PSI - Issue 28

Domenico Ammendolea et al. / Procedia Structural Integrity 28 (2020) 1981–1991 Author name / Structural Integrity Procedia 00 (2019) 000–000

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assess the integrity of cracked structures. Several methods were developed for crack propagation simulations, such as the finite element method (FEM), the extended finite element method (XFEM), the boundary element method (BEM), and meshless methods. The FEM is the prevalent numerical method adopted for crack growth simulations, because of its flexibility to model complex systems. In general, FE models are classified in implicit and explicit approaches according to the way they represent internal discontinuities. The implicit approaches reproduce the presence of cracks through constitutive relationships with softening damage laws consistent with Continuum Damage Mechanics (CDM) (Bruno et al. (2013), Öchsner (2016), Scuro et al. (2018a), Scuro et al. (2018b)). These methods offer good predictions but suffer from mesh dependence issues and convergence difficulties. The explicit approaches provide a geometric representation of cracks since they use node-release or node-decoupling numerical techniques (Stylianou and Ivankovic (2002), Greco et al. (2018)). In this framework, the Cohesive Zone Model (CZMs) approach (Dugdale (1960), Barenblatt (1962)) is the most used modeling strategy for assessing the integrity of fractured structures (Morano et al. (2020), Pascuzzo et al. (2020)). However, explicit approaches are effective when cracks develop along pre-defined paths, such as interfaces between dissimilar materials. In cases of arbitrary crack trajectories, geometry evolution requires re meshing actions for each step of the propagation process, thus affecting computational efficiency. To avoid re-meshing events, several strategies have been developed, such as diffusive cohesive interface approaches (De Maio et al. (2019), De Maio et al. (2020), Greco et al. (2020b)). Although these approaches avoid re-meshing, the computational costs increase significantly, making prohibitive its adoption in the case of large computational domains. The XFEMmethod (Belytschko and Black (1999), Sukumar et al. (2000)) extends the classical FEM approach by including discontinuous enrichment functions to the finite element approximation to account for the presence of cracks. Also, it provides a fine representation of stress singularities near crack tips. In this context, crack growth mechanisms are traced by using reliable numerical techniques such as the level set method. Although XFEM avoids re-meshing actions since the crack path is embedded in mesh elements, complexities arise in formulating finite elements, material law, and performing numerical integrations. The BEM (Portela et al. (1993), Khoei et al. (2015)) discretizes only the boundaries of the domain, thus saving relevant computational cost because the re-meshing procedure becomes much easier to be implemented. However, the method applies to problems for which Green’s functions can be calculated, then linear homogenous problems only. The meshless methods (e.g. collocation methods (Fan et al. (2018)), and Petrov-Galerkin method (Yau et al. (1980)) describe the computational domain in terms of scattered nodes. In this framework, crack propagation processes are reproduced by moving computational nodes. Although meshless methods avoid the recourse to re-meshing procedure, generally, they require more computational efforts since many nodes should be inserted near crack tip in case of unknown crack paths. Previous discussion, presented above, has highlighted that each method presents its strengths and weaknesses, thus making it quite difficult to identify the best one. In the last decades, several attempts have been made to develop hybrid approaches, which join the advantages of standard methodologies (Greco et al. (2020a)). In this framework, efficient approaches have been proposed, such as the scaled boundary finite element method (SBFEM), which combines BEM and FEM approaches (Yang (2006)), and the element free Galerkin method (Belytschko et al. (1995)). In (Lonetti (2010), Funari et al. (2018a), Funari et al. (2018b)) a moving mesh (MM) strategy consistent with the Arbitrary Lagrangian Formulation (ALE) has been combined with fracture mechanics concepts to analyze multiple delamination phenomena in composite structures. The primary advantage of MM for FE crack propagation simulations consists of limiting re-meshing. Note that, the ALE approach has been applied to several computational investigations providing relevant benefits in terms of computational savings (see for instance Lonetti and Maletta (2018), Greco et al. (2020c), Greco et al. (2020d)). This study aimed to develop an efficient FE numerical modeling, which combines the moving mesh (MM) method and fracture mechanics concepts to predict arbitrary crack propagation mechanisms in linear elastic continuum media. The moving mesh method, based on the Arbitrary Lagrangian-Eulerian Formulation, is adopted to describe the evolution of discontinuities within the computational domain. Fracture variables at crack tips are evaluated by the interaction integral method (Yau et al. (1980), Kim and Paulino (2003)), which has been adopted in several crack propagation investigations. This paper is organized as follows. The first section gives a brief overview of theoretical formulations used in the present method. In the second section, the numerical implementation is discussed. Finally, in the last section, the reliability of the proposed methodology is assessed through comparison results with experimental data and other numerical approaches reported in the literature.