# Interfacial Shear Properties of Red Clay and Polyurethane with Different Densities
## 4 Model Validation
### Finite Element Module Method  
A three-dimensional finite element model is developed with dimensions consistent with the test sample. The model has a diameter of 61.8 mm and a height of 20 mm, with the upper and lower portions representing polyurethane and red clay, respectively. Zero-thickness cohesive elements are inserted at the interface to simulate the bonding between polyurethane and red clay. To accurately simulate interface damage, the finite element model is meshed using an O-shaped segmentation technique, with refinement at the interface damage location. The model consists of a total of 8832 elements. Polyurethane and red clay are modeled using linear hexahedral elements (C3D8R), while the cohesive elements are represented by COH3D8. The finite element mesh of the sample is shown in Figures 8 and 9.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \begin{tabular}{c} **Density** \\ **[g/cm\({}^{3}\)]** \\ \end{tabular} & \begin{tabular}{c} **Normal Stress** \\ **[kPa]** \\ \end{tabular} & \begin{tabular}{c} **Shearing** \\ **Rigidity** \\ **[N/mm\({}^{3}\)]** \\ \end{tabular} & \begin{tabular}{c} **Shearing** \\ **Strength** \\ **[kPa]** \\ \end{tabular} & \
\begin{tabular}{c} **Shearing** \\ **Displacement** \\ **[mm]** \\ \end{tabular} &
\begin{tabular}{c} **Shear Damage** \\ **Energy** \\ **[N/mm]** \\ \end{tabular} \\ \hline \multirow{4}{*}{0.2} & 100 & 78.0 & 193.2 & 2.72 & 2.62 \\  & 200 & 79.4 & 241.5 & 3.09 & 3.72 \\  & 300 & 92.9 & 239.8 & 3.55 & 4.26 \\  & 400 & 87.9 & 352.1 & 4.54 & 7.88 \\ \hline \multirow{4}{*}{0.5} & 100 & 996 & 181.6 & 1.94 & 1.76 \\  & 200 & 99.3 & 258.6 & 2.84 & 3.68 \\  & 300 & 105.6 & 333.4 & 3.59 & 5.98 \\  & 400 & 111.5 & 416.0 & 4.32 & 8.99 \\ \hline \multirow{4}{*}{0.8} & 100 & 95.0 & 200.8 & 2.42 & 2.43 \\  & 200 & 106.9 & 289.8 & 2.89 & 4.20 \\ \cline{1-1}  & 300 & 112.3 & 381.7 & 3.82 & 7.29 \\ \cline{1-1}  & 400 & 109.9 & 476.7 & 4.56 & 10.88 \\ \hline \hline \end{tabular}
\end{table}
Table 5: Cohesive unit parameters of interface between red clay and polyurethane with different densities.  
To ensure model accuracy and realism, the boundary conditions are set based on the actual working conditions of the composite direct shear test. A reference point RP-1 is placed at the left end of the upper polyurethane section and coupled to the upper polyurethane surface. Fixed constraints are applied at reference point RP-1 to restrict displacement in all directions. Vertical displacement is restricted on the upper surface of the polyurethane, and surface loads are applied in accordance with the test conditions, while vertical displacement on the lower surface of the red clay is also constrained. A reference point RP-2 is placed at the right end of the red clay, at the lower end of the specimen, and coupled to the lower surface of the polyurethane. A displacement load is applied along the x-direction at reference point RP-2, with reaction force data also being output. The finite element simulation is solved using the explicit solver Abaqus/Explicit, and the composite direct shear test process is modeled using quasi-static explicit analysis. The boundary conditions are shown in the Figure 10.  
Figure 8: Finite element mesh division of specimen.  
Figure 9: Zero-thickness cohesive element meshing.