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Title: Extended finite element method with edge-based strain smoothing (ESm-XFEM) for linear elastic crack growth
Authors: Chen, L. 
Rabczuk, T.
Bordas, S.P.A.
Liu, G.R.
Zeng, K.Y. 
Kerfriden, P.
Keywords: Convergence rate
Edge-based smoothed finite element method
Extended finite element method
Fracture analysis
Numerical method
Stress intensity factor
Issue Date: 1-Feb-2012
Citation: Chen, L., Rabczuk, T., Bordas, S.P.A., Liu, G.R., Zeng, K.Y., Kerfriden, P. (2012-02-01). Extended finite element method with edge-based strain smoothing (ESm-XFEM) for linear elastic crack growth. Computer Methods in Applied Mechanics and Engineering 209-212 : 250-265. ScholarBank@NUS Repository.
Abstract: This paper presents a strain smoothing procedure for the extended finite element method (XFEM). The resulting "edge-based" smoothed extended finite element method (ESm-XFEM) is tailored to linear elastic fracture mechanics and, in this context, to outperform the standard XFEM. In the XFEM, the displacement-based approximation is enriched by the Heaviside and asymptotic crack tip functions using the framework of partition of unity. This eliminates the need for the mesh alignment with the crack and re-meshing, as the crack evolves. Edge-based smoothing (ES) relies on a generalized smoothing operation over smoothing domains associated with edges of simplex meshes, and produces a softening effect leading to a close-to-exact stiffness, "super-convergence" and "ultra-accurate" solutions. The present method takes advantage of both the ES-FEM and the XFEM. Thanks to the use of strain smoothing, the subdivision of elements intersected by discontinuities and of integrating the (singular) derivatives of the approximation functions is suppressed via transforming interior integration into boundary integration. Numerical examples show that the proposed method improves significantly the accuracy of stress intensity factors and achieves a near optimal convergence rate in the energy norm even without geometrical enrichment or blending correction. © 2011 Elsevier B.V.
Source Title: Computer Methods in Applied Mechanics and Engineering
ISSN: 00457825
DOI: 10.1016/j.cma.2011.08.013
Appears in Collections:Staff Publications

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