A Node-Based Smoothed eXtended Finite Element Method (NS-XFEM) for Fracture Analysis

N. Vu-Bac, H. Nguyen-Xuan, L. Chen, S. Bordas, P. Kerfriden, R. N. Simpson, G. R. Liu, Timon Rabczuk

Research output: Contribution to journalArticlepeer-review

107 Citations (Web of Science)


This paper aims to incorporate the node-based smoothed finite element method (NS-FEM) into the extended finite element method (XFEM) to form a novel numerical method (NS-XFEM) for analyzing fracture problems of 2D elasticity. NS-FEM uses the strain smoothing technique over the smoothing domains associated with nodes to compute the system stiffness matrix, which leads to the line integrations using directly the shape function values along the boundaries of the smoothing domains. As a result, we avoid integration of the stress singularity at the crack tip. It is not necessary to divide elements cut by cracks when we replace interior integration by boundary integration, simplifying integration of the discontinuous approximation. The key advantage of the NS-XFEM is that it provides more accurate solutions compared to the XFEM-T3 element. We will show for two numerical examples that the NS-XFEM significantly improves the results in the energy norm and the stress intensity factors. For the examples studied, we obtain super-convergent results.

Original languageEnglish
Pages (from-to)331-356
Number of pages25
Issue number4
Publication statusPublished - Mar 2011
Externally publishedYes


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