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

Enhanced XFEM Framework with Modular Enrichment for Nonlinear and Mixed-Mode Crack Propagation | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Enhanced XFEM Framework with Modular Enrichment for Nonlinear and Mixed-Mode Crack Propagation Mahmoud Fadhel Idan This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-7809090/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract 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. Mechanical Engineering Extended Finite Element Method (XFEM) Nonlinear Fracture Plasticity Mixed-Mode Crack Propagation J-Integral Damage Mechanics Module Theory Computational Mechanics Full Text Additional Declarations The authors declare no competing interests. Cite Share Download PDF Status: Posted Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. 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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\u0026ndash;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. 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