Figure 3
The horizontal axis is labeled “Porosity, V f” and ranges from 0 to 0.2 in increments of 0.05 units. The vertical axis is labeled “Normalized Young’s Modulus, E over E subscript 0” and ranges from 0 to 1.6 in increments of 0.2 units. Four series are shown in the legend: “Analytical solution”, “Numerical results-S C”, “Numerical results-B C C”, and “Numerical results-F C C”. All series start at 1.0 at zero porosity and decrease as porosity increases. At 0.05, values are around 0.9 to 0.92; at 0.1, around 0.8 to 0.85. At 0.15, around 0.72 to 0.78; and at 0.2, around 0.65 to 0.72. The analytical solution remains slightly higher than the numerical results across all porosity values, while the B C C and F C C results appear slightly lower. Note: All numerical data values are approximated.Normalized Young’s modulus as a function of porosity for the three periodic closed-cell porous structures. A representative analytical expression is also included