Analysis of the Stress Concentration Factor at the Circular Holes Near Materials Border Assessed by the Extended Finite Element Method

Despite the widespread use of the finite element method (FEM) in stress analysis, traditional FEM faces significant limitations in accurately modeling discontinuities such as cracks or holes—especially when these features are located near material interfaces. This scientific gap hampers precise estimation of stress concentration factors (SCFs) in composite and multi-material structures, where stress behavior is highly sensitive to material transitions.

To address this limitation, our study leverages the extended finite element method (XFEM), implemented in MATLAB, to analyze SCFs around circular holes situated near the boundary between two isotropic materials. XFEM overcomes the meshing challenges inherent in classical FEM by enriching the displacement field with discontinuous functions based on the partition of unity framework. This allows for an efficient and accurate representation of geometric discontinuities without the need for mesh refinement around singularities.

We apply XFEM to a rectangular plate with a circular opening near the material interface and demonstrate its capability to deliver high-fidelity stress predictions. The numerical results show excellent agreement with classical FEM and analytical solutions, while also exhibiting improved accuracy in capturing stress variations near the interface. These findings validate XFEM as a robust and efficient tool for interface problems, filling a critical gap in the modeling of stress concentrations in heterogeneous materials.