PSI - Issue 41

Fabrizio Greco et al. / Procedia Structural Integrity 41 (2022) 576–588 Author name / Structural Integrity Procedia 00 (2019) 000–000

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1 Introduction Several engineering fields extensively use quasi-brittle materials in their applications ( e.g. , ceramic, concrete, functionally graded materials) because of the excellent thermal properties, the high resistance to aggressive environment media, and the long durability. However, such materials are highly vulnerable to dynamic loadings, such as seismic-induced vibrations, wind forces, and the impact of foreign objects (Barretta et al. (2015a), Barretta et al. (2015c)). Dynamic loadings generate rapid crack propagation phenomena inside the material that, once triggered, develop in an unstable fashion, thus compromising the overall integrity (Greco et al. (2018a), Greco et al. (2022)). Therefore, proper investigation approaches for predicting dynamic fracture phenomena in quasi-brittle materials are essential to assess the integrity of both novel and existing engineering applications. Besides, accurate analysis tools can effectively identify suitable strategies to improve the overall performances of key components made of quasi-brittle materials, thus lengthening their operative life (Barretta et al. (2015b), Gaetano et al. (2022)). In recent years, there has been an increased interest in developing numerical methods to investigate the fracture behavior of materials because of the possibility of achieving a compressive overview of all critical factors involved in fracture processes with reduced economic resources. Most of the numerical approaches reported in the literature have been developed in the Finite Element Method (FEM) framework, given its flexibility in modeling material pieces with complex geometries (as usually occurs in modern engineering applications) (Luciano and Willis (2005), Greco et al. (2020c), Greco et al. (2021b)). In addition, FEM approaches have always been the primary means of analysis in many research and development sectors of both academic and industrial contexts (Luciano and Willis (2001), Barretta et al. (2018), Greco et al. (2018b), Greco et al. (2020a), Greco et al. (2020b), Pranno et al. (2022)). Pioneer FE models reproduced crack propagation phenomena inside the computational mesh using simple nodal release techniques (Ando et al. (1977), Nishioka and Atluri (1980)). Although such techniques are relatively simple to implement, the numerical models suffer from significant mesh dependency issues because the crack can grow only along the boundaries of the configured computational mesh. This drawback determines the loss of accuracy in the associated numerical solution, especially when the fracture behavior presents randomly growing cracks, as typically occurs in dynamic fracture processes in quasi-brittle materials. As a remedy to these mesh dependency issues, recent FE models have adopted advanced remeshing techniques (Koh et al. (1988), Swenson and Ingraffea (1988)), which refresh the computational mesh at each step of the crack advance according to crack path evolution. Despite their benefits, such techniques are computationally onerous, thus increasing notably the time required to perform numerical simulations. Besides, the updating process may compromise the reliability of numerical solutions because traditional solvers may incur convergence difficulties, thereby compromising the stability of numerical computation. Instead of conventional FE procedures, numerical models based on the Cohesive Zone Model (CZM) approach developed by Dugdale and Barenblatt have been proposed (Dugdale (1960), Barenblatt (1962)). These approaches effectively reproduce fracture phenomena occurring along known crack trajectories, such as de-cohesion fracture processes at material interfaces (Pascuzzo et al. (2020), Ekhtiyari and Shokrieh (2022)). However, when the crack path is unknown in advance, CZM-based modeling strategies become rather cumbersome and onerous. Indeed, advanced modeling strategies serve to trace arbitrarily growing cracks, such as, for instance, those consistent with the Diffuse Interface Modeling (DIM) approaches (De Maio et al. (2019a), De Maio et al. (2020a), De Maio et al. (2022), Pascuzzo et al. (2022)). DIM strategies consist of introducing zero-thickness cohesive interface elements along all the boundaries of the computational mesh. Hence, the crack is not forced to grow along a pre-defined path, but it can develop naturally using any boundary of computational mesh, even reproducing coalescence and branching events. Despite its efficacy, DIM approaches are computationally expensive. Indeed, reproducing random growing crack implicates the necessity for highly refined computational meshes, which determine significant increment of the number of Degrees of Freedom (DOFs) to be solved for. This drawback limits the operative range of the DIM approach to computational domains of reduced sizes (De Maio et al. (2019b), De Maio et al. (2020b), De Maio et al. (2021)). Besides numerical models based on CZM approaches, several works reported in the literature have developed advanced modeling strategies using XFEM procedures (Belytschko et al. (2003), Wen and Tian (2016)). In XFEM methods, standard finite element formulations are enriched by discontinuous displacement fields (defined through enriched shape functions), allowing accurate representations of crack trajectories and singularity fields near crack