Mechanical and Acoustic Behavior of 3D-Printed Hierarchical Mathematical Fractal Menger Sponge

Structural materials that feature hierarchical architectures (e.g., fractals) display remarkable mechanical properties. Menger sponge is one of the fractal geometries defined in Mathematics and made up of a unit cube with three orthogonal cavities. The precise fractal dimensions are fabricated using 3D printing. Experiments and simulations are conducted on the structure under uniaxial compression. The effect of increasing the levels of orthogonal cavities of the Menger sponge structure as well as the changing shape of the cavity are studied. The results show an interesting correlation between mechanical properties and the effective density of the structure. Multiple levels of hierarchy are analyzed in terms of different cavity shapes. These comparisons suggest that hierarchical structures are used to obtain better performance with a lower effective density of the resulting structures. Damage initiation for the different cavity shapes shows how each of the cavity shapes behaves under compressive loading. Herein, it is discerned how hierarchical architecture is used to access the unique properties of structures, providing insight into the role of design in regulating the mechanical properties of such mechanical structures. The result of acoustic investigation shows that it is a better absorber as compared with commercial sponge in the low-frequency regime.