Quasi-static and dynamic compressive behaviour of additively manufactured Menger fractal cube structures

This paper presents the first-ever investigation of Menger fractal cubes' quasi-static compression and impact behaviour. Menger cubes with different void ratios were 3D printed using polylactic acid (PLA) with dimensions of 40 mm × 40 mm × 40 mm. Three different orders of Menger cubes with different void ratios were considered, namely M1 with a void ratio of 0.26, M2 with a void ratio of 0.45, and M3 with a void ratio of 0.60. Quasi-static Compression tests were conducted using a universal testing machine, while the drop hammer was used to observe the behaviour under impact loading. The fracture mechanism, energy efficiency and force-time histories were studied. With the structured nature of the void formation and predictability of the failure modes, the Menger geometry showed some promise compared to other alternatives, such as foams and honeycombs. With the increasing void ratio, the Menger geometries show force-displacement behaviour similar to hyper-elastic materials such as rubber and polymers. The third-order Menger cubes showed the highest energy absorption efficiency compared to the other two geometries in this study. The findings of the present work reveal the possibility of using additively manufactured Menger geometries as an energy-efficient system capable of reducing the transmitting force in applications such as crash barriers.