PSI - Issue 33

Umberto De Maio et al. / Procedia Structural Integrity 33 (2021) 954–965 Author name / Structural Integrity Procedia 00 (2019) 000 – 000

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to capture cracking phenomena, such interface elements can be inserted at the beginning of the simulation, according with the intrinsic-type formulation (Xu and Needleman, 1994), or adaptively during the simulation, once a certain stress criterion is satisfied, by following the so-called extrinsic-type formulation (Camacho and Ortiz, 1996; Cendón et al., 2000). The cohesive fracture models are often employed to investigate the damage processes in both layered structures, where the crack path is a priori known (Pascuzzo et al., 2020), and innovative functionally graded materials (Ammendolea et al., 2021), also by using moving mesh techniques to reduces the well-known directional mesh-bias dependency issues (Greco et al., 2021a). Due to the effectiveness in predicting accurate fracture properties, such cohesive models have been incorporated within multiscale approaches to investigate the mechanical behavior of quasi brittle materials under general loading conditions (Greco et al., 2020a, 2020b, 2020c). Moreover, a diffuse interface model, based on an intrinsic cohesive formulation, has been widely used to perform failure analyses of reinforced concrete structures externally strengthened with FRP systems also enhanced with graphite nanoplatelets (De Maio et al., 2019a, 2020a). Numerical simulations of complex failure mechanisms in fiber-reinforced composite materials, including micro-cracking and contact evolution, have been performed through fracture models based on homogenization approaches and cohesive zone models (De Maio et al., 2020d; Greco et al., 2018a, 2018b), also considering nacre-like microstructures (Greco et al., 2021b). On the other hand, the intra-element models embed the crack-induced discontinuity into the displacement field of the cracked element through suitable kinematic enrichment functions either at the nodal or element level. Such a modeling strategy allows the cracks propagation with unknown paths to be simulated almost independently of the adopted finite element mesh. The well-known extended finite element methods (XFEM) rely on a nodal-based formulation to reproduce the displacement jump by introducing extra degrees of freedom at the nodes of the cracked finite elements (Moës and Belytschko, 2002; Zi and Belytschko, 2003). In the standard phantom nodes method (PNM), usually employed together with cohesive zone models, the cracked elements are replaced by new superimposed finite elements equipped with phantom nodes, thus allowing the crack discontinuity to be modeled at an arbitrary location in the FE mesh (Song et al., 2006; Gasser and Holzapfel, 2005). However, such fracture methods require a high computational effort due to the fact that double the usual number of nodes in the cracked elements is needed during the simulation. In the embedded strong discontinuity approaches, successfully used to predict concrete cracking processes along nonprescribed paths, the displacement discontinuity is taken into account by modifying the classical continuum kinematic descriptions of the finite element (Simo et al., 1993; Oliver, 1996a; Dvorkin et al., 1990). However, the numerical models based on such fracture approaches need sophisticated tracking algorithms to ensure the correct location and direction of the crack as well as to enforce the crack path continuity (Kawashita and Hallett, 2012). Given the high number of numerical fracture models available in the technical literature, suitable comparative studies are very useful to the scientific community to evaluate the most appropriate fracture approach for cracking analysis. To this end, in the present work two different discrete fracture models, i.e., the diffuse interface model (DIM) and the embedded crack model (ECM), presented by some of the authors in (De Maio et al., 2019b, 2020c) and in (Sancho et al., 2007; Morales-Alonso et al., 2018) respectively, are compared and in-depth analyzed. The paper is organized as follows: in Section 2, the two adopted models are briefly described, providing some theoretical and computational details. Then, after to perform several simulations by these two models involving plain concrete specimens under general loading conditions, in Section 3, are reported the comparison between the numerically predicted results together with available numerical and experimental results, in terms of loading curve and crack patterns. In Section 4 of this paper, concluding remarks are provided. 2. Description of the adopted numerical fracture models In this section the two numerical fracture models adopted for comparison purposes, i.e., the DIM and ECM, based on an inter- and intra-element fracture approach respectively, are briefly described. 2.1. The diffuse interface model The diffuse interface model simulates the cracking behavior in quasi-brittle materials through zero-thickness interface elements, equipped with a cohesive traction-separation law, inserted along all boundaries of the finite