## 3 Compression Experiments  
In order to validate the FEA predictions, a series of compression experiments were conducted. The samples tested are prismatic rectangular blocks 152.4 mm \(\times\) 50.8 mm \(\times\) 50.8 mm (\(6^{\prime\prime}\times 2^{\prime\prime}\times 2^{\prime\prime}\)) printed of Ultimaker toughened PLA on an Ultimaker 5 machine using a 0.4 mm nozzle with layer height 0.2 mm, extruder-temperature 205 \({}^{\circ}\)C, bed-temperature 60 \({}^{\circ}\)C, and print-speed 70 mm/s. Density was adjusted using the \"Infill Density\" and \"Infill Line Multiplier\" parameters in the Cura slicer. Wall thickness and top /bottom thickness parameters set to 0 to print bare infill. All other parameters remain default for an Ultimaker 5 machine. The size was chosen in order to capture the bulk behavior of the gyroid infill better than the standard compression specimen (which is much smaller) due to the printed unit-cell size. Cell-size and wall-thickness are the two driving factors for gyroid relative density. Since wall-thickness is fixed by the printer's bead-width, the slicer adjusts relative density by changing the cell-size. The double-bead printed specimens at 25%, for example, are only 6 unit-cells wide. A smaller specimen would likely have significant edge-effects at this relative density. While the majority of these specimens are printed so that the testing direction corresponded with the z-axis of the printer, others are printed in the x-, and y-directions, respectively, in order to capture any directional effects. These specimens are labeled separately in the results. All of the specimens were tested using an Instron 100 kN servohydraulic test frame in quasi-static compression. Compression was chosen so as to capture longitudinal stresses while avoiding potential issues with gripping a porous structure. This test was based on ASTM D695 [44], but with the aforementioned deviation in specimen size. These experiments are displacement-controlled with a feed rate of 1.27 mm/min (0.05 in/min). In addition, any extraneous moments due to fixture misalignment are eliminated by using a swiveling top platen (see Figure 6).  
Load data is captured using a 100 kN load cell and strain data is captured using digital image correlation (DIC). DIC data is captured in the form of a pointwise displacement field based on a series of dots adhered to the surface of each specimen. Analyzing this data using the GOM Correlate software, a surface is generated wherein the dots become the corner nodes of a mesh. The longitudinal and transverse strains are then calculated at each node using the built-in analysis tools. It is noteworthy that neither longitudinal nor transverse strain vary noticeably across the measured region (Figure 7 demonstrates how little the transverse strain varies), which indicates that the gauge region is sufficiently distant from the testing fixtures as to be outside the edge-effected area.  
Figure 5: Deformed shape and stress distribution of a gyroid solid model (50% relative density). (**a**) Longitudinal deformation and stress (\(\sigma_{x}\)); (**b**) shear deformation and stress (\(\tau_{xy}\)).  
This test was performed with several specimens each at 25%, 50%, 75%, and 100% nominal relative density. For each relative density (except 100%) two different geometries are used: one-bead and two-bead wall thicknesses. This is in order to determine whether the wall-thicknesses are a significant factor in the response. Nominal density of each specimen is defined as a parameter in the slicing software, while the actual density is determined by measuring its size and mass. This is then divided by the published density of PLA to convert to relative density.