## 1 Introduction  
In addition to allowing fault detection, the acoustic emission (AE) technique has garnered growing interest as a method for improving our understanding of the fracture processes of composite materials. There is a strong interest in AE for real-time diagnostics and prognostics [1; 2; 3; 4]. Damage processes in composites materials, such as fiber breakage, induce local changes in the stress states and radiate elastic waves. If the amplitude of the elastic waves is large enough to be detected by sensors applied directly on the surface of the samples, AE can give an indication of the damage mechanisms. Due to inhomogeneity of the composites, the elastic waves are considerably affected. However, we can consider that the AE signal contains some features characteristic of the source. Indeed, the opportunity to identify AE signatures of several damage mechanisms is an established field [5; 6; 7; 8; 9; 10; 11]. In the phenomenological approach, it is assumed that signals are affected by propagation and acquisition but that they remain images of sources. In this context, the different types of failures such as fiber breaks, fiber/matrix debonding, several kinds of matrix cracking and delamination are identified thanks to their AE signature, described by descriptors or features such as amplitude, energy, peak frequency, frequency centroid, etc. In most of the studies dealing with failures in polymer matrix composites, higher frequency and higher amplitude are assigned to fiber breaks and lower frequency and amplitude are attributed to matrix cracking. Certainly, the possibility to separate matrix cracking from fiber failure and fiber/matrix debonding depends on different visco-elastic relaxation processes [12; 13; 14]. Intrinsic frequencies \(f_{i}\) and velocities \(c_{i}\) of relaxation processes are different in fiber and matrix due to the relationship between the relaxation times \(\tau_{i}\), elastic moduli \(E_{i}\) and densities, according \(\rho_{i}\) to the following equation:  
\[f_{i}\ \sim\frac{1}{\tau_{i}}\sim c_{i}\ \sim\sqrt{\frac{E_{i}}{\rho_{i}}} \tag{1}\]Figure 1 represents the whole AE process. The AE signal is the convolution of the AE source mechanism and the different transfer functions of the propagation medium, of the sample geometry, of the sensor and of the acquisition system. The propagation of acoustic signals is subject to boundary effects; in addition, the propagation of the elastic waves is subject to attenuation that modifies the waves. In fact, besides the type of failures, the AE signals depend on other parameters such as type of sensor, the sample geometry and propagation distance. All these parameters influence the AE signal [15; 16; 17; 18; 19; 20; 21; 22]. In AE analysis, it is important to distinguish the effect of the AE source from the influence of the propagation medium and the recording system. The quantitative AE method requires understanding and modelling of all the components in Figure 1. The influence of the propagation medium and its geometry cannot be separated. Nevertheless, the estimation of the transfer function of the sensor and the amplifier can be established with experimental methods. Based on experimental tests, it is not possible to comprehend the impact of the different parameters. Nevertheless, modelling of AE using analytical or numerical methods allows us to go further and establish a quantitative relationship between the AE source and the signal. Various authors have applied analytical or numerical methods to the simulation of AE formation and AE propagation [23; 24; 25; 26; 27; 28; 29; 30; 31; 32; 33; 34; 35; 36; 37; 38]. Following the works of [PERSON] and [PERSON] [28], who proposed a generalized theory of AE by using the integral formulation of elastodynamics, AE sources can be modelled using buried dipoles sources. The AE source was classically modelled as point force couple utilizing a multi-scale approach. In addition, various source-time function are employed which model kinematics.