## 4 Case Study
### Results  
Experimental and numerical results appear together in Figure 6, which also includes photos from the actual test as well as the simulated damage configuration for instants of particular interest during the test (labeled as (\(a\)) to (\(e\))). Loading declivities are similar for the first testing phases until the global displacement reaches approximately \(1\,\mathrm{mm}\). At that point, corresponding to the normalized instant \(t=0.52\) in Figure 7, the main fissure closes and the \"triangle\" on the specimen's top contacts its \"main body\" underneath, leading to significant hardening effects in the experimental response. From that moment onward, simulation results cease to mimic the experiment in a reliable sense, as evidenced  
Figure 5: (**a**) Geometry of the test body with the boundary conditions used. (**b**) Final configuration obtained in the LDEM simulation (broken bars indicated in red, damage bars indicated in blue, and undamaged bars indicated in gray. Figure 6: Comparison between experimental and numerical results in terms of Global Reaction measured vs. applied displacement at constant velocity. (**a–c**) evolution of damage at the indicated points of the experimental result; (**d–f**) of LDEM. by the differences in the actual and simulated specimens' final configurations (Figure 6c,f). Therefore, the behavior of both indexes as failure predictors are not expected to agree with those from the experiments and are included here only for the sake of completeness. Instead, the main usefulness in discussing the simulations lies in evaluating the proposed alternative method for calculating the DPH index, since the simulated response provides access to the system's internal energy to compare with the simulated work applied by the testing machine. Figure 8 depicts the temporal evolution of the AE parameters calculated from the data collected during the experiment. The time scale is normalized with respect to the rupture time (216.49 s). The graph on top illustrates the load evolution (red) accompanied by the AE measurements from sensor \(S_{l}\). Since the measurements from both sensors were very similar, only one data set was used in the remainder of the work. The second graph concerns the \(b\)-value parameter computed from the mentioned sensor's signals using windows of 35 samples with three-sample overlaps. Finally, the bottom graph presents the evolution of the DPH parameter, inferred by taking the time derivative of the product between the applied displacement and the measured reaction forces on the specimen's supports. The gray line indicates the computed values for each instant, whereas the red one corresponds to its filtered counterpart. The three plots presented in Figure 8a (top, middle, and bottom) are divided into four different intervals by lightly colored shadows, identified as (I) red, (II) green, (III) blue, and (IV) gray, corresponding to each characteristic behavior identified visually during the test and registered as a video. Figures 7 and 8b aid in the interpretation of the intervals, which are characterized as follows:  
1. A localized vertical fissure develops in the superior right corner. Notice that no prefissure is discernible in that region until the normalized time approaches 0.3 (Figure 7a) but its appearance is anticipated by significant AE activity since \(t\cong 0.25\). 2. The prefissure begins to close with visible damage in its supporting region, while the damage in the superior right corner continues to develop. At this interval's end (normalized time = 0.52, displacement = 1 mm), there is significant hardening in the load vs. global displacement response. The partial closing of the prefissure is confirmed by Figure 7b. 3. The diagonal prefissure is entirely closed while the damage continues to increase in the superior right corner (Figure 7c). 4. A new fissure propagates from the head of the diagonal prefissure (Figures 6c and 8b).