## 3 Numerical Research  
### Preparation of Numerical Model  
The numerical research was carried out using the finite element method and commercially available LS-PrePost/LS-Dyna (LSTC, Livermore, CA, USA) software. The multilayered composite could be modeled in a few scales. The modeling scale is related to the homogenization of the composite strength properties. In the case of modeling the composite as a one part, homogenization of the mechanical properties should be performed for the whole composite. Modeling in this scale makes it impossible to observe some processes occurring inside the composite material, for example, delamination, which, as mentioned in the introduction, is an energy absorbing process. A different approach is to model the composite with respect to the division on the reinforcing layers. In this approach, the strength properties should be homogenized in the level of the reinforced layer (used reinforcing fabric and the matrix). This modelling scale allows observing the delamination between the reinforcing layers. There is also the possibility to observe the movement between the adjacent reinforcing layers and the consideration of the friction between them. Woven composites could also be modeled with respect to the reinforcing fiber geometry. The mechanical properties of the fiber and the matrix are defined individually. Observation of the delamination process is also possible. Moreover, modelling in that scale allows to observe the deformation of each fiber and the friction between the fibers. If the modeling scale is more accurate, the physical model takes into account more energy absorbing phenomena. Therefore, the choice of the modeling scale and level of homogenization of strength properties has an impact on the obtained result. The selection of the modeling scale is related to use of the simplifications. Each simplification will be associated with the omission of some energy absorbing phenomenon. However, it should be remembered that, if the physical model is more advanced, the computational cost will be greater. Modeling of the composite with respect to the division on the reinforcing layers (homogenization of the strength properties in the reinforcing layer level) gives satisfactory results, which are in accordance with experimental research [51]. It was decided to model the composite material in a macro scale. It means that each reinforced layer was modeled as an individual part. This approach is widely used [51; 52; 53; 54] in the case of impact analysis. A flat surface with dimensions of \(50\times 100\) mm (height \(\times\) width) was created, and then it was discretized into the finite elements. The surface was divided into Belytschko-Tsay type shell elements with \"hourglass\" control based on stiffness. A total of 5000 Belytschko-Tsay shell elements were created in this way. It was assumed that the thickness of each layer, regardless of the reinforced material, was 0.5 mm, which allowed the physical model to achieve the overall thickness of the composite used in the experiment (7 mm). On the basis of this assumption, 13 subsequent surfaces were created, spaced 0.5 mm from the previous layer along the axis perpendicular to the surface of the layers. The composite model created in this way consists of 70,000 shell elements. As a composite material model, the MAT58 *MAT_LAMINATED_COMPOSITE_FABRIC [55] was used. This model requires the definition of homogeneous strength properties of the used materials. Taking into account the destruction of the physical model, the finite elements are controlled by the ERODS parameter. The ERODS parameter is calculated based on the deformation in defined fiber directions in the reinforced plane and on the shear deformation. In this material, model stress increases nonlinearly until the maximum strength is reached (\(X_{\mathrm{T}}\)). When the maximum strength is reached, the stress is reduced by the SLIMx factor and held until material reaches the strain specified by the ERODS parameter.