PSI - Issue 39

Fabrizio Greco et al. / Procedia Structural Integrity 39 (2022) 638–648 Author name / Structural Integrity Procedia 00 (2019) 000–000

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1. Introduction Modeling of cracking mechanisms in quasi-brittle materials (e.g., concrete and ceramics) has been the subject of several investigations during the last decade. Many efforts have been spent to define effective numerical strategies for reproducing the nucleation and propagation of cracks. However, a precise reproduction of the fracture behavior of quasi-brittle materials through numerical simulations is technically challenging. Indeed, from a physical point of view, the formation and subsequent growth of cracks is a complex phenomenon, which involves the coalescence of diffuse micro-cracks up to the complete material failure. These mechanisms become more complex for masonry structures because of the presence of different materials arranged in articulated configurations. In the literature, several numerical strategies concerning the modeling of the fracture behavior of quasi-brittle materials have been proposed, most of which in the framework of the Finite Element Method. Usually, numerical strategies are collected according to the way cracks are represented. Hence, one can recognize ( i ) smeared crack and ( ii ) discrete models. Smeared crack models adopt proper constitutive models based on nonlinear strain-softening laws that reduce the mechanical properties of the material (i.e., stiffness and strength) when failure conditions occur ( Mazars and Pijaudier‐ Cabot (1989), Oliver (1989)). These models are computationally cheap and easy to use (Greco et al. (2013)). However, they can suffer from convergence drawbacks ( i.e. , numerical instabilities) and mesh dependency issues, which affect the reliability of the numerical solution. On the other hand, discrete models reproduce the presence of cracks by introducing explicit geometric or kinematic discontinuities into the standard finite element discretization. Depending on the location of these discontinuities, discrete models can be distinguished into intra-element and inter-element fracture approaches. Discrete models can be grouped into ( i ) intra-element and ( ii ) inter-element approaches. In the intra-element approaches, cracks propagate within the finite elements of the computational mesh. To permit this representation, finite element formulations are enriched by kinematic displacement fields of either element-type (e.g., Strong Discontinuities Approaches (SDA) (Sancho et al. (2007))) or nodal-type (e.g., XFEM (Bordas et al. (2007))). These approaches reproduce the nucleation and propagation of arbitrarily growing cracks correctly without using re meshing actions. However, the use of enriched functions adds extra degrees of freedom to the governing equations of the problem. This may cause numerical instabilities in the case of multiple propagating cracks, as frequently occur in quasi-brittle materials. In addition, very refined mesh frames are necessary to handle random growing cracks, thereby increasing the need for computational resources. Such inconvenience implies that intra-element strategies may be unpracticable with larger and articulated geometries. In the inter-element approaches, cracks propagate along the boundaries of the finite elements of the mesh. Such approaches employ interface elements to reproduce crack formation and propagation. One of the most used constitutive models is the cohesive zone model proposed Dugdale and Barenblatt (Dugdale (1960), Barenblatt (1962)) represents one of the widely used approaches to defining the constitutive behavior of interface elements. Usually, interface elements are inserted within certain boundaries of the computational mesh before the analysis. Then, this approach is useful for reproducing fracture mechanisms occurring along known crack paths like debonding problems (Greco et al. (2020a), Pascuzzo et al. (2020)). However, if crack paths are unknown in advance, this modeling strategy became quite cumbersome. Indeed, to reproduce growing random cracks, special procedures that change the mesh configuration according to the crack development must be used. Such procedures update the mesh frame and inject cohesive elements using peculiar insertion criteria (Camacho and Ortiz (1996)). This procedure leads to the need for continuous remeshing actions, thereby spending relevant computational resources to perform the entire simulation. Besides, re-meshing actions may generate convergence issues during the transition stage. As an alternative to traditional approaches, novel strategies based on the use of either advanced numerical techniques or refined fracture models have been proposed (Greco et al. (2018a), Greco et al. (2020c)). In (Ammendolea et al. (2021), Greco et al. (2021a)), a standard finite element model has been combined with a moving mesh technique consistent with the Arbitrarily Lagrangian-Eulerian (ALE) formulation (Greco et al. (2020d)). Such a modeling strategy offers several advantages, such as a considerable reduction of remeshing actions to reproduce the geometry variations induced by growing cracks. However, it can currently investigate fracture cracking problems with initial pre-cracks only.