Journal
INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING
Volume 113, Issue 2, Pages 252-276Publisher
WILEY
DOI: 10.1002/nme.5611
Keywords
crack propagation; geometrical enrichment; linear enrichment; vector level sets; XFEM
Funding
- European Research Council [279578]
- Fonds National de la Recherche Luxembourg FWO-FNR [INTER/FWO/15/10318764]
- Swiss National Science Foundation [200021_153379]
- EPSRC [EP/G042705/1] Funding Source: UKRI
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We present a three-dimensional vector level set method coupled to a recently developed stable extended finite element method (XFEM). We further investigate a new enrichment approach for XFEM adopting discontinuous linear enrichment functions in place of the asymptotic near-tip functions. Through the vector level set method, level set values for propagating cracks are obtained via simple geometrical operations, eliminating the need for solution of differential evolution equations. The first XFEM variant ensures optimal convergence rates by means of geometrical enrichment, ie, the use of enriched elements in a fixed volume around the crack front, without giving rise to conditioning problems. The linear enrichment approach, significantly simplifies implementation and reduces the computational cost associated with numerical integration, while providing nonoptimal convergence rates similar to standard finite elements. The 2 dicretization schemes are tested for different benchmark problems, and their combination to the vector level set method is verified for nonplanar crack propagation problems.
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