## 3 Finite Element Simulation of Acoustic Emission (AE) Signal  
### Fiber Break Model  
In this study, we perform all FEM simulations using the ABAQUS software (Dassault Systemes Simulia Corp., Providence, RI, USA) with dynamic calculations. We model the full geometry of the sample. Figure 3 shows the boundary conditions. Clamping jaws are taken into account as boundary conditions. The geometry is meshed using tetrahedral elements (C3D4), the element size varies between 0.01 mm and 0.2 mm and the calculation step time is 0.1 us. The resolution of the finite mesh is gradually refined from 0.2 mm down to 0.01 mm close to the model source. The element size determines the frequency range that can be modelled: smaller elements are required to capture higher frequencies. A total duration of 170 us was calculated. Sensitivity studies are conducted on mesh refinement and for the size of the time step. The selected step size and mesh element size are appropriate to obtain convergent results in the frequency range between 10 kHz and 1500 kHz. Simulation results are filtered with Butterworth passband filter [20 kHz, 1.2 MHz]. Table 1 shows the main properties of the material. Epoxy is modelled by elastoplastic material with damping properties. The viscoelasticity of the matrix is taken into account by the Rayleigh parameters (\(\alpha_{R}~{}=~{}50,000~{}s^{-1}\) et \(\beta_{R}~{}=~{}10^{-8}~{}s\)). Fiber direction is oriented along the x-axis. We place the origin of the coordinate system at the centre of the specimen. The fiber breakage is mimicked by an instantaneous separation of nodes, which forms fracture faces and generates elastic waves. During the modelling of AE signals, the failure process is supposed to occur without change in its rate. [PERSON] et al. initially [46] showed that \begin{table}
\begin{tabular}{c c c} \hline  & **Descriptor** & **Unit** \\ \hline  & Amplitude & dB \\ \cline{2-3}  & Duration & μs \\ \cline{2-3} Calculated descriptors & Energy & J \\ in the time domain & Zero crossings rate & \% \\ \cline{2-3}  & Rise time & μs \\ \cline{2-3}  & Time centroid & μs \\ \cline{2-3}  & Temporal decay & - \\ \hline  & Frequency centroid & kHz \\ \cline{2-3}  & Peak frequency & kHz \\ \cline{2-3}  & Spectral spread & kHz \\ \cline{2-3}  & Spectral skewness & - \\ \cline{2-3}  & Spectral kurtosis & - \\ \cline{2-3}  & Spectral slope & kHz\({}^{-1}\) \\ \cline{2-3}  &
\begin{tabular}{c} Roll-off frequency \\ Cut-off frequency \\ (95 \%) \\ \end{tabular} & kHz \\ \cline{2-3}  & Spectral spread to \\ \cline{2-3}  & peak & kHz \\ \cline{2-3}  & Spectral skewness & - \\ \cline{2-3}  & to peak & - \\ \cline{2-3}  & Spectral kurtosis to \\ \cline{2-3}  & peak & - \\ \cline{2-3}  & Roll-on frequency \\ Opening frequency & & kHz \\ (5\%) & & \\ \hline \end{tabular}
\end{table} 
Table 2: AE-signal features calculated from the numerical signals or the experimental signals. the depth of an acoustic emission event significantly affects the wave modes excited and the spectral content of the signal. For this reason, two depths of fiber position are considered (0.5 mm from the surface, and in the middle of the specimen). Three thicknesses of the sample are also investigated (1 mm, 1.7 mm and 2.8 mm). The in-plane direction is the direction perpendicular to the fiber (Y axis in Figure 3) and the out-of-plane direction is normal to the specimen's surface (Z axis in Figure 3). For the fiber failure, the major displacement is along the fiber axis, while the dominant source emissions are in the xy plane (in-plane). The AE numerical signals from a single node provide the out-of-plane top surface velocity (v\({}_{\mathrm{z}}\)) corresponding to a virtual perfect point-contact sensor located on the surface of the specimen. The AE numerical signals from a single node on the lateral surface provide the in-plane lateral surface velocity (v\({}_{\mathrm{y}}\)) corresponding to a virtual perfect point-contact sensor located on the lateral surface.