# Pressure-Reducing Design of 3D-Printed Diabetic Shoe Midsole Utilizing Auxetic Lattice Structure
## 2 Research Methods
### Mechanical Characterization and FE Modeling  
This study used a universal testing machine (Inspekt Table Blue 5 KN, Hegewald & Peschke, Dresden, Germany) to obtain the tensile and compression set properties of the 3D-printed TPU material. The testing referenced the ASTM D638 standard method [34] for testing the tensile properties of plastics and used dog bone-shaped samples with nominal dimensions of 33 mm (L) \(\times\) 6 mm (W) \(\times\) 3.2 mm (T) for the tensile test. The ASTM D395 standard method [35] for testing rubber properties in compression was also referenced, utilizing standard test specimens that were 13 mm in diameter and 6 mm thick. This study  
Figure 2: Motion capture setup for measuring gait data: (**A**) walking state, (**B**) running state, (**C**) measurement preparation, (**D**) results of gait data measurement. inputted the testing results into ABAQUS FEA software (Dassault, France, version 2021) to simulate compression. The FEM was configured as a combination of five components, including the soft tissues and bones of the foot, inside, midsole, and ground. The placement of each component in the FEM is illustrated in Figure 3B. A researcher converted all components to the STEP format and imported them into ABAQUS FEA software (Dassault, France, version 2021). ABAQUS processed the 3D models by meshing them into grids with a finite number of 'elements' with the mesh size set to 2 mm. The TPU models were based on the Yeoh formulation [36] as a hyperelastic constitutive model:  
\[W=\sum_{i=1}^{N}c_{i}(\overline{I_{1}}-3)^{i}+\sum_{k=1}^{N}\frac{1}{d_{k}}(J- 1)^{2k} \tag{1}\]  
\[\frac{\partial W}{\partial I_{1}}=\sum_{i=1}^{N}ic_{i}(\overline{I_{1}}-3)^{i -1}J^{-2/3} \tag{2}\]  
\[\frac{\partial W}{\partial I_{2}}=0 \tag{3}\]  
\[\frac{\partial W}{\partial I_{3}}=\sum_{k=1}^{N}\frac{k}{d_{k}J}(J-1)^{2k-1} \tag{4}\]  
where \(W\) is the strain energy; \(I_{1}\), \(I_{2}\), and \(I_{3}\) are the principal invariants; and \(J\) is the Jacobian. The result from the tensile test was fitted to the third-order deformation model, and the strain energy function of the simplified Yeoh model was stated as follows:  
\[W=c_{1}(\overline{I_{1}}-3)^{1}+c_{2}(\overline{I_{1}}-3)^{2}+c_{3}(\overline {I_{1}}-3)^{3}+\frac{1}{d_{1}}(J-1)^{2}+\frac{1}{d_{2}}(J-1)^{4}+\frac{1}{d_{ 3}}(J-1)^{6} \tag{5}\]  
Table 2 displays each part's material properties and element types within the FE model. Uniaxial test data of TPU material samples allowed the characterization of hyperelastic material properties. They were imported into the ABAQUS FEA software (version 2021) to set the material properties of the shoe midsole section. Based on the calculation of the uniaxial test data of the TPU material samples using MatEditor software (a material editor software program for engineers, version 2019), the coefficients of the hyperelastic material for the shoe midsoles are shown in Table 3. The ground part employed rigid body constraint, fixing six degrees of freedom for translation and rotation. A tie constraint was used between the foot and the insole. Frictional contact with a coefficient of friction of 0.2 was applied between the shoe midsole and the floor. The displacement in the FE foot model originated from the displacement data acquired through motion capture testing. The node coordinates measured by motion capture were updated every 10 ms, where the displacement in the \(y\)-axis direction at the ankle meas  
Figure 3: The FEM for simulating the foot–footwear interface (**A,B**) and the actual placement of the 3D-printed shoe midsoles (**C**). onto the ankle coordinates of the FE foot model. The simulation loaded a mass point of 69.8 kg into the FE model at the human center-of-mass coordinates obtained from motion capture testing and added a global gravitational acceleration of 9800 mm/s\({}^{2}\). The FE model assumed a rigid link between the center of mass and the ankle.