PSI - Issue 66

Umberto De Maio et al. / Procedia Structural Integrity 66 (2024) 495–501 Author name / Structural Integrity Procedia 00 (2025) 000–000

498 4

A stress-based criterion is applied to identify the initiation of the crack. When the normal stress across a mesh boundary surpasses the material's critical tensile strength, the corresponding element is selected and aligned with the predicted crack path. This direction is determined by maximizing the energy release rate (ERR), calculated via a J integral approach along a closed contour around the crack tip (Mindess et al., 1977; Rigby and Aliabadi, 1993). The crack is then oriented, according to the kinking angle derived from this ERR calculation, by using the Arbitrary Lagrangian-Eulerian (ALE) method able to adjust the mesh by relocating nodes along the updated crack trajectory. ERR is computed by using the J-integral with respect to a closed path containing the crack tip and a local coordinate system aligned with the crack direction. 3. Numerical results The proposed model is employed to simulate the well-known single-crack expansion gravity dam experimentally and numerically analyzed by (Barpi and Valente, 2000; Carpinteri, 1989; Shi et al., 2013). In particular, a 1:40 scale concrete gravity dam model, with the geometric and boundary conditions depicted in Fig. 2a, is simulated. The material properties and the cohesive parameters required by the traction-separation law are reported in Table 1. Hydrostatic pressure is present on the upstream side of the dam, which can be equivalently represented by four concentrated loads, as shown in Fig. 2a. The magnitude of this pressure progressively increases until it reaches a critical point, leading to the dam's failure.

Fig. 2. Tested benchmark: (a) geometric and boundary conditions, and (b) adopted computational discretization.

Table 1. Material properties and cohesive parameters adopted for the analysis. Elastic modulus [MPa] Poisson ratio Density [kg/m 3 ] Fracture energy [N/m]

Tensile strength [MPa]

35700

0.1

2400

184

3.6

The numerical discretization adopted for the analysis has been reported in Fig. 2b. In particular, within the critical zone ahead of the pre-crack, a suitable mesh refinement has been performed, using a uniform (isotropic) Delaunay tessellation and imposing a maximum edge length of 5 cm. In this area the moving mesh technique is applied, while the remaining area is taken fixed. The test is carried out by controlling the CMOD. In Fig. 3 the numerical results obtained by the proposed model are depicted. In particular, Fig. 3a shows the predicted load versus CMOD curve together with a comparison with available numerical and experimental outcomes. The load initially increases to a peak value, after which it decreases due to progressive damage arising in the material. We can see that the numerical curve predicted by the proposed model is in good agreement to the numerical results. However, it is evident that the post-peak response observed in the experiment was notably higher than that of the numerical simulations, indicating a larger crack opening displacement (CMOD) in the experiment under identical loading conditions. This discrepancy might be attributed to the unexpected rigid body rotation