. Sukumar (2017), "Modeling Crack Discontinuities without Element-Partitioning in the Extended Finite Element Method," International Journal for Numerical Methods in Engineering, Vol. 110, Number 11, pp. 1021–1048. [PDF]
  • J.-H. Prévost and N. Sukumar (2016), "Faults Simulations for Three-Dimensional Reservoir-Geomechanical Models with the Extended Finite Element Method," Journal of the Mechanics and Physics of Solids, Vol. 86, pp. 1–18. [PDF]
  • N. Sukumar, J. E. Dolbow and N. Moës (2015), "Extended Finite Element Method in Computational Fracture Mechanics: A Retrospective Examination," International Journal of Fracture, Vol. 196, Number 1–2, pp. 189–206. [PDF]
  • J.-H. Prévost and N. Sukumar (2015), "Multi-scale X-FEM Faults Simulations for Reservoir-Geomechanical Models," 49th US Rock Mechanics/Geomechanics Symposium, American Rock Mechanics Association. [PDF]
  • E. B. Chin, J. B. Lasserre and N. Sukumar (2015), "Numerical Integration of Homogeneous Functions on Convex and Nonconvex Polygons and Polyhedra," Computational Mechanics, Vol. 56, Number 6, pp. 967–981. [PDF]
  • G. Hattori, R. Rojas-Díaz, A. Sáez, N. Sukumar and F. García-Sánchez (2012), "New Anisotropic Crack-Tip Enrichment Functions for the Extended Finite Element Method," Computational Mechanics, Vol. 50, Number 5, pp. 591–601. [PDF]
  • S. E. Mousavi, J. E. Pask and N. Sukumar (2012), "Efficient Adaptive Integration of Functions with Sharp Gradients and Cusps in n-Dimensional Parallelepipeds," International Journal for Numerical Methods in Engineering, Vol. 91, Number 4, pp. 343–357. [PDF] Available at arXiv:1202.5341
  • R. Rojas-Díaz, N. Sukumar, A. Sáez and F. García-Sánchez (2011), "Fracture in Magnetoelectroelastic Materials using the Extended Finite Element Method," International Journal for Numerical Methods in Engineering, Vol. 88, Number 12, pp. 1238–1259. [PDF]
  • G. Hattori, R. Rojas-Díaz, A. Sáez, F. García-Sánchez and N. Sukumar (2011), "El Método de los Elementos Finitos Extendidos (X-FEM) para Medios Bidimensionales Fisurados Totalmente Anisótropos," Anales de Mecánica de la Fractura, Vol. 28, Number 2, pp. 451–455. [PDF]
  • S. E. Mousavi and N. Sukumar (2011), "Numerical Integration of Polynomials and Discontinuous Functions on Irregular Convex Polygons and Polyhedrons," Computational Mechanics, Vol. 47, Number 5, pp. 535–554. [PDF]
  • S. E. Mousavi, E. Grinspun and N. Sukumar (2011), "Higher-Order Extended Finite Elements with Harmonic Enrichment Functions for Complex Crack Problems," International Journal for Numerical Methods in Engineering, Vol. 86, Number 45, pp. 560–574. [PDF]
  • S. E. Mousavi, E. Grinspun and N. Sukumar (2011), "Harmonic Enrichment Functions: A Unified Treatment of Multiple, Intersecting and Branched Cracks in the Extended Finite Element Method," International Journal for Numerical Methods in Engineering, Vol. 85, Number 10, pp. 1306–1322. [PDF]
  • J. X. Shi, D. Chopp, J. Lua, N. Sukumar and T. Belytschko (2010), "Abaqus Implementation of Extended Finite Element using a Level Set Representation for Three-Dimensional Fatigue Crack Growth and Life Predictions," Engineering Fracture Mechanics, Vol. 77, Number 14, pp. 2840–2863. [Top 25 Hottest article (July 2010-present)] [PDF]
