## 2 Materials and Methods
### Fixture Design
#### 2.1.1 Design Using FEA
The energy failure value and compressive and shear residual stresses were obtained by the use of an optimization technique developed by [PERSON] et al. [26]. The energy failure value is the \(W_{p}\) described in Equation (1) and is one of the failure criteria available as part of the CRASURV model that retains the integrity of the element until the element absorbs energy equal to the failure value, after which softening takes place until the compressive and shear residual stress values shown in Table 2. As a macroscale model was used that modeled the composite plate with stacked shell elements only, to obtain computational efficiency, strain energy release rate (SERR) was not used, as SERR is typically used for mesoscale models where the interface is modeled. The tested CFRP material plate was composed of four plies made of \(2\times 2\) woven fabric material. The layup of the plies was [0 90 0 90]. The thickness of each ply was 0.64 mm, thereby resulting in a laminate 2.54 mm thick. Properties in 1 and 2 directions were assumed equal as the material was quasi-isotropic. Steel components were modeled using the Johnson-Cook elastoplastic material model. An elastoplastic model was used because the top plate needed to be optimized for thickness to ensure there was no plasticity upon impact. After optimization of the top plate, the same material model for the top plate was used for the entire analysis as the optimization resulted in a top plate that only deformed in an elastic manner. C40 steel parameters were obtained from the Total Materia database [27] and are reported in Table 3. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Parameter** & **Value** & **Parameter** & **Value** \\ \hline Density & 1.56 g/cm\({}^{3}\) & Shear Yield Strength & 10 MPa \\ Young’s Modulus & 70 GPa & Ult. Shear Strength & 65 MPa \\ Poisson’s Ratio & 0.075 & Failure Strain & 0.018084 \\ Shear Modulus & 4 GPa & Energy Failure Value & 0.0846 J/mm\({}^{3}\) \\ Ult. Tensile Strength & 911 MPa & Compressive Residual Stress & 132 MPa \\ Ult. Compressive Strength & 334 MPa & Shear Residual Stress & 34 MPa \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Material properties of carbon-fiber-reinforced epoxy specimen. Anti-buckling supports were modeled with a 1 mm element size to capture the curvature and were modeled as rigid bodies for all simulations to enable the respective elements belonging to the rigid bodies to deform synchronously. The boundary condition applied to the supports prevented them from any translational or rotational degrees of freedom (DoFs). The top and bottom plates were modeled with a 5 mm element size and were modeled as rigid bodies. An exception was the case where optimization was performed on the top plate to determine its appropriate thickness. In this case, the top plate was not modeled with a rigid body element, thereby permitting the elements to deform nonsynchronously. After optimizing the top plate and ensuring that the deformations were purely elastic, rigid body elements were introduced for the subsequent runs. Boundary conditions applied to the bottom plate were similar to those for the supports, thereby not allowing it to translate or rotate in any direction, resulting in zero DoFs. The top plate was only allowed to translate in the y-direction to permit crushing. Again, the exception was the optimization of the top plate thickness case, wherein no boundary conditions were applied for the same, thereby allowing all DoFs. All components were modeled with fully integrated Batoz shell elements. A 4 mm element size was adopted for the composite specimen, which was considered optimal, considering the tradeoff between accuracy and efficiency, based on previous studies conducted on the crashworthiness of composite materials that recommended an element size between 3 and 5 mm [6; 18; 28].