PSI - Issue 39

Umberto De Maio et al. / Procedia Structural Integrity 39 (2022) 677–687 Author name / Structural Integrity Procedia 00 (2019) 000–000

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equal to 36.5 GPa and 0.1, respectively. The cohesive parameters of the embedded interfaces, required by the mixed mode traction-separation law, described in Section 2.1, are reported in Table 1.

Fig. 4. Simulated three-point bending test: (a) geometric configuration and (b) adopted mesh.

Table 1. Material parameters for the traction-separation law used in the three-point bending test. nc t [MPa] sc t [MPa] Ic G [N/m] IIc G [N/m] 0 n K [N/m 3 ] 0 s K [N/m 3 ] DIM 3.19 4.51 50 500 5.85e14 4.05e14

In order to reduce the computational effort, the cohesive elements are inserted only in a rectangular region dominated by a shear/bending stress state (Figure 4b). Such a region is meshed with a Delaunay tessellation by prescribing a maximum element size of 10 mm, resulting in an average mesh size of about 7.5 mm. The numerical analysis has been conducted by a classical displacement-control solution scheme, with constant displacement increments of 5e-3 mm. The resulting load versus deflection curve predicted by the proposed model for the tested concrete specimen is reported in Figure 5a, together with the numerical results obtained by Carpinteri and Colombo (1989) taken to comparison purposes.

Fig. 5. Simulated three-point bending test: (a) load versus deflection curves and (b) deformed configurations obtained by the proposed model.

The structural response predicted by the model is globally in good agreement with the reference one but results to be slightly stronger at peak load and post-peak stage due to the artificial toughening effect induced by the employed unstructured mesh. However, the relative error on the peak load predicted by the model with respect to the reference, being only 4%, is judged acceptable for engineering purposes.