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Civil-Comp Proceedings
ISSN 1759-3433
CCP: 89
Edited by: M. Papadrakakis and B.H.V. Topping
Paper 126

The Extended Finite Element Method: A Review

L. Cahill1, C. McCarthy1 and S. Bordas2

1Composites Research Centre, Materials & Surface Science Institute, Department of Mechanical and Aeronautical Engineering, University of Limerick, Ireland
2Department of Civil Engineering, University of Glasgow, United Kingdom

Full Bibliographic Reference for this paper
L. Cahill, C. McCarthy, S. Bordas, "The Extended Finite Element Method: A Review", in M. Papadrakakis, B.H.V. Topping, (Editors), "Proceedings of the Sixth International Conference on Engineering Computational Technology", Civil-Comp Press, Stirlingshire, UK, Paper 126, 2008. doi:10.4203/ccp.89.126
Keywords: extended finite element analysis, level sets method.

Discontinuities in structures exist in many forms such as cracks, inclusions, material interfaces and holes. A reliable numerical simulation of these discontinuities is important from a design perspective. The finite element method (FEM) is a numerical tool which is widely used in industry and has proven very effective. However, in finite element analysis, modelling discontinuities within a domain can prove very troublesome due to the requirement that the displacement field across elements be continuous at all times. Hence, for discontinuity representation using the standard FEM, the discretisation must conform to the discontinuity, and remeshing must be carried out after each step. This often leads to a very dense mesh close to the discontinuity and a computationally inefficient model. Re-projecting the solution on the updated mesh is not only a costly operation but may also have a troublesome impact on the quality of the results [1].

The extended finite element method (XFEM) proposed by Belytschko and Black [2] is an extension of the standard finite element method. It is a numerical tool for modelling discontinuities within a standard finite element framework [3]. XFEM allows for mesh independent modelling of discontinuities and inhomogeneities and eliminates the requirement for a discontinuity to conform to element boundaries. This allows a discontinuity to be arbitrarily placed in an element, thus enabling the domain to be discretised without explicitly meshing the discontinuity. This article presents an overview and recent developments in the extended finite element method in modelling discontinuities. The method is detailed and its advantage over the standard FEM explained. The paper summarises the important milestones achieved using XFEM and draws attention to new and potential developments in this research area.

Y. Abdelaziz, A. Hamouine, "A survey of the extended finite element", Computers and structures, 86, 1141-1151, 2008. doi:10.1016/j.compstruc.2007.11.001
T. Belytschko, T. Black, "Elastic crack growth in finite elements with minimal remeshing", International Journal of Numerical Methods in Engineering, 45, 601-20, 1999. doi:10.1002/(SICI)1097-0207(19990620)45:5<601::AID-NME598>3.0.CO;2-S
N. Sukumar, J.H. Prevost, "Modelling quasi-static crack growth with the extended finite element method Part 1: Computer Implementation", International Journal of Solids and Structures, 40, 7513-7537, 2003. doi:10.1016/j.ijsolstr.2003.08.002

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