## 4 Second Application: Three-Point Bending Test and Comparison to Experimental Data
### Results  
The results from the simulated model are shown in Figures 11-16. In Figure 11, simulation results are directly compared to the corresponding experimental results obtained by [41], for \(\zeta=0\%\). The best approximation from the numerical model occurred when \(CV(G_{f})=65\%\), as observed in Section 4.1. Figure 11: Comparison of experimental [41] and simulated LDEM results for (\(\zeta=0\%\)). Figure 12: The AE evolution during the simulation for both analyzed configurations. The load vs. normalized time is also presented. Figure 12 depicts the progression of the AE events in normalized time, accompanied by the load applied to both configurations. The simulated increases in the kinetic and dissipated energies are also presented. As in Section 3, there was a clear correspondence between the identified AE events and the energy spikes that signaled damage. Figure 13 illustrates the global energy balances of the two configurations. The structure was more fragile when the fissure was not centered (\(\zeta=40\%\)), which was corroborated by the sharper spike in the damage energy in the off-centered case. Figure 14 illustrates the simulated configurations immediately before and after the main fissure's unstable propagation. Damaged elements (i.e., those with \(\varepsilon\geq\varepsilon_{p}\)) are in blue, whereas the fractured elements (when \(\varepsilon\geq\varepsilon_{r}\)) are in red. For the centered case (Figure 14a), a spasmodic local failure appeared at the normalized instant \(t=0.85\), which was identified as many damaged bars around the pre-fissure's head and confirmed by the energy balance in Figure 13a. It was also apparent that the non-centered case generated many more broken and damaged bars than the centered example. That was also confirmed in Figure 13: the energy dissipated by damage was nearly \(50\%\) greater than the non-centered pre-fissure. Finally, it was also clear that the energy had dissipated due to the final collapse because the \(\zeta=40\%\) configuration was substantially higher than that of \(\zeta=0\%\), as evidenced by the number of damaged/broken bars (Figure 14a,b) and the corresponding variations in the dissipated (i.e., damage) energies in the energy balance at the failure instant, as shown in Figure 13.  
The simulated acoustical energy release was calculated in the same way in these tests, as described in Section 3.2, and then compared to the experimental results in [41]. The corresponding energy values for the latter were estimated from the AE data according to \(E\propto A_{\text{max}}\)2, where \(A_{\text{max}}\) is the maximum amplitude of each AE signal, and their spatial localization was performed through the standard procedure according to [31]. The comparison between the experimental and simulation results is shown in Figures 15 and 16, considering the events between 0.9 and 1 in normalized time. When the fissure was displaced from the center by \(40\%\), it became inclined with respect to the applied load. Therefore, a new coordinate system was established, with its origin at the tip of the fissure and aligned  
Figure 13: Simulated energy balances for the two configurations are presented. with the expected fracture path. Mathematically, these coordinate transformations were expressed as follows:  
\[ \begin{split} x_{0}&=x\cos(\psi)-(y-11)\sin(\psi)\\ y_{0}&=x\sin(\psi)-(y-11)\cos(\psi)\end{split}  \tag{16}\]  
where all displacements are given in mm. The angle \(\psi\) corresponded to the inclination of the fracture path, as shown in Figure 16, as \(27.8^{\circ}\) for \(\zeta=40\%\). At first, the simulation results suggested a significant deviation from the experiment due to the large number of AE events that occurred left of the origin, as shown in Figure 16. However, such events were relatively sparse, as compared to those immediately around the fissure, indicating that most of the AE emissions tended to be concentrated in the same region, as in the experiment.