International Journal of Fracture

, Volume 181, Issue 2, pp 189–208

# A simple and efficient XFEM approach for 3-D cracks simulations

• Himanshu Pathak
• Akhilendra Singh
• Indra Vir Singh
Original Paper

## Abstract

In this work, a simple and efficient XFEM approach has been presented to solve 3-D crack problems in linear elastic materials. In XFEM, displacement approximation is enriched by additional functions using the concept of partition of unity. In the proposed approach, a crack front is divided into a number of piecewise curve segments to avoid an iterative solution. A nearest point on the crack front from an arbitrary (Gauss) point is obtained for each crack segment. In crack front elements, the level set functions are approximated by higher order shape functions which assure the accurate modeling of the crack front. The values of stress intensity factors are obtained from XFEM solution by domain based interaction integral approach. Many benchmark crack problems are solved by the proposed XFEM approach. A convergence study has been conducted for few test problems. The results obtained by proposed XFEM approach are compared with the analytical/reference solutions.

### Keywords

3-D cracks SIFs LEFM Level sets Enrichment XFEM

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## Authors and Affiliations

• Himanshu Pathak
• 1
• Akhilendra Singh
• 1
• Indra Vir Singh
• 2