# Pressure-Reducing Design of 3D-Printed Diabetic Shoe Midsole Utilizing Auxetic Lattice Structure
## 2 Research Methods  
### Midsole Design Based on Re-Entrant Hexagonal Lattice Structure  
The orthotropic re-entrant hexagonal lattice structure is one of the typical forms of auxetic structures. Its fundamental characteristics [27; 28] continue to be explored for applications in various fields [29]. For this study, a midsole design using the re-entrant hexagonal lattice structure was adopted to compare the impact of the internal angles of the lattice cells on the pressure-relieving capacity of a midsole, and lattice cells were designed with three different internal angles (60\({}^{\circ}\), 75\({}^{\circ}\), and 90\({}^{\circ}\)). Structures with internal angles of 90\({}^{\circ}\) or above do not possess auxetic properties. Therefore, in the experiments, midsoles with re-entrant structures at internal angles of 60\({}^{\circ}\) and 75\({}^{\circ}\) were denoted as A60 and A75, respectively. The non-auxetic midsole with an internal angle of 90\({}^{\circ}\) was marked as N90. Figure 1 shows each lattice cell's three-dimensional structure and geometric characteristics, with the rib thickness of each unit being 2.4 mm and the height being 12 mm. The lattice cells within the three-dimensional space of a midsole were uniformly arranged, with each midsole aligned longitudinally as two lattice cells. Despite the design challenges, this study attempted to maintain a consistent volume of lattice material in the three midsoles (Table 1), keeping the ratio of the material volume similar to reduce the impact of relative density on the mechanical performances of the midsoles. The lattice-structured shoe midsoles were constructed from thermoplastic polyurethane (TPU) that could be produced via 3D printing. According to the DIN EN ISO 10993-5 [30] and 10993-10 standards [31], TPU also meets the requirements for medical devices regarding cytotoxicity and skin sensitization. Three-dimensional models of the shoe midsoles were constructed using the Rhino 7\({}^{\circled{B}}\) and Grasshopper\({}^{\circled{B}}\) 3.5 programs.  
These lattice midsoles were fabricated using Fused Deposition Modeling (FDM) 3D printing technology. This study used a UP300 3D printer from Tiertime (Beijing, China) for sample printing, with the pre-designed midsole models imported via the accompanying UP Studio software (version 3.1.2). The nozzle displacement accuracy of the device was  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Midsole** & **Volume (mm\({}^{\text{3}}\))** & **Ratio (\%)** \\ \hline Auxetic 60\({}^{\circ}\) & 128,345 & 23.56 \\ Auxetic 75\({}^{\circ}\) & 124,221 & 22.80 \\ Non-auxetic 90\({}^{\circ}\) & 125,464 & 23.03 \\ \hline \hline \end{tabular}
\end{table}
Table 1: The material volumes of the lattice structures in the shoe midsoles and the ratios of the total midsole volumes.  
Figure 1: Comparison of design features of three types of lattice-structured shoe midsoles: differences in internal angles (**A**–**C**) and geometric characteristics of each unit cell (**D**–**F**).  
2, 2, and 0.5 microns on the \(x\), \(y\), and \(z\) axes, respectively, and the printing precision reached 0.1 mm. The layer thickness was set to 0.2 mm, and the infill density was set to the maximum during printing. All samples were printed using TPU material (95A) provided by Tiertime. The material cost for printing a single TPU lattice midsole was approximately 15 United States dollars, but the FDM printing process was time-consuming, taking about 50 h to print one midsole. As 3D printing technology advances, printing times and costs are expected to decrease [32], facilitating the application of auxetic lattice designs in footwear products.