## 1 Introduction  
Composite materials are increasingly adopted in structural-mechanical applications thanks to their optimal characteristics in terms of light weight, mechanical strength and stiffness, corrosion resistance, energy absorption capacity, and noise attenuation. However, many factors limit their widespread diffusion, such as the high cost of raw materials or requirements for high production volumes. Among the others, the complexity of the damage evolution plays a key role in their limitation, especially for structural component applications. Several interacting failure modes are typical of composite materials and a progressive and rapid decrement of the mechanical properties can be observed [1]. In this regard, methodologies for assessing damage level and predicting the residual structural strength of composite materials are becoming increasingly important. Many techniques have been developed for non-destructively assessing the structural health state of composite components [2]. Non-destructive tests (NDTs) are commonly adopted for quality assessment of a manufacturing process or for damage evaluation in structures during service. Most of the techniques intend to provide information on internal damages, in terms of size, shape, location, and orientation. Microscopy (based on atomic force, optic system, and scanning and transmission electron) [3], \(X\)-ray micro-CT (micro-computed tomography) [3; 4], and infrared thermography [3; 5] are among the most used for composite applications. However, the qualitative information provided by these techniques can be exploited by designers with difficulty. Further, methods based on ultrasounds and vibrational analysis are usually adopted for globally analyzing the dynamic response of a structure [6]. In particular, the use of the Impulse Excitation Technique (IET), which is regulated by ASTM Standards for metallic materials [7; 8], has been recently extended to composite specimens [9]. However, local damages and defects are still revealed with difficulty in real-world structures since the presence of anomalies is mitigated by the global response of the system. Therefore, as pointed out in [10], current methodologies do not allow a direct evaluation of the local residual properties. In this paper, the detecting Damage Index (\(DI_{d}\)) technique was adopted for assessing the local residual elastic properties of a composite laminate. This methodology was brought in the realm of the non-destructive characterization for components made of composite material by [PERSON] et al. in [11; 12; 13; 14; 15]. The \(DI_{d}\) technique consists of two sets of experimental tests: a preliminary characterization activity which is performed to identify the correlation between residual elastic properties of the material and the \(DI_{d}\) parameter and the proper non-destructive test to estimate the local residual elastic properties of the investigated component from the \(DI_{d}\). In [15], the methodology was demonstrated to properly predict residual elastic properties of a series of laminate plates damaged through impacts at different energy levels. Tensile tests on specimens cut from laminate plates allowed validation of results predicted with the \(DI_{d}\). Here, the finite element method was adopted to validate elastic properties assessed with the \(DI_{d}\). The combination of non-destructive tests and finite element method is typical in damage assessment, particularly in vibration-based techniques [16]. Various approaches are available to numerically model multi-layered composite materials and their multiple failure modes [17; 18]. In particular, the use of cohesive elements disposed between layers of shells currently represents one of the most adopted solutions [19; 20; 21]. Thanks to their specific formulation, cohesive elements allows to simulate damages due to delamination without significantly affecting computational cost. In this paper, the \(DI_{d}\) technique is thus used in combination with the finite element method.