## 3 Numerical Research
### Preparation of Numerical Model
When strain reaches the value defined as an ERODS, the finite element is deleted [56]. The typical stress-strain curve for the selected MAT58 composite material model is shown in Figure 5.  
On the basis of the research [56], ERODS = 0.4 was adopted. Because the values of SLIMx coefficients do not have their physical interpretation [57], their value was adopted in accordance with the recommendations [55]. The impact of individual factor values on the convergence with an experimental solution is presented, among others, in the work of [56]. The used material properties of epoxy composites with carbon and aramid reinforcement (in two directions) are shown in Table 4.  
The delamination is an important energy absorption mechanism in the case of low velocity impact [51]. In case of the modeling approach used in research, the connection between successive layers of reinforcing material can be modeled in several ways [52; 59; 60; 61]. Modeling of the bonding connection \begin{table}
\begin{tabular}{c c c} \hline \hline
**Material Properties** & **Epoxy Resin/Carbon Fiber** & **Epoxy Resin/Aramid Fiber** \\ \hline Young’s modulus \(\mathrm{E_{1}=E_{2}\) [MPa] & 70,000 & 30,000 \\ Shear modulus \(\mathrm{G_{12}\) [MPa] & 5000 & 5000 \\ Tensile strength \(X_{\mathrm{T}}=Y_{\mathrm{T}}\) [MPa] & 600 & 480 \\ Compressive strength \(X_{\mathrm{C}}=Y_{\mathrm{C}}\) [MPa] & 570 & 190 \\ Shear strength \(S\) [MPa] & 90 & 50 \\ Tensile strain \(\varepsilon_{X\mathrm{T}}=\varepsilon_{Y\mathrm{T}}\) [\%] & 0.85 & 1.6 \\ Compressive strain \(\varepsilon_{\mathrm{XC}}=\varepsilon_{Y\mathrm{C}}\) [\%] & 0.8 & 0.6 \\ Shear strain \(\varepsilon_{\mathrm{S}}\) [\%] & 1.8 & 1 \\ Density [g/cm\({}^{3}\)] & 1.6 & 1.4 \\ Poisson’s Ratio & 0.1 & 0.2 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Mechanical properties of epoxy composites reinforced by carbon and aramid fibers [58]. Figure 5: Typical stress—strain curve for the selected MAT58 composite material model. between adjacent reinforcing layers could be realized using cohesive elements [54; 62]. This approach involves inserting additional cohesive elements between elements of adjacent reinforcing layers. In the initial phase, these elements may have zero thickness. The behavior of the cohesive elements can be described, for example, using a bilinear curve. These curves describe the dependence between the cohesive element stresses from its deformation [54; 59; 60; 62]. If the cohesive element is not damaged, its stiffness is constant. However, if an element is damaged, its stiffness decreases as deformation increases [62]. The use of cohesive elements requires high computational costs [52]. A broader description of this type of connection has been described, among others, in the literature [54; 59; 60; 62]. The second approach of modeling the bonding connection between the adjacent reinforcing layers is the use of the bilateral constraints (tiebreak contact type). This contact allows for the simplification of crack propagation based on the cohesive element [51]. After reaching normal and shear stresses, damage is a linear function of the distance between points that were initially in contact. After reaching the defined critical crack opening, the bonding connection is broken and further contact behaves like unilateral constraints. This approach does not require the use of additional elements and, shown in the work of [51], this bonding connection modelling method give results in accordance with experimental research. In the conducted research, it was decided to use the bilateral constraint contact with strength criterion (\"AUTOMATIC_SURFACE_TO_SURFACE_TIEBREAK [63]). This contact type behaves like a bonded connection before the strength criterion is exceeded. After exceeding the strength criterion, this contact behaves like a unilateral constraint contact without a bonded connection. There are several possibilities to define the bonded connection using the selected contact type. In the case of shell elements, the definition OPTION = 8 is most commonly used [59].