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

Abstract

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.

Microstructure and mechanical properties of hierarchical porous parts of Ti-6Al-4V alloy obtained by powder bed fusion techniques

“…As shown, the E eff values obtained for Menger pre-fractal sponge of Ti-6Al-4V alloy using Xie's approach fitted quite well to the Gibson and Ashby model with n = 2 (Figure 9). However, slopes proximal to n = 1 were reported in porous parts with the conventional formation sequence of Menger sponge but made of NiTi alloy (Zhao et al , 2021) and PLA (Kushwaha et al , 2021). In NiTi parts, Zhao et al (2021) reported stress-induced martensite transformation during the compressive testing.…”

“…The stretch deformation predominates for high values of N . PLA parts with similar pore architecture also presented a similar deformation behavior in the pores independently of their size, involving a bending of horizontal struts in the direction of applied force (Kushwaha et al , 2021).…”

“…Furthermore, Miyamoto et al (2005) manufactured Menger pre-fractal sponge with N equal to 3 using the vacuum fusion method and a low melting point metal (Bi-Pb-Sn-In eutectic alloy, T F = 70°C), which was poured into a resin mold manufactured by AM, with the inverted form of a Menger pre-fractal sponge. Recently, Kushwaha et al (2021) and Zhao et al (2021) reported obtaining Menger pre-fractal sponges using AM techniques from Polylactide (PLA) filament and NiTi alloy powder, respectively, with N from 1 to 3.…”

“…They observed that deformation concentrated around half-height of each porous model, agreeing with the numerical simulation results. Menger pre-fractal sponges were also experimentally and numerically analyzed when submitted to compressive test by Kushwaha et al (2021) and Zhao et al (2021). Kushwaha et al (2021) studied the influence of pores shape (square, cylindrical, hexagonal and elliptical) and porosity volume, controlled by N value, in the mechanical properties of PLA parts; besides evaluated the acoustic behavior of the porous parts with elliptic pore shape.…”

Atomic Scale Structure Inspired 3D‐Printed Porous Structures with Tunable Mechanical Response

“…Among these, 3D printing is the finest technique to fabricate complex porous geometry due to design freedom and sustainability. [10][11][12][13][14][15] Development of structures with dual nature of deformation (hard and soft) is a challenge; therefore, mainly researchers prefer multimaterials, [16] blends/alloys, [17] and composites, [18] but then the interface of such a system becomes vulnerable. Sajadi et al demonstrated unique mechanical properties (strength, modulus, and impact resistance) in 3D-printed complex schwarzites structures (such as primitive and gyroid structure).…”