## 5 Results
### Simulations Results
Figure 13: Energy balance obtained using the peridynamic simulations: (**a**) Config. 1; and (**b**) Config. 2. Acoustic emission tests were also simulated in Config. 1 and Config. 2. Accelerations perpendicular to the surface placed in the same positions as sensor 1 and sensor 2 were captured, and these were considered AE signals. The temporal derivative of the kinetic energy computed with the model \(d(E_{k}(t))/dt\), here called \(\Delta E_{k}(t)\), will have the same acoustic emission signal distribution pattern with time, as was pointed out in [34]. The difference between \(\Delta E_{k}(t)\) and the signal distribution obtained with each sensor is that \(\Delta E_{k}(t)\) is computed using the kinetic energy measure in the model. This avoids the loss or distortion of information due to the wave traveling in the solid from the event source to the AE device. In Figure 13(a), energy balance details of when an event happens are presented, where the elastic, dissipated, and kinetic energies change during the event. In the same Figure, the derivative of the dissipated energy, \(\Delta E_{d}(t)\), and the kinetic energy, \(\Delta E_{k}(t)\), are presented. It is easy to perceive that the pattern of \(\Delta E_{k}(t)\) is like the typical AE signal. In [35; 36], the indirect link between the energy dissipated by the event and the AE signal is discussed. In this discussion, it remains clear that the AE signal relates to the energy that makes noise; that is, the kinetic energy creates an indirect relation between the fall in the elastic energy and the dissipated energy. The signals captured with the device, \(A(t)\), \(\Delta E_{k}(t)\), and \(\Delta E_{d}(t)\), are presented in Figure 13(b). The similarity between the \(A(t)\) signature and \(\Delta E_{k}(t)\) is evident. In the details of the same Figure 13(b), the delay between \(\Delta(t)\) and \(\Delta E_{k}(t)\), \(\Delta E_{d}(t)\), is indicated. \(\Delta E_{k}(t)\) is computed directly from the model energy balance and is then manifested when the event happens; the acoustic emission signal (\(A(t)\)) has a delay in comparison with \(\Delta E_{k}(t)\) because the signal is captured in the AE device after the elastic wave arrives in the sensor. The possibility to compute \(\Delta E_{k}(t)\) as an alternative measure of \(A(t)\) is only possible in the simulation, but comparing the numerical \(\Delta E_{k}(t)\) and \(A(t)\) could obtain complementary information to interpret the AE experimental test. Figure 14: The link between the information computed during the energy balance and its relationship with the acoustic emission signal. (**a**) The energy balance for a typical event during a process where the variation in \(E_{e}\)\(E_{d}\)\(E_{k}\) is presented. In the same plot, the derivatives of the dissipated energy, \(\Delta E_{d}\), and kinetic energy, \(\Delta E_{k}\), are shown. (**b**) The superposition of \(\Delta E_{k}\)\(\Delta E_{d}\) and the EA signal are illustrated. The beginning of the curves is presented to demonstrate the delay between \(A\), \(\Delta E_{d}\), and \(\Delta E_{k}\). In Figures 15 and 16, the results related to the simulation of the AE tests are presented for Config. 1 and Config. 2. All parameters are plotted vs. normalized time. In (a), the global load is presented. In (b), the AE signal obtained for sensor 1 and sensor 2 (placed as indicated in Figure 5c) is shown. In (c), the accumulated number of signals (Acum \(S_{1}\) and Acum \(S_{2}\)) and the number of events measured from \(\Delta E_{k}\) are plotted. In the same plot, information on accumulated AE energy is presented. In (d), \(b\)-value evolution is computed using the acoustic emission signal for sensors 1 and 2, and the \(b\)-value is computed using the \(\Delta E_{k}(t)\) information, which is also presented. In (e), DPH index evolution, which was computed using the product of the displacement prescribed times the correspondent reaction force (\(d(fu)/dt\)), is illustrated.