Stable GFEM (SGFEM): Improved conditioning and accuracy of GFEM/XFEM for three-dimensional fracture mechanics

• Proposed SGFEM provides significantly better conditioning and accuracy than GFEM.
• Condition number of the SGFEM is of the same order as in the FEM.
• SGFEM is more accurate than GFEM for both geometrical and topological enrichments.
• SIFs may deteriorate with mesh refinement if topological enrichment is adopted.
• Vector-valued singular enrichments yield better conditioning than scalar-valued.

In this paper, we present an extension of the Stable Generalized FEM (SGFEM) for 3-D fracture mechanics problems. Numerical experiments show that the use of available singular enrichment bases derived from the 2-D asymptotic crack tip solution leads to a severe loss of accuracy in the SGFEM. An enrichment scheme based on singular bases and linear polynomials is shown to recover the optimal convergence of the SGFEM. The proposed SGFEM for 3-D fractures delivers the same rate of growth in condition number as the standard FEM for proper choice of singular enrichment functions. The accuracy and conditioning obtained with the SGFEM is compared with the Generalized FEM (GFEM) for different types of singular enrichment bases. A fully 3-D fracture mechanics problem is considered to highlight issues that arise only in 3-D problems. The convergence of Stress Intensity Factors (SIFs) extracted from GFEM and SGFEM solutions and the effect of the size of enrichment sub-domains on the accuracy of extracted SIFs are also studied. It is shown that the accuracy of SIFs may deteriorate with mesh refinement when the topological enrichment strategy is adopted. The proposed SGFEM delivers much better accuracy than the GFEM for both geometrical and topological enrichment strategies.