MATLAB Implementation of Extended Finite Element Method

In this article, we present a program written in MATLAB that simulates crack propagation using the Extended Finite Element Method (XFEM). This implementation is particularly valuable as it enables engineers and researchers to better understand fracture mechanics and make more accurate predictions about material strength and durability. The code architecture incorporates key XFEM components including enrichment functions for crack tip singularity modeling and level set methods for tracking crack interfaces. Users can configure various parameters through structured input files, including material properties (Young's modulus, Poisson's ratio), stress conditions, and environmental factors to simulate crack behavior under different scenarios. The program features modular functions for mesh generation (using MATLAB's PDE toolbox), stress calculation, and crack propagation criteria evaluation. Post-processing modules provide visualization capabilities through contour plots and animated crack growth sequences, allowing users to intuitively analyze simulation results. The implementation utilizes MATLAB's sparse matrix operations for efficient solving of enriched finite element equations. This tool serves as a practical resource for research in materials science and mechanical engineering, offering both educational value and practical application potential.