Mechanical and Acoustic Behavior of 3D‐Printed Hierarchical Mathematical Fractal Menger Sponge,Advanced Engineering Materials

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Mechanical and Acoustic Behavior of 3D‐Printed Hierarchical Mathematical Fractal Menger Sponge
Advanced Engineering Materials ( IF 3.4 ) Pub Date : 2021-01-12 , DOI: 10.1002/adem.202001471
Brijesh Kushwaha ₁ , Kush Dwivedi ₂ , Rushikesh S. Ambekar ₁ , Varinder Pal ₁ , D. P. Jena ₃ , D. Roy Mahapatra ₂ , Chandra Sekhar Tiwary ₁

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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.

中文翻译：

3D打印分层数学分形Menger海绵的力学和声学行为

具有分级体系结构（例如，分形）的结构材料显示出显着的机械性能。Menger海绵是数学中定义的分形几何形状之一，由具有三个正交腔的单位立方体组成。分形的精确尺寸是使用3D打印制作的。在单轴压缩下对该结构进行了实验和模拟。研究了增加Menger海绵结构的正交空腔水平以及改变空腔形状的影响。结果表明，机械性能与结构的有效密度之间存在有趣的关联。根据不同的腔体形状分析了多个层次结构。这些比较表明，分层结构可用于以较低的有效结构密度获得更好的性能。不同腔体形状的破坏开始显示了每个腔体形状在压缩载荷下的行为。在本文中，可以看出如何使用分层体系结构访问结构的独特属性，从而洞察设计在调节此类机械结构的机械属性中的作用。声学研究的结果表明，在低频范围内，与商用海绵相比，它是一种更好的吸声材料。可以看出如何使用分层体系结构访问结构的独特属性，从而深入了解设计在调节此类机械结构的机械属性中的作用。声学研究的结果表明，在低频范围内，与商用海绵相比，它是一种更好的吸声材料。可以看出如何使用分层体系结构访问结构的独特属性，从而深入了解设计在调节此类机械结构的机械属性中的作用。声学研究的结果表明，在低频范围内，与商用海绵相比，它是一种更好的吸声材料。

更新日期：2021-01-12

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