The Young’s modulus values and strength values are listed in Table. 2. The monotonic Young’s modulus and strength values are calculated from the linear region of the curves shown in Fig.5a. The cyclic Youngs’ modulus is calculated from the slope of the unloading part of the curve shown Fig. 5b. The cyclic modulus values are higher than the monotonic values indicating that the samples reach stabilization after the first loading cycle. Comparing the values with respect to the topology, the effect of the presence of vertical struts is clearly evident: cubic regular samples had the highest Young’s modulus followed by cubic irregular, trabecular and star-based structures. Cross-based structures with only oblique struts had the lowest stiffness. Similar conclusions can be made on the yield strength and maximum compressive strength values.
Further considerations can be made by observing how the irregularity affects the outcomes. The irregularity decreases the stiffness and strength by introducing bending dominated behavior in the structure. This effect is highly pronounced in structures having vertical struts. In cube-based structures, a decreases of 38% in cyclic modulus, 36% in yield stress and 24% in maximum stress was observed. In star-based structures, a decreases of 28% in cyclic modulus, 25% in yield stress and 21% in maximum stress was observed. In cross based structures, the irregularity had least effect with only 4-6% decrease in cyclic modulus and stress values. The modulus and the stress values of trabecular structures were similar to those of cubic irregular and star regular samples. The random orientation of the struts seems to help in terms of an isotropic distribution of load among struts.

Fatigue test

The S-N curves obtained from the fatigue tests for all the specimens are compared in Fig.7. The curve fitting parameters and the scatter in the fatigue data are as indicated in Table 3. The S-N curves clearly indicate the effect of cell topology on the fatigue behavior. As shown in Fig. 7a, cubic regular specimens represented exceptional fatigue properties and maintained their structural integrity up to 107 cycles under any applied load below 0.8σy. During the experimental tests, buckling mechanism dominated the failure of cubic regular structures under compression. In this case, the absence of any sort of bending mechanism retards the fatigue crack growth36. As a consequence, an expected curve is obtained by increasing the load slightly above 0.8σy. Similar behavior that none of the specimens failed for all ranges of porosity31, was also reported by Yavari et al. for cubic cellular structures . By contrast, the S-N curve of cubic irregular specimens in Fig.7a indicates significantly lower fatigue strength. The effect of displacement of the nodes to induce irregularity was clearly seen and it was much more significant than the effect seen in the quasi-static compression test, where a decrease of only 24-36% of strength values was observed. The fatigue crack starts to grow at a relatively early stage because the randomly displaced nodes and the inclined struts introduce bending moments in the structure. Similar to the cubic specimens, star shaped and cross shaped specimens show lower fatigue strengths due to the irregularity, as shown in Fig. 7b and 7c. Despite the presence of vertical struts in star regular specimen, an early fatigue failure was observed when compared to the cubic specimens due to the oblique struts which induce bending moment in the specimen. Generally, a clear reduction of fatigue strength can be seen for all irregular topologies. Even though the irregularity caused a decrease of only 21-25% in the static strength values as previously evidenced in the compression test, the decrease of the S-N data points is much higher, increasing up to 80% in the the high-cycle part of the plot. However, a smaller difference between the regular and irregular topologies was observed for cross structures. Interstingly, also in static compression test the differences between regular and irregular cross-based structures were quite low. The fatigue behavior of trabecular structure Fig.7d was inferior to the regular cubic and star structures, but it was superior to the irregular cubic and star structures. The advantages of the quasi-isotropic structure induced by the randomization are more evident in this fatigue test configuration rather than in the static compression test . The S-N curves of cross based specimens show that the specimens were not able to sustain more than 106 cycles even at the lower range of the applied load. Therefore, the fatigue strength of all the structures were calculated at 106 cycles and is reported in Table. 4