# A Novel Bionic Structure Inspired by Lufta Sponge and Its Cushion Properties
## 2 Materials and Methods  
### Geometry of Bionic Structure  
The luffa sponge used in this experiment were purchased from Yiwu Nuannuan Products Co., Ltd. (Zhejiang, China). To ensure the uniformity of experimental samples, this study selected a luffa sponge with as similar a structure as possible. In this study, the texture of the luffa sponge was analyzed by micro-computed tomography (micro-CT) technology (AX-2000 CT, Always Imaging Co., Ltd., Shanghai, China) to observe the internal morphology of the luffa sponge. The three-hole luffa sponge was selected for observation. The sizes of luffa sponge slices were similar in height (50 mm) and diameter (70 mm).  
The results of the micro-CT show that the I layer is more densely arranged in three high-density areas, as shown in Figure 3. Arranged along the circle of the cross-section of the luffa sponge, density of the C layer and the rib part connected to the I layer is lower. Generally, for porous materials, the higher the density, the stronger the resistance to external forces. It is found that the fiber arrangement in the I layer shows a certain regularity in the random arrangement of local fibers. Secondary fibers are continuously split from the primary fibers, and there are crossovers and splits between the secondary fibers. Extracting the fiber texture of the I layer can be simplified into a tree-like structure, similar to the trunk and branches of a tree. In our experiment, it is observed that the fiber of the I layer is stronger than other sections, and the local texture has a certain self-similarity relationship with the overall texture, which is a satisfied fractal theory. More details can be seen in Appendix A, Figure A1.  
Figure 2: The flow chart of bionic research.  
In this section, we used Python 3.7 programming language to design a fractal 2D structure and then import it into CAD software and get a 3D fractal model. By mirroring and arraying the left and right representative volume element (RVE), the final bionic model is obtained, as shown in Figure 4.  
The bionic model was designed by fractal theory based on the morphology of the lufa sponge I layer. The RVE of the bionic model is shown in Figure 5. RVE model is composed of three order layers, corresponding to \(1^{st},2^{nd},3^{rd}\). Every rib orientates \(\theta\) degrees along the axis of symmetry. The first order contains only one rib, corresponding to \(a\); the second-order contains two ribs, corresponding to \(b_{1}\) and \(b_{2}\); the third-order contains four ribs, corresponding to \(c_{1}\), \(c_{2}\), \(c_{3}\) and \(c_{4}\). The length and width of REV correspond to \(l\) and \(w\) respectively, and \(a=b_{1}=b_{2},l>l_{2}>l_{1}\).  
Figure 4: The evolution of bionic structures: (**a**) Three different fractal styles by Python programming; (**b**) Mirror representative volume element (RVE) model; (**c**) Array model of 15 degrees bionic structure.  
Figure 3: The micro-computed tomography (micro-CT) scan picture of lufa sponge: (**a**) Cross section of lufa sponge; (**b**) Three high-density areas of lufa sponge; (**c**) Cross section of nature lufa; (**d**) Vertical section of lufa sponge; (**e**) Texture of I layer; (**f**) Simplified structure of I layer.  
In order to understand RVE model and calculate the length and angle, the RVE model is simplified to simple geometry as shown in Figure 5b, but that doesn't represent real RVE model. RVE is parameterized by lengths \(a\), \(b\), \(c\), \(l\), \(w\) and angle \(\theta\). More details can be seen in Appendix B.