PSI - Issue 39

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

645

8

Table 1. Material properties of the brick masonry couplets. Material Young’s modulus E (MPa)

Poisson’s ratio ν

Brick

16605

0.15 0.15

Mortar

2370

Steel

200000

0.3

Figure 4-a compares the stress ( σ ) vs elongation (u) ( i.e. , the LVDTs measurement) curves gained by the proposed DIM (without imperfections) with those predicted by the auxiliary models ( i.e. , SIM 1 and SIM 2). The graph also reports a zoomed view of the curves around the peak of stress. Figure 4-b depicts snapshots of the deformed shapes of the couplet corresponding to elongation values marked in Figure 4-a by Roman numerals. The results denote that the three models predict the same linear elastic behavior up to u=0.0027 mm (point I). For u>0.0027 mm, both the up and bottom interfaces damage, and different responses are observed. As expected, the metastable solution, corresponding to the perfect case ( i.e. , SIM 2), provides a very strong overestimation of the actual dissipated energy (induced by the simultaneous dissipation of both interfaces). Such a condition does not possess physical meaning. Contrarily, the stable model ( i.e. , SIM 1) predicts a steep softening branch because the dissipation source arises from one interface only. The proposed DIM model suffers from non-uniqueness issues in the numerical solution. As highlighted in the zoomed view of Figure 4-a, once that the peak stress is reached, stability issues affect the model, and both the up and bottom interfaces damage. Such a condition determines that the softening branch of the DIM overlaps the metastable one up to u=0.0087 mm. Figure 4-b, the damage scenario II of the DIM (corresponding to u=0.0086 mm) shows the simultaneous damage of both interfaces, like SIM 2. On the other hand, by observing the deforming shape of SIM 1, it can be observed that, for u=0.0086 mm, one of the two B-M interfaces should be clearly damaged. For u>0.0086, the numerical solver utilized by the DIM finds the stable solution and the structural response progressively became like that predicted by SIM 1. This behavior is highlighted by the sudden drop in the elongation-tension curve. The DIM and SIM models overlap starting from u=0.04 mm and at u=0.07 mm, they present the same fracture configuration, involving the damaging of a single interface only (snapshots III in Figure 4-b).

Figure 4. (a) Stress vs elongation curves achieved using the proposed DIM model (without imperfections) and the auxiliary models SIM 1 and SIM 2; (b) Snapshots of the deformed configurations of the brick masonry couplets relative to the elongation values marked by Roman numerals.