## 3 LDEM Simulation
### Simulation Results and Discussion  
Figure 11a presents both numerical and experimental results in terms of failure configurations. The numerical crack patterns are compatible with those from the experiment, Figure 11a, especially along the vertical direction.  
Further comparisons between numerical and experimental data are shown in Figure 12a in terms of applied load versus time, normalized to the instant when the load returns to 80% of the peak load after that peak is reached. This return period is shorter for the LDEM because it is impossible to directly prescribe the displacement in the experiment, as the hydraulic-press-manipulated variable is the pressure it applies to the specimen. However, the load peak is very similar for both cases, differing by less than 10%.  
The energy balance computed during the simulation appears in Figure 12b, where the kinetic energy is multiplied by 50 to facilitate visualization. Since this energy component is at significantly lower levels than those for the other two, the quasi-static condition is reached in the simulation.  
Figure 11: **(a)** Model discretization, boundary conditions, and simulated final rupture configuration. The red color represents fractured bars, and blue indicates partially damaged ones. Undamaged bars are omitted for enhanced visualization. **(b)** Experimental final rupture configuration.  
The acoustic emission activity during the simulation was calculated through two methods: (_i_) computing the increment kinetic energy [10], \(\Delta E_{k}\), and (_ii_) using a virtual sensor [38], shown at the position S1 in Figure 11a. The increment kinetic energy is defined by [PERSON] et al. [10] between two successive integration times as:  
\[\Delta E_{k}=E_{k}(t_{i})-E_{k}(t_{i-1}) \tag{8}\]  
where \(E_{k}\) is kinetic energy in the discretized time during the simulation. Since \(E_{k}\) during a given event is proportional to that event's AE energy, \(\Delta E_{k}(t_{i})\) is proportional to the time derivative of \(E_{k}(t_{i})\), implying that \(\Delta E_{k}(t_{i})\) is also proportional to the signal's peak distribution.  
The acquisition of the AE waves in the simulation was performed by a virtual sensor placed on a node on the simulated cube's surface. Such a sensor registers the node's acceleration perpendicular to the surface where it stands, thus emulating the effect of the piezoelectric accelerometers used in the AE experiment.  
Figure 13 shows a comparison of the acoustic emission activity using the two approaches. The vertical axis is normalized with respect to the highest signal captured before the specimen reached the peak load. Notice that the \(\Delta E_{k}\) distribution in Figure 13a is measured directly in the event source, whereas the acceleration wave must travel through the body to reach the virtual AE sensor. The identification of the same event through both methods is shown in detail in Figure 13c.  
As an AE parameter precursor of the failure of the numerically analyzed structure, only the natural time was used. Using the computed \(\Delta E_{k}\) (Figure 13a) as the measure of AE activity, the calculation of the natural time parameters followed the same procedure used with the experimental data, that is, using hit-by-hit and considering \(Q_{k}\) to be equal to the event's AE energy.  
Figure 14 shows the evolution of the NT parameters during the simulation. The region with critical behavior appears between normalized instants, 0.81 and 0.92, where the four parameters \(\kappa_{1}\), \(S\), \(S_{rev}\) and \(<D>\) reach the characteristics limits indicated in Section 1.  
Figure 12: (a) Comparison between experimental and numerical results in terms of load versus normalized time. (b) Energy balance presented during the simulation.