PSI - Issue 79

Umberto De Maio et al. / Procedia Structural Integrity 79 (2026) 386–393

387

1. Introduction Understanding material failure is fundamental to ensuring the safety and reliability of complex engineering structures. The study of how damage initiates and propagates, particularly in quasi-brittle construction materials, thus remains a critical field of research. Historically, the foundations of fracture mechanics were established through analytical models and experimental testing (Barenblatt, 1962). However, these traditional approaches often struggle to capture the behavior of complex geometries, specialized microstructures, or unique loading conditions. This gap has driven the development of advanced numerical methods, which have become essential tools for simulating complex fracture mechanisms efficiently and reliably (Sedmak, 2018; Funari et al., 2020; Greco et al., 2022; Gaetano et al., 2022; De Maio et al., 2025). Indeed, computational modeling plays a crucial role across diverse engineering applications, from predicting the behavior of randomly structured composites (Barretta et al., 2015; Pranno et al., 2025) and analyzing advanced functional materials under complex loading conditions (Tocci Monaco et al., 2021), to characterizing novel materials for modern manufacturing processes (Farina et al., 2019). In recent decades, numerical modeling of fracture has grown extensively, with models becoming crucial to the study of the subject. Among the various strategies, Cohesive Zone Models (CZM) are widely employed to describe the nonlinear crack propagation process. Pioneering works, such as that by Xu and Needleman (Xu and Needleman, 1994), proposed solutions for dynamic crack growth by inserting cohesive surfaces. Later, Camacho and Ortiz (Camacho and Ortiz, 1996) developed a cohesive model for arbitrary crack growth. The modeling of damage phenomena such as mixed-mode cracking in concrete and debonding failures at FRP-concrete interfaces has been a significant area of research, often employing cohesive zone or interface damage models (Bruno et al., 2009, 2007; Greco et al., 2002; Greco and Lonetti, 2009). However, standard CZM approaches suffer from significant limitations. They are highly dependent on the finite element mesh, and simulating arbitrary crack paths that do not align with pre defined element boundaries requires complex and computationally expensive re-meshing procedures (Álvarez et al., 2014). To overcome the mesh-dependency of CZMs, several alternative strategies have been proposed. Intra-element approaches enrich the kinematics of the problem, either at the element level, such as the strong discontinuity approach (SDA) (Sancho et al., 2007), or at the nodal level, which requires additional degrees of freedom, as seen in the phantom node method (PNM) (Song et al., 2006) and the extended finite element method (XFEM) (Moës and Belytschko, 2002). More recently, phase-field models (PFM) have gained popularity for simulating both quasi-static and dynamic brittle fracture with extensions proposed for cohesive fracture (Ammendolea et al., 2025c). Nevertheless, PFM approaches typically require considerable mesh refinement to accurately capture the transition from undamaged to damaged regions, thus increasing the computational burden. The challenge of fracture simulation is further amplified in heterogeneous and multiphase materials, such as concrete or composites (De Borst, 2008). In these materials, fracture is an inherently multiscale phenomenon where processes at the microscopic scale influence the global structural behavior (De Maio et al., 2024; Gaetano et al., 2025; Greco et al., 2017, 2015; Unger and Eckardt, 2011). The crack path is complex, often deflecting along the weaker interfaces between the matrix and inclusions. Accurately modeling this behavior requires a numerical framework that can not only follow an arbitrary path but also explicitly account for the presence of material discontinuities (Greco et al., 2025; Haslach, 2002; Luciano and Willis, 2003). Recent developments have attempted to address these issues through meshless methods (Zhang et al., 2024) or by dynamically inserting cohesive elements based on propagation criteria. Other approaches utilize moving mesh techniques, where finite elements are moved and refined around the crack tip during the analysis (Ammendolea et al., 2025a, 2025b, 2023; Greco et al., 2021). However, the computational cost of such models remains high due to the re meshing algorithms required. Therefore, there is still a clear need for numerical models capable of overcoming the limitations of standard cohesive approaches, particularly mesh dependence and the need for re-meshing, while maintaining computational efficiency. To address these persistent computational challenges, the present work proposes a novel numerical framework that integrates a cohesive fracture model with an Arbitrary Lagrangian–Eulerian (ALE) formulation. This integration is the key to our strategy. The ALE kinematic allows the finite element mesh to move and dynamically conform to the geometry of the propagating crack. Consequently, cohesive elements can be adaptively inserted along element boundaries as the crack advances, entirely bypassing the need for computationally expensive re-meshing procedures.