## 2 Materials and Methods  
Composite materials are drawing significant attention from both academic and industrial environments due to their diverse range of applications. Generally, such materials consist of a matrix and a reinforcement phase. The latter is commonly composed of glass or carbon fibers, whereas the matrix can be of various types, including polymeric, ceramic, or metallic. In the aerospace industry, composite materials play a crucial role to obtain the most convenient trade-off among lightness, performance, and reliability, so that polymeric-matrix carbon-based material is one of the most promising solutions [21; 22; 23].  
The material of the panels analyzed in this paper (which will be presented in Section 3) is here introduced and characterized. The objective is to obtain properties to be used to reproduce a 2D equivalent orthotropic finite element model of the composite complete laminate. In detail, a carbon/PEEK composite material made of seven laminates is considered:the two external layers (top and bottom) are realized in bidirectional pre-preg Tenax-E_TPWF-PEEK-HTA40, while the five internal ones are unidirectional (UD) laminates of Tenax-E_TPUD-PEEK-HTS45. Both materials were purchased from Teijin Carbon Europe GmbH (Germany). The stacking sequence is \(45^{\circ}/0^{\circ}/0^{\circ}/0^{\circ}/0^{\circ}/0^{\circ}/-45^{\circ}\), with the \(0^{\circ}\) as shown in Figure 1. The overall thickness of the laminate package is determined by adding up the thicknesses of each individual layer, resulting in an approximate measurement of 1.3 mm.  
Figure 2 depicts the flowchart illustrating the various phases of characterization, which are elaborated on in the subsequent sections. The complete set of material properties is generally not fully provided in datasheets. Therefore, to obtain the desired quantities, a series of numerical simulations and experimental tests was carried out at the SASLab, DIAEE Sapienza University of Rome. In the first phase, the individual layers were modeled in Digimat finite element environment, starting from the known properties of the constituent phases (fibers and matrix). Unknown parameters were found by matching simulation results with available information from datasheets, thus achieving a full characterization of each lamina. Then, the numerically computed data were validated by conducting quasi-static three-point bending tests on the laminate, and by modeling the flexural tests in the finite element software Abaqus, adopting the properties of the individual laminate previously determined via Digimat. Classic Laminate Theory (CLT) was followed to compose the set of the constitutive matrices (namely, the extensional stiffness matrix \(\mathbf{A}\), the coupling stiffness matrix \(\mathbf{B}\) and bending stiffness matrix \(\mathbf{D}\)) for the composite material, to be used as input in subsequent analyses. Finally, the longitudinal storage modulus and the structural damping factor were evaluated experimentally as functions of temperature via dynamical mechanical analysis (DMA).  
Figure 1: Laminate stacking sequence of carbon/PEEK composite material.  
Figure 2: Flowchart of the material characterization activities: the two types of layers (i.e., Tenax-E_TPWF-PEEK-HTA40 and Tenax-E_TPUD-PEEK-HTS45) were numerically characterized starting from the datasheet properties, then the laminate package equivalent orthotropic properties were obtained using CLT. Experimental tests were conducted and simulated to validate the characterization. Dedicated tests were carried out to find the damping factor.