## 3 Results and Discussion
### Composite Performance Tuning  
Using the axis with the greatest compressive stiffness as the primary axis, eight elementary models were combined to form each composite model. As shown in Figure 5, three composite models were designated P1, P2, and P3. All eight elementary models in P1 were oriented along the Z-axis, while four elementary models in P2 and P3 were oriented to be orthogonal to the Z-axis. Visual results of compression simulations of composites P1, P2, and P3 are shown in Figure 5.  
As shown in Figure 6, composites formed by distinct arrangements of elementary models resulted in varying compressive behaviors along the Z and Y axes. As depicted by Figure 6a, the compressive stiffness of P1 was significantly greater than that of P2 and P3 in the Z direction, while P2 had the greatest compressive stiffness in the Y direction. Figure 5: Composites designed through the permutation of elementary models and compression simulations on composites (using the simulation method described in Section 3.3). Let the elementary model be orientated as shown in Figure 7a, with its primary axis along the Z-axis. Let cross sections of the elementary model be represented by the feature value of 1 and longitudinal sections the feature value of 0, as shown in Figure 7b. As depicted in Figure 7c, let elementary models along the X-axis be designated as Columns (C) from 1 to \(i\), models along the Y-axis as Rows (R) from 1 to \(j\), and models along the Z-axis as Layers (L) from 1 to \(k\). Therefore, any slice, vertical or horizontal, could be represented by a matrix of the feature values for models with primary axes in any of the X/Y/Z directions. For example, the \(k\)th slice orthogonal to the Z-axis could be represented by:  
\[\left[ \begin{array}{ccc}C_{i}R_{1}L_{k}&\cdots&C_{i}R_{j}L_{k}\\ \vdots&\ddots&\vdots\\ C_{1}R_{1}L_{k}&\cdots&C_{1}R_{j}L_{k}\end{array} \right]\]  
The sum of the column/row/layer sum maxima of \(k\) feature matrices could be used to represent the material's compressive stiffness in the Z direction. Figure 6: Displacements along the Z and Y axes under compression with a loading level of 0.5 MPa. (**a**) The displacement of stressed surface along the Z-axis; (**b**) The displacement of the stressed surface along the Y-axis. The sums of row/column/layer sum maxima of feature matrices are plotted by the red line. Figure 7: Tensor formation methodology for composite models: (**a**) Elementary model; (**b**) Feature value of the elementary model in the X/XZ/YZ planes; (**c**) Positions of each elementary model in the composite model; (**d**) Tensor representation of composite models P1, P2, and P3 in feature values. The \(i\)th slice orthogonal to the Y-axis could be represented by:  
\[\left[ \begin{array}{ccc}C_{i}R_{1}L_{k}&\cdots&C_{i}R_{j}L_{k}\\ \vdots&\ddots&\vdots\\ C_{i}R_{1}L_{1}&\cdots&C_{i}R_{j}L_{1}\end{array} \right]\]  
The sum of column/row/layer sum maxima of \(i\) feature matrices could be used to represent the material's compressive stiffness in the Y direction. The \(j\)th slice orthogonal to the X-axis could be represented by:  
\[\left[ \begin{array}{ccc}C_{1}R_{j}L_{k}&\cdots&C_{i}R_{j}L_{k}\\ \vdots&\ddots&\vdots\\ C_{1}R_{j}L_{1}&\cdots&C_{i}R_{j}L_{1}\end{array} \right]\]  
The sum of column/row/layer sum maxima of \(j\) feature matrices could be used to represent the material's compressive stiffness in the X direction. Forming tensors (3D matrices) as described in Figure 7d, we obtained:  
Arrangement P1:  
Two matrices orthogonal to the Z-axis could be formed. For layer 1 along the Z-axis, we have the feature matrix \(\left[ \begin{array}{cc}1&1\\ 1&1\end{array} \right]\) with a maximum row sum of 2 and column sum of 2. For layer 2 along the Z-axis, we have the feature matrix \(\left[ \begin{array}{cc}1&1\\ 1&1\end{array} \right]\) with a maximum row sum of 2 and column sum of 2. For slices parallel to the Z-axis, we have a maximum layer sum of 2. Thus, the sum of row/column/layer sum maxima is \(2+2+2+2=10\). Two matrices orthogonal to the Y-axis could be formed.