PSI - Issue 66

Umberto De Maio et al. / Procedia Structural Integrity 66 (2024) 495–501 Author name / Structural Integrity Procedia 00 (2025) 000–000

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1. Introduction The accurate prediction of fracture behavior in quasi-brittle materials is crucial for ensuring the structural integrity and long-term performance of engineering systems. The onset and propagation of cracks, driven by inherent material flaws and external stress conditions, are key phenomena in the failure analysis of these materials. A comprehensive understanding of crack initiation and growth can help prevent catastrophic failures in various applications, from civil engineering to aerospace industries. Fracture mechanics has long recognized the significance of inherent defects that combine stress concentrations to initiate cracks, threatening structural safety and reliability (Xu and Needleman, 1994; De Maio et al., 2024a; Lens et al., 2009). While laboratory experiments and analytical approaches provide foundational insights into fracture behavior, they are often limited in scope, particularly for complex geometries or loading conditions. Numerical simulations, on the other hand, offer an efficient and flexible means to study crack propagation in a wide range of scenarios (Bruno et al., 2009; Camacho and Ortiz, 1996; De Maio et al., 2023b; Greco et al., 2014, 2007). One of the most widely employed methods for simulating fracture is the finite element method (FEM), particularly through cohesive zone models (CZM). These models are capable of simulating crack propagation by introducing cohesive interfaces that represent the material’s fracture toughness and energy dissipation during crack evolution (Cusatis and Schauffert, 2009; Bažant and Li, 1997). Despite their widespread use, the application of CZM in FEM presents challenges, such as mesh dependence and the need for remeshing, particularly when arbitrary crack paths need to be captured in a mesh-independent manner (Álvarez et al., 2014; De Maio et al., 2023a; Zhou and Molinari, 2004). Recent advancements in adaptive cohesive interface models address these limitations by dynamically inserting cohesive elements based on crack propagation criteria, ensuring accurate tracking of crack paths without a priori knowledge of the fracture location (Geißler et al., 2010; Marfia et al., 2022; Paulino et al., 2008). Such techniques have been effectively employed in various studies, demonstrating their robustness in predicting crack trajectories in both mode I and mixed-mode fractures (De Maio et al., 2024b). By integrating adaptive mesh refinement and cohesive zone insertion, these models allow for efficient and accurate fracture simulations in complex geometries (Park et al., 2012; Truster, 2018). In (Yang and Chen, 2004) an energy-based crack propagation criterion is used in combination with a simple remeshing procedure to accommodate crack propagation and a local arc-length method is employed to solve the material nonlinear system equations characterized by strong snap-back. A macroscopic branching criterion, based on an energy integral, is proposed in (Chiaruttini et al., 2012) to track the crack path in an adaptive manner, however, mesh updating is needed as the simulation proceeds. Similar procedure is proposed by (Cheng and Zhou, 2020; Theocaris et al., 1989)and in (Gupta et al., 2022; Wu and Nguyen, 2018) for the phase-field method. A dynamic insertion of cohesive elements, based on the maximal energy release rate criterion to compute the crack direction, is developed by (Uribe Suárez et al., 2020) which obtain mesh-independent numerical results, in terms of crack propagation, considering different fracture conditions. An interesting model for simulating brittle fracture in elastic solids using a variational approach integrated into the finite element method (FEM) in proposed by (Miehe and Gürses, 2007). The model is built on a thermodynamic framework, where crack propagation follows the principles of energy dissipation and is driven by configurational forces. These forces are derived from the Clausius–Planck inequality and are guided by the classical Griffith criterion, which aims to maximize local dissipation and minimize the incremental energy release at the crack tip. Alternative models, able to avoid remeshing procedures, are based on the Arbitrary Lagrangian-Eulerian (ALE) kinematic description, where the mesh nodes arbitrarily move with respect to the material frame, providing smallest distortions of the finite elements during the crack propagation (Ammendolea et al., 2023; Greco et al., 2015). This paper presents an adaptive cohesive interface model for analyzing fracture in quasi-brittle materials, which dynamically inserts cohesive elements at critical locations, through the synergic work offered by the ALE and CZM formulations. The proposed method is validated against experimental and numerical benchmarks, highlighting its capability to predict arbitrary crack paths and its advantages over traditional methods. The results provide a comprehensive framework for simulating complex fracture behaviors in engineering materials, contributing to safer and more reliable structural designs.