XFEM (Extended Finite Element Method)
XFEM (Extended Finite Element Method): Theoretical Foundations
What is XFEM?
Professor, what's so great about XFEM?
Principle of XFEM
Adds enrichment functions to the FEM displacement field:
- First term: Standard FEM
- Second term: Heaviside function $H$ — Discontinuity (jump) at the crack surface
- Third term: Crack tip enrichment $F_\alpha$ — Singular field of $\sqrt{r}$
You can add cracks without changing the mesh. No remeshing even during crack propagation!
This is the revolutionary advantage of XFEM. The crack position is described using the Level Set method.
Summary
The Birth of XFEM: The 1999 Revolution
XFEM (eXtended FEM) was proposed in 1999 by Belytschko and Black (Northwestern University). In conventional FEM, remeshing was required every time a crack propagated, but XFEM "adds" Heaviside and crack tip enrichment functions to the existing mesh, allowing crack representation without changing the mesh. Practical application accelerated with improvements by Moës and Dolbow in 2004.
Computational Methods for XFEM (Extended Finite Element Method)
XFEM FEM Settings
```
*ENRICHMENT, NAME=crack, TYPE=STATIONARY CRACK
element_set
*CONTOUR INTEGRAL, XFEM, CONTOURS=5, TYPE=J
```
STATIONARY CRACK (J/K evaluation for static cracks) or PROPAGATION CRACK (crack propagation).
Crack Propagation Criteria
Summary
Tracking Cracks by Combining with Level Set Method
XFEM is typically combined with the Level Set Method (LSM) to track crack geometry. Two Level Set functions, ψ (normal direction) and φ (tangential direction), describe the crack surface and tip, and the Level Sets are updated according to the crack growth direction. Both ANSYS SMART and Abaqus XFEM modules internally integrate LSM and XFEM, requiring users to only set crack growth criteria (maximum principal stress, SIF comparison, etc.).
XFEM (Extended Finite Element Method) in Practice
XFEM in Practice
Simulation of crack nucleation and propagation. Cracks in welded structures, fatigue cracks in piping.
Practical Checklist
Predicting Crack Growth in Welded Structures Using XFEM
EPRI (Electric Power Research Institute, USA) adopted XFEM for crack growth evaluation in nuclear power plant piping welds. Compared to the conventional manual crack shape update method, automatic tracking with XFEM reduced analysis time by 80%. The superiority of XFEM, which can track crack propagation even when cracks bend under thermal stress without remeshing, was demonstrated.
XFEM (Extended Finite Element Method): Software & Solver Comparison
XFEM Tools
Example of Utilizing Abaqus XFEM Module
XFEM is implemented in Abaqus/Standard via the *ENRICHMENT function, controlling crack propagation with SIGEPS (maximum principal strain criterion) or KCRIT (critical SIF criterion). EDF (Électricité de France) uses Abaqus XFEM for SCC (stress corrosion cracking) propagation analysis in nuclear primary system piping, achieving a more physically detailed evaluation than the conventional Engineering Assessment (FA-3) method with only a 10% increase in time.
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