  • S. E. Mousavi and N. Sukumar (2010), "Generalized Gaussian Quadrature Rules for Discontinuities and Crack Singularities in the Extended Finite Element Method," Computer Methods in Applied Mechanics and Engineering, Vol. 199, Number 4952, pp. 3237–3249. [PDF]
  • S. E. Mousavi and N. Sukumar (2010), "Generalized Duffy Transformation for Integrating Vertex Singularities," Computational Mechanics, Vol. 45, Number 2–3, pp. 127–140. [PDF]
  • R. Rojas-Díaz, N. Sukumar, A. Sáez and F. García-Sánchez (2009), "Crack Analysis in Magnetoelectroelastic Media using the Extended Finite Element Method," in Proceedings of the International Conference on Extended Finite Element Methods – Recent Developments and Applications, Eds. T.-P. Fries and A. Zilian, Aachen, Germany, pp. 181–186. [PDF]
  • J. Shi, J. Lua, L. Chen, D. Chopp and N. Sukumar (2009), "X-FEM for Abaqus (XFA) Toolkit for Automated Crack Onset and Growth Simulation: New Development, Validation, and Demonstration," 2009 SIMULIA Customer Conference. [PDF]
  • W. Aquino, J. C. Brigham, C. J. Earls and N. Sukumar (2009), "Generalized Finite Element Method using Proper Orthogonal Decomposition," International Journal for Numerical Methods in Engineering, Vol. 79, Number 7, pp. 887–906. [PDF]
  • E. Giner, N. Sukumar, J. E. Tarancón and F. J. Fuenmayor (2009), "An Abaqus Implementation of the Extended Finite Element Method," Engineering Fracture Mechanics, Vol. 76, Number 3, pp. 347–368. Journal [Top 25 Hottest article (2009-present)] [PDF]
  • E. Giner, N. Sukumar, F. J. Fuenmayor and A. Vercher (2008), "Singularity Enrichment for Complete Sliding Contact using the Partition of Unity Finite Element Method," International Journal for Numerical Methods in Engineering, Vol. 76, Number 9, pp. 1402–1418. [PDF]
  • E. Giner, N. Sukumar, F. D. Denia and F. J. Fuenmayor (2008), "Extended Finite Element Method for Fretting Fatigue Crack Propagation," International Journal of Solids and Structures, Vol. 45, Number 22–23, pp. 5675–5687. [PDF]
  • J. Shi, J. Lua, H. Waisman, P. Liu, T. Belytschko, N. Sukumar and Y. Liang (2008), "X-FEM Toolkit for Automated Crack Onset and Growth Prediction," 49th AIAA Conference, Schaumburg, IL, April 2008, pp. 1–22. [PDF]
  • N. Sukumar, D. L. Chopp, E. Béchet and N. Moës (2008), "Three-Dimensional Non-Planar Crack Growth by a Coupled Extended Finite Element and Fast Marching Method," International Journal for Numerical Methods in Engineering, Vol. 76, Number 5, pp. 727–748. [PDF]
  • A. Tabarraei and N. Sukumar (2008), "Extended Finite Element Method on Polygonal and Quadtree Meshes," Computer Methods in Applied Mechanics and Engineering, Vol. 197, Number 5, pp. 425–438. [PDF]
  • N. Sukumar, J. Dolbow, A. Devan, J. Yvonnet, F. Chinesta, D. Ryckelynck, Ph. Lorong, I. Alfaro, M. A. Martínez, E. Cueto and M. Doblaré (2005), "Meshless Methods and Partition of Unity Finite Elements," International Journal of Forming Processes, Vol. 8, Number 4, pp. 409–427. [PDF] (proof)
  • Z. Huang, Z. Suo, G. Xu, J. He, J. H. Prévost and N. Sukumar (2005), "Initiation and Arrest of an Interfacial Crack in a Four-Point Bend Test," Engineering Fracture Mechanics, Vol. 72, Number 17, pp. 2584–2601. [PDF]
  • N. Sukumar, Z. Y. Huang, J.-H. Prévost and Z. Suo (2004), "Partition of Unity Enrichment for Bimaterial Interface Cracks," International Journal for Numerical Methods in Engineering, Vol. 59, Number 8, pp. 1075–1102. [Abstract] [PDF] [PS]
  • N. Sukumar and D. J. Srolovitz (2004), "Finite Element-Based Model for Crack Propagation in Polycrystalline Materials," Computational & Applied Mathematics , Vol. 23, Number 2–3, pp. 363–380 [PDF] [HTML]
  • N. Sukumar (April 2003), "Meshless Methods and Partition of Unity Finite Elements," in Proceedings of the Sixth International ESAFORM Conference on Material Forming, Ed. V. Brucato, pp. 603–606. [PDF] [PS]
  • T. Belytschko, C. Parimi, N. Moës, N. Sukumar and S. Usui (2003), "Structured Extended Finite Element Methods for Solids Defined by Implicit Surfaces," International Journal for Numerical Methods in Engineering, Vol. 56, Number 4, pp. 609–635. [PDF]
  • N. Sukumar and J.-H. Prévost (2003), "Modeling Quasi-Static Crack Growth with the Extended Finite Element Method. Part I: Computer Implementation," International Journal of Solids and Structures, Vol. 40, Number 26, pp. 7513–7537 [Abstract] [PDF] [PS]
  • R. Huang, N. Sukumar and J.-H. Prévost (2003), "Modeling Quasi-Static Crack Growth with the Extended Finite Element Method. Part II: Numerical Applications," International Journal of Solids and Structures, Vol. 40, Number 26, pp. 7539–7552 [Abstract] [PDF] [PS]
  • D. L. Chopp and N. Sukumar (2003), "Fatigue Crack Propagation of Multiple Coplanar Cracks with the Coupled Extended Finite Element/Fast Marching Method," International Journal of Engineering Science, Vol. 41, Number 8, pp. 845–869 [Abstract] [PDF]
  • N. Sukumar, D. L. Chopp and B. Moran (2003), "Extended Finite Element Method and Fast Marching Method for Three-Dimensional Fatigue Crack Propagation," Engineering Fracture Mechanics, Vol. 70, Number 1, pp. 29–48 [Abstract] [PDF] [PS]
  • N. Sukumar, D. J. Srolovitz, T. J. Baker and J.-H. Prévost (2003), "Brittle Fracture in Polycrystalline Microstructures with the Extended Finite Element Method," International Journal for Numerical Methods in Engineering, Vol. 56, Number 14, pp. 2015–2037 [PDF]
  • N. Sukumar, D. L. Chopp, N. Moës and T. Belytschko (2001), "Modeling Holes and Inclusions by Level Sets in the Extended Finite–Element Method," Computer Methods in Applied Mechanics and Engineering, Vol. 190, Number 46–47, pp. 6183–6200 [Abstract] [PDF] [PS]
  • N. Moës, N. Sukumar, B. Moran and T. Belytschko (2000), "An Extended Finite Element Method (X-FEM) for Two- and Three-Dimensional Crack Modeling," in ECCOMAS 2000, Barcelona, Spain, September 11–14, 2000 [PDF]
  • N. Sukumar, N. Moës, B. Moran and T. Belytschko (2000), "Extended Finite Element Method for Three-Dimensional Crack Modelling," International Journal for Numerical Methods in Engineering, Vol. 48, Number 11, pp. 1549–1570 [PDF] [PS]
  • C. Daux, N. Moës, J. Dolbow, N. Sukumar and T. Belytschko (2000), "Arbitrary Branched and Intersecting Cracks with the Extended Finite Element Method," International Journal for Numerical Methods in Engineering, Vol. 48, Number 12, pp. 1741–1760 [PDF] [PS]
Presentations

C++ Code

Mesh Generation

  • Finite element mesh generator: gmsh
Simulations


You are visitor number to this page since June 06, 2002.


© Copyright 1999-2015, N. Sukumar. All rights reserved.