### Abstract

This paper shows how the strain smoothing technique recently proposed by G.R.Liu [1] coined as smoothed finite element method (SFEM) can be coupled to partition of unity methods, namely extended finite element method (XFEM) [2] to give birth to the smoothed extended finite element method (SmXFEM), which shares properties both with the SFEM and the XFEM. The proposed method suppresses the need to compute and integrate the derivatives of shape functions (which are singular at the tip in linear elastic fracture mechanics). Additionally, integration is performed along the boundary of the finite elements or smoothing cells and no isoparametric mapping is required, which allows elements of arbitrary shape. We present numerical results for cracks in linear elastic fracture mechanics problems. The method is verified on several examples and comparisons are made to the conventional XFEM.

Original language | English |
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Title of host publication | Proceedings of the 6th International Conference on Engineering Computational Technology |

Publication status | Published - 2008 |

Event | 6th International Conference on Engineering Computational Technology, ECT 2008 - Athens, Greece Duration: 2008 Sep 2 → 2008 Sep 5 |

### Publication series

Name | Proceedings of the 6th International Conference on Engineering Computational Technology |
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### Other

Other | 6th International Conference on Engineering Computational Technology, ECT 2008 |
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Country | Greece |

City | Athens |

Period | 08/9/2 → 08/9/5 |

### Keywords

- Cracks without remeshing
- Extended finite element method
- Fracture mechanics
- Partition of unity methods
- Smoothed finite element method
- Strain smoothing

### ASJC Scopus subject areas

- Computer Science(all)

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## Cite this

*Proceedings of the 6th International Conference on Engineering Computational Technology*(Proceedings of the 6th International Conference on Engineering Computational Technology).