ISSN 打印: 1543-1649
ISSN 在线: 1940-4352

# 国际多尺度计算工程期刊

DOI: 10.1615/IntJMultCompEng.2013006523
pages 597-631

## IMPROVED CRACK TIP ENRICHMENT FUNCTIONS AND INTEGRATION FOR CRACK MODELING USING THE EXTENDED FINITE ELEMENT METHOD

Nicolas Chevaugeon
LUNAM Universite, GeM UMR6183, Ecole Centrale de Nantes, 1 Rue de la Noe, 44321 Nantes, France
Nicolas Moes
LUNAM Universite, GeM UMR6183, Ecole Centrale de Nantes, 1 Rue de la Noe, 44321 Nantes, France
Hans Minnebo
LUNAM Universite, GeM UMR6183, Ecole Centrale de Nantes, 1 Rue de la Noe, 44321 Nantes, France

### ABSTRACT

This paper focuses on two improvements of the extended finite element method (X-FEM) in the context of linear fracture mechanics. Both improve the accuracy and the robustness of the X-FEM. In a first contribution, a new enrichment strategy is proposed to take into account the singular stress field at the crack tip that is meant to replace the traditional four-crack-tip enrichment functions. The efficiency of the new approach is demonstrated on mesh convergence experiments for two-dimensional straight and curved crack problems, using first- and second-order shape functions, both in terms of convergence rates and in terms of condition number of the system to solve. The second contribution revisits the problem of the numerical integration of the stiffness operator when singular functions like the tip enrichment functions are used. An original algorithm to build accurate and fast integration rules for elements in the enrichment zone, touching the crack tip singularity, or not, is presented. The effects on convergence rate of the choice of the integration rule are illustrated on numerical examples.

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