Fig. 4 (a) Measured strut thickness (b) Normal distribution of measured strut thickness for different strut orientation
Relating the strut thickness to porosity, the random struts had the highest thickness and hence trabecular structures had the lowest porosity. Cross based structures with oblique struts had the highest porosity, followed by star based structures which had one extra vertical strut when compared to cross based structures. But, the thickness difference in the horizontal and irregular struts can be clearly seen when comparing the porosity of cubic regular and cubic irregular structures. The lower thickness of horizontal struts increases the porosity of cubic regular structures by 5% when compared to cubic irregular.

Quasi-static compression test

The typical stress-strain curve for cellular structures consists of three regions, linear elastic deformation followed by plastic deformation forming a plateau region and finally densification of strain takes place when the failed struts come in contact with each other. The plastic deformation and the shape of the plateau region are highly dependent on the topology and density of the material30. In this study, the testing was stopped before all the struts failed and before the densification stage. This was done in order to better identify a posteriori; the location of the weak areas that first yielded or failed. The stress-strain curves of all the specimens are shown in Fig.5. The stress-strain curves were quite different for different topologies under monotonic testing as shown in Fig. 5a. The curve of the regular cubic structure indicates that the stress drops down to 20 MPa at very small strain, showing a catastrophic failure of struts. The failure is mainly due to buckling of vertical struts under axial loading and due to the absence of struts in other directions which introduce bending moment29.