A discrete variational framework for crack propagation via potential energy minimization in the DBEM

This paper presents a novel energetic framework for modeling crack propagation in isotropic linear elastic media, established upon a discrete variational formulation. Diverging from traditional local growth criteria that rely on the extraction of asymptotic crack-tip fields, the proposed methodology is grounded in the fundamental Principle of Minimum Potential Energy and implemented via the Dual Boundary Element Method (DBEM). The core innovation of this research is the Potential Energy Minimization Algorithm (PEMA), which redefines incremental crack evolution as a discrete shape-optimization sequence. By identifying optimal propagation trajectories through global energetic stationarity, the algorithm effectively circumvents the numerical instabilities and mesh sensitivities inherent in explicit Stress Intensity Factor (SIF) evaluations or specialized crack-tip enrichment strategies. The robustness and predictive accuracy of the PEMA are validated through a comprehensive suite of benchmark problems, encompassing mixed-mode loading, localized stress concentrations, and complex multi-crack interactions. Quantitative comparative analysis demonstrates that the PEMA maintains high fidelity relative to the Maximum Tangential Stress (MTS) criterion and experimental data while providing enhanced trajectory stability. By formulating the energetic functional strictly in terms of boundary integrals, the framework offers a computationally efficient and physically consistent approach to structural integrity assessment, establishing a rigorous foundation for modeling fracture in complex geometric configurations.