## 3 Numerical Simulation of AE Signals
### Fiber Break and Surrounding Medium  
We first recalled the numerical procedure for fiber break simulation (more details can be found in [51]). A 3D FE model of the single fiber specimen was set up using Abaqus(tm) Standard, with the same dimensions as those of the experimental specimens. The fiber and matrix behavior were considered linear, elastic and isotropic. The acoustic emission source was a crack in the fiber, covering the whole fiber section and perpendicular to the fiber neutral line. It was located at a distance of 12 mm from the sensor C along the (Ox) direction and 0.5 mm from the top surface along the (Oz) (Figure 2a). The nodes lying on the fiber break plane were doubled so as to enable the surface separation at this location (Figure 2b). A two-step simulation was adopted to represent the fiber break. A quasi-static step was firstly applied. During this step, the imposed force reached the experimentally measured value at first fiber break (i.e., 346 N). Displacement constraints were set on the fiber break plane nodes so that no surface separation was allowed during this step. Then, the displacement constraints on these nodes were released in the second dynamic step  
Figure 1: (**a**) View of the specimen with two sensors C1 and C2. (**b**) Sensitivity function of nano 30 sensor in reception mode. (**c**) Axial stress and location of the AE signals localized by the nano 30 sensors as a function of axial strain. (Figure 2b), enabling the surface separation and vibration which resulted in the generation of elastic waves that further propagated within the specimen with possible reflections at the specimen boundaries. Frequencies up to 1 MHz are generally involved in AE analysis, which requires a 0.1 \(\upmu\)s maximum time increment in the FE model to be able to accurately represent these waves. Moreover, the FE mesh must contain small enough elements in order to resolve spatial features (from 0.2 mm down to 0.01 mm close to the model source). The simulated waveforms were calculated on single nodes from the epicenter of the source to the boundaries of the gauge length on the top surface (Figure 2a, red line) and at the position of sensor C.  
Acoustic waves are subjected to geometric damping where the source energy spreads through a larger volume. Geometric damping is a function of distance and wave type. However, for these specimens, the main source of damping of the AE waves is the dissipation due to the viscoelasticity property of the propagation medium, which can be modeled using Rayleigh parameters. It is a frequency-dependent model, formulated as a combination of mass proportional and stiffness proportional damping (Figure 3). The loss factor (\(\eta_{R}\)) is the sum of two terms, one proportional to frequency (multiplicating coefficient \(\alpha_{\text{R}}\)) and one inversely proportional to frequency (multiplicating coefficient \(\beta_{\text{R}}\)). The influence of \(\alpha_{\text{R}}\) and \(\beta_{\text{R}}\) is respectively negligible for high and low frequencies. Figure 3 represents the variation of the damping ratio as a function of the frequency for a given case. The curve shows nonlinearity in the low-frequency regime (<400 kHz), and beyond that, the variation becomes linear due to the domination of the term \(\beta_{\text{R}}\omega\). Figure 2: (**a**) Location of the simulated fiber break and sensors. The location of the experimental sensor is denoted as C. The fiber break at position P was located 12 mm from the experimental sensor C. (**b**) Schematic view of fiber break at position P.  
In Section 4, the influence of the surrounding medium on the AE signature due to fiber break is analyzed. In the case of elastic modeling, wave velocity is directly proportional to Young's modulus of the matrix.