# Acoustic Emission and Modal Frequency Variation in Concrete Specimens under Four-Point Bending
## Acoustic Emission Monitoring
### Dissipated and Emitted Energies  
Another interesting feature of the AE signals is that they can give insights into the process of energy dissipation and emission during the loading process. In this context, experimental analyses have evidenced that the scaling of the cumulative number of AE events by varying the specimen dimension can profitably be used to determine the physical dimension of the damage domain in disordered materials. In fact, the total number of AE events at the end of the test varies with the specimen size according to a power-law having a noninteger exponent that is directly related to the fractal character of the damage domain [3; 22]. Alternatively, the characterization of the damage domain can also be obtained by means of a statistical analysis of the distribution of AE events in a single test [22]. From the viewpoint of energy dissipation and emission, the cumulative number of AE events and the energy content of the AE events are usually correlated to the mechanical energy dissipated during the complete failure process: namely, fracture energy in tension and crushing energy in compression [23; 24]. However, recent studies carried out by [PERSON] and co-workers focusing on the catastrophic failure of rock specimens in compression have suggested that such a correlation is not always correct [25]. In particular, it was evidenced that a large amount of AE activity takes place during the post-peak snap-back instability. The typical shape of the load vs. displacement curve, when the global unstable behavior is fully captured--e.g., by controlling the compression test by means of the circumferential expansion instead of the longitudinal deformation--is that shown in Figure 2a. However, this very brittle mechanical response can also be observed under tension and bending loading conditions when brittle materials are tested in large and/or slender specimens. The behavior shown in Figure 2a is consequent to the fact that the energy dissipated through material damage is less than the elastic energy stored in the body. In this case, the portion of energy that is not dissipated by material damage (area \(E\) in Figure 2a) is abruptly emitted producing mechanical vibrations with propagation of elastic waves. From the diagram in Figure 2a, therefore, three different energy components can be distinguished: the energy dissipated by material damage (gray area \(D\)), the surplus of elastic energy with respect  
Figure 1: Typical waveforms for tensile and shear events. \(A\) is the amplitude and RT is the rise time (time between the onset and the point of maximum amplitude) of the waveforms. Reproduced with permission from [7], Elsevier, 2016.  
to the dissipated one (red-dashed area \(E\)), and the total released energy \(R\), which is the sum of the two previous areas. When a catastrophic failure occurs, the AE energy seems to be correlated with the surplus of elastic energy [25]. Accordingly, such an energy component can be referred to as the emitted energy. Certainly, global snap-back instabilities take place only under specific conditions (large sizes and slendernesses, and/or brittle materials), whereas in most cases a more stable response, represented by a softening behavior, is obtained. However, even in such cases, local discontinuities --which are an indication of snap-back or snap-through instabilities--are usually noticed in heterogeneous materials such as aggregative and fiber-reinforced materials. Such local phenomena evident at a microscale level are due to the fact that cracks grow in a discontinuous manner, with sudden propagations and arrests due to the bridging action of the secondary phases as well as by the rise and coalescence of microcracks in the process zone [26; 27]. A load-displacement curve representative of a global softening behavior perturbed by multiple local instabilities is shown in Figure 2b. Each drop in the load carrying capacity occurring in the post-peak phase is related to a sudden crack propagation due, for instance, to the rupture of a reinforcing fiber.