International Journal of Fracture

, Volume 178, Issue 1–2, pp 51–70

# Crack propagation criteria in three dimensions using the XFEM and an explicit–implicit crack description

Original Paper

## Abstract

This paper studies propagation criteria in three-dimensional fracture mechanics within the extended finite element framework (XFEM). The crack in this paper is described by a hybrid explicit–implicit approach as proposed in Fries and Baydoun (Int J Numer Methods Eng, 2011). In this approach, the crack update is realized based on an explicit crack surface mesh which allows an investigation of different propagation criteria. In contrast, for the computation of the displacements, stresses and strains by means of the XFEM, an implicit description by level set functions is employed. The maximum circumferential stress criterion, the maximum strain energy release rate criterion, the minimal strain energy density criterion and the material forces criterion are realized. The propagation paths from different criteria are studied and compared for asymmetric bending, torsion, and combined bending and torsion test cases. It is found that the maximum strain energy release rate and maximum circumferential stress criterion show the most favorable results.

### Keywords

Three dimensional fracture Crack propagation criteria Extended finite element method XFEM Explicit crack description Implicit crack description Maximum circumferential stress Maximum strain energy release rate Minimum strain energy density Material forces

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