Enhanced XFEM Framework with Modular Enrichment for Nonlinear and Mixed-Mode Crack Propagation

Fracture and crack propagation are central challenges in computational mechanics, particularly when nonlinear material behavior and mixed-mode interactions govern structural failure. The extended finite element method (XFEM) enables efficient modeling of discontinuities without requiring remeshing; however, traditional enrichment schemes often encounter numerical instability, excessive computational cost, and difficulties extending to nonlinear regimes. This study proposes an enhanced XFEM framework based on modular enrichment theory, systematically organizing enrichment functions to ensure algebraic consistency and numerical stability. The formulation is extended to incorporate nonlinear constitutive behavior, plasticity, damage, and cohesive softening and to simulate mixed-mode (I–II) crack growth under disproportionate loading conditions. To enhance the evaluation of stress intensity factor (SIF), the framework combines interaction and J-integral methods for robust computation of fracture parameters. The modular enrichment structure simplifies the management of crack-tip singularities and discontinuities, ensuring scalability and facilitating integration with topology optimization schemes such as the Solid Isotropic Material with Penalization (SIMP) method. MATLAB-based numerical experiments validate the approach for both linear-elastic and nonlinear cases, demonstrating excellent agreement with analytical and benchmark solutions. Results confirm that the enhanced XFEM framework accurately captures crack initiation, growth, and branching, while maintaining computational efficiency and robustness. This study establishes a unified and extendable foundation for analyzing nonlinear and mixed-mode fracture in lightweight and dynamically loaded structures.