A Comparative Assessment of XFEM and FEM for Stress Concentration at Circular Holes near Bi-Material Interfaces

Accurately predicting stress concentration factors (SCFs) is essential for assessing the structural integrity of components containing holes or discontinuities, especially in multi-material systems. Traditional Finite Element Method (FEM) models often require substantial mesh refinement near geometric discontinuities, whereas the Extended Finite Element Method (XFEM) allows discontinuities to be represented independently of the mesh through enrichment functions. This study provides a comparative assessment of FEM and XFEM for evaluating SCFs around a circular hole located near a bi-material interface. Both methods are implemented in MATLAB R2019a using the level-set approach to describe the hole. The displacement and stress fields obtained from FEM and XFEM are compared, followed by an evaluation against an established analytical reference solution. The findings show that while both methods reproduce global fields with good agreement, differences arise in the accuracy of SCF prediction. These results highlight the conditions under which XFEM may offer advantages over conventional FEM when modeling discontinuities in heterogeneous materials.