## 2 Materials and Methods
### Fixture Design
#### 2.1.1 Design Using FEA  
In the design process, the fixture needed to be sufficiently robust to handle the maximum energy level of the drop tower, and the top plate was optimized for the same reason. The effects of different diameters and distances between anti-buckling columns were assessed by means of numerical simulation to arrive at their optimum values. After the design was finalized, a carbon-fiber-reinforced polymer (CFRP) plate 15 mm thick was tested, once again, using simulations to study the robustness of the fixture in coping with specimens made of different thicknesses and materials. The final design was a fixture suitable to conduct in-plane compression testing on composite plates made of a variety of materials with thickness up to 16 mm. Composite specimens with dimensions up to 100 \(\times\) 150 mm could be tested, and provisions were made to allow smaller sized plates to be tested at up to 1850 J with unsupported heights up to 50 mm. Within the HyperWorks Suite, HyperMesh was used for preprocessing, HyperGraph and HyperView were used for post-processing, and Radioss was used as a solver. CFRP flat plates were modeled for the investigation due to the availability of material characterization data for the same. The simulation model, as shown in Figure 2, was constructed. It was simplified as compared to the fixture seen in Figure 1 to reduce the effect of contact modeling on the results. As a result of the simplification, most constraints such as lateral supports and support plates were replaced with different boundary conditions and rigid body elements depending on the test being performed. The boundary conditions and rigid bodies used are defined in the subsequent sections, as they were dependent on the load case being analyzed. Figure 1: Image of the newly developed fixture with the carbon-fiber-reinforced flat specimen. Figure 2: Final model setup isometric view and relevant material and contact modeling information. The numerical fixture model constituted a composite flat plate that stood on a steel base. It was laterally supported by four steel anti-buckling columns and impacted by a steel plate. The composite material was modeled using Law 25's CRASURV formulation of the RADIOSS material model library, which modeled orthotropic behavior as elastic until yield and plastic (for shear) afterward. CRASURV formulation is a more robust formulation of the Tsai-Wu criteria. It allows different hardening (for shear) and failure parameters in all directions for tension, compression, and shear. Failure occurrence is strain- and/or energy-based and a combination of the two could be selected. For this study, failure initiation was modeled by a combination of the two based on which failure event occurred first. Equation (1) shows the yield-surface equation of the CRASURV formulation, where \(W_{p}\) represents plastic work, and puts in evidence how this is different from the classical Tsai-Wu formulation, wherein yield stresses are functions of \(F_{ij}\) factors and are not a function of \(W_{p}\). No strain rate behavior was modeled as all tests were conducted between 4-8 m/s, a range too narrow to observe any strain rate effects. \[F\big{(}W_{p},\sigma\big{)}=F_{1}\big{(}W_{p,1}\big{)}\sigma_{1}+F_{2}\big{(}W_ {p,2}\big{)}\sigma_{2}+F_{11}\big{(}W_{p,1}\big{)}\sigma_{1}^{2}+F_{22}\big{(}W _{p,2}\big{)}\sigma_{2}^{2}+F_{44}\big{(}W_{p,12}\big{)}\sigma_{12}^{2}+2F_{12} \big{(}W_{p}\big{)}\sigma_{1}\sigma_{2} \tag{1}\]  
where \(F\) is the variable coefficients, \(W_{p}\) is the plastic work per unit volume, \(\sigma\) is the stress in the material coordinate system, and \(1,2\) are the principal directions. Table 2 reports material information about the used carbon-fiber-reinforced epoxy material, properties of which were obtained from characterization tests undertaken according to ASTM standards D3039 (tensile), D0790 (flexural), D3518 (shear), and D3410 (compression).