PSI - Issue 66

Domenico Ammendolea et al. / Procedia Structural Integrity 66 (2024) 396–405 Author name / Structural Integrity Procedia 00 (2025) 000–000

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4. Numerical results This section presents numerical results aimed at assessing the accuracy and effectiveness of the present modeling approach. In particular, two case studies are examined, and the results are compared with experimental data and the predictions of other numerical strategies. The first case study, reported in Section 4.1, consists of a mixed-mode failure test of a notched concrete beam, which is employed to validate the ability of the process described in Section 3.2. The second case study, reported in Section 4.2, involves a three-point bending test of a perforated beam with an eccentric crack, which is used to evaluate the reliability of the proposed Adaptive approach in accurately predicting crack initiation, propagation and failure in heterogeneous structures under general loading conditions. 4.1. Mixed-mode failure test of a notched concrete beam Fig. 3-a depicts the notched concrete beam under a mixed-mode failure test, together with the adopted boundary conditions. The beam, already analyzed from an experimental point of view by Gálvez et al. (Gálvez et al., 1998) is 675 mm long ( D = 150 mm) and has a rectangular cross section of 50 mm width and 150 mm height. Typical material properties of concrete are considered: Young’s modulus E = 38 GPa, Poisson’s ratio ν = 0.2, tensile strength f t = 3 MPa, and fracture energy G c = 69 N/m. Plane stress conditions are assumed. In addition, the internal length scale l 0 is set equal to 2.5 mm and the Cornelissen’s softening curve is adopted to model the material degradation during crack growth. The computational domain is divided into 288 square macro-subdomains of side D /8 = 18.75 mm (Fig. 3-b). The initial zone of interest consists of 4 micro-subdomains. The fine mesh of a single micro-subdomain (see the zoomed view in Fig. 3-b) involves 2017 nodes and 3912 triangular elements arranged according to Delaunay scheme. Several Authors have investigated numerically the fracture behavior of this beam through advanced numerical strategies. Among these, Cervera et al. (Cervera et al., 2010) have replicated crack propagation by using a smeared damage approach, while Wu et al. (Wu et al., 2020) have employed a phase-field model. Fig. 4-a reports a comparison in terms of load (F) versus crack mouth opening displacement (CMOD) between the proposed adaptive method, the experimental data of Gálvez et al. (Gálvez et al., 1998) and the results achieved using the numerical methodologies taken as reference.

Fig. 3. Mixed-mode failure test of a notched concrete beam: (a) a schematic of the geometry and boundary conditions; (b) initial mesh configuration adopted for the fracture analysis and a zoomed view of the mesh of a single micro-subdomain.