# Damage Evolution Analysis in a \"Spaghetti\" Bridge Model Using the Acoustic Emission Technique
## 1 Introduction  
The damage process in structures or materials undergoing unstable collapse is a widely studied topic, because it occurs in many different situations, including catastrophic events with heavy human and economic tolls. This process is particularly important in the case of heterogeneous materials, such as rocks, concrete ceramics, and other composites, either natural or artificial. According to [PERSON] [1], the main phenomena characterizing damage processes in these materials are: (i) significant size-effects in the strength and failure strain, (ii) transitions from uniform damage distribution to a clear discontinuity process, known as cracks localization, and (iii) the associative effect among clusters of micro-cracks, which can either intensify or inhibit damage propagation throughout the structure during the process.  
Continuous regularization functions can represent model parameters describing damage evolution, which filter a series of discontinuities distributed throughout space and time, thus providing valuable information regarding the ongoing damage process, indicating how and when a significant loss of material resistance can occur. In its turn, collapse study by means of an apparently simple theoretical models allows for one to avoid the specifics of each structure and to perceive tendencies that are common to several systems, regardless of building materials, boundary conditions, and problem scale. Some such models are discussed in [2]. Being aided by these models, one can describe laws that apply to processes ranging from the rupture of biological materials of microscopic dimensions [3], to seismological events throughout hundreds of kilometers [4; 5].  
Besides pure Mechanics, similar patterns can be found in other realms of Physics, most notably the method of renormalization groups that was proposed by [PERSON] [6], whichallows for coping with instability problems, such as the disruption of solids and phase changes. These ideas also apply to other instability problems, like those found in time series of economic indexes [7], the degradation of social systems [8], and the collapse of ancient civilizations [9]. In all of these cases, studying the evolution of local instabilities throughout space and time is a fundamental step in predicting global instability.  
In mechanics, a suitable way to register local instabilities is the Acoustic Emission (AE) technique. Whether caused by a chemical reaction (metal corrosion), the spasmodic growth of vegetal, or an impact from an external source, among many other examples, when a local instability occurs, it is said to generate an event in a specific structure location, called source. This event causes the propagation of mechanical waves that are perceived by sensors on the structure's surface. By placing various sensors on suitable locations of the structure, space and time distribution of these events can be determined, and the parameters that are calculated from such measurements are a sensitive means for tracking changes within the studied structure.  
Here, we apply the AE technique to track a small-scale bridge that is built from spaghetti sticks. As the bridge is subjected to increasing load, two sensors acquire the AE signals. Measurement results are compared to theoretical predictions according to the Bundle Model [10], which is widely used in this field [11]. This comparison's primary goal is to highlight the possibility of an underlying universal pattern for structures in collapse, which is often masked by specifics in geometry and boundary conditions imposed on each structure. The use of a spaghetti bridge as the basic structure for the study facilitates the execution of typical material tests --e.g., three-point bending and uniaxial compression in a cylinder-- on an easy to build, inexpensive specimen. [PERSON] et al. [12] have also explored this possibility, applying artificial intelligence methods to determine the collapse load on a similar bridge